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Area Under Curve Calculator | Free Online Calculator Tool

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Area Under Curve Calculator

Area Under Curve Calculator solves the input function and gives the output in the blink of an eye. Enter input function and range in the fields of the input section and press on the calculate button to find the area under the given curve in the fraction of seconds.

Area Under Curve Calculator: Are you searching for a tool that solves the area under the given curve? Then you are at the right place. This handy calculator tool will help you to get the accurate answer along with the step by step process easily. Get to know the process on how to find the area under curve by hand in the following sections.

How to Solve Area Under the Curve?

Area under the given function having lower and upper limits are given by the definite integration. Have a look at the below sections to get the clear step by step explanation to find the area under curve manually.

  • Let us take any function f(x) and limits x = a, x = b
  • Apply the definite integration to the function with limits upper as b and lower limit as a.
  • Calculate the integration and substitute a and b values in the result.
  • Subtract f(b) from f(a) to get the answer.

Example

Question: Find the area of the region under the curve y = x2 + 1 having x = 0 and x = 1?

Solution:

Given that,

y = x2 + 1

Area = ∫01 x2 + 1 dx

= x3/3 + x ]01

= (1/3 + 1) – (0/3 + 0)

= 1+3 / 3

= 4/3

Area = 4/3

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

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FAQs on Area Under Curve Calculator

1. What is the formula to calculate the Area Under the Curve?

The simple formula to get the area under the curve is as follows

A = ∫ab f(x) dx.

Where, a and b are the limits of the function

f(x) is the function.

2. What is the definition of area under the curve?

Area under the curve is the definite integral of a curve that describes the variation of a drug concentration in blood plasma as a function of time. It is a measure of how much drug reaches the person bloodstream in a period of time after a dose is given. This information is helpful in determining dosing and identifying potential drug interactions.

3. Why does the antiderivative of a function give you the area under the curve?

If you integrate the function f(x), then you will get the anti derivative of F(x). By evaluating the antiderivative over a specific domain [a, b] gives the area under the curve. Otherwise, perform F(b) – F(a) to find the area under f(x).

4. Calculate the area under the curve of a function, f(x) = 7 – x2, the limit is given as x = -1 to 2?

f(x) = 7 – x2 and limits x = -1 to 2

Area = ∫-12 (7 – x2) dx

= 7x – x3/3 ]-12

= (7×2 – 23 / 3) – (7(-1) – (-1)3/3)

= [(42 – 8)/3] – [(1 – 21)/3]

= (34 + 20)/3

= 54/3

Area = 18

Trapezoidal Rule Calculator | Online Free Calculator Tool

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Trapezoidal Rule Calculator

Trapezoidal Rule Calculator simply requires input function, range and number of trapezoids in the specified input fields to get the exact results within no time. So, enter your details in the below input box and click on the calculate button to get the answer in fraction of seconds.

Trapezoidal Rule Calculator: No need to feel solving any function using trapezoidal rule is a bit difficult. Our handy calculator tool gives the answer easily and quickly. Along with this free calculator, you can also get the detailed explanation to solve the integration functions using trapezoidal rule. Have a look at the example, trapezoidal rule definition and formula in the below sections.

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Steps to Solve Integration Function using Trapezoidal Rule

Follow these simple and easy guidelines to solve any function integration using trapezoidal rule manually.

  • Take any function f(x) with integration and lower, upper limits i.e a,b.
  • Also, know the number of trapezoids n.
  • The formula to compute trapezoidal rule of any function is
  • ∫ab f(x)dx ≈ Δx/2 [f(x0) + 2f(x1) + 2f(x2)+. . . +2f(xn-1) + f(xn)
  • Where, Δx = (b-a)/n.
  • Divide the given interval into n portions of length Δx.
  • In the subintervals last one is b and first one is a.
  • Evaluate the functions at those subinterval values.
  • Substitute the obtained values in the formula of trapezoidal rule and sum up the values to get the approximate value.

Example

Question: Use the Trapezoidal Rule with n = 5 to approximate ∫a=0b=1 √(1+sin3(x).

Solution:

Given that,

function f(x) = √(1+sin3(x)

a= 0, b= 1, n=5.

Trapezoidal Rule dtates that

∫ab f(x)dx ≈ Δx/2 [f(x0) + 2f(x1) + 2f(x2)+. . . +2f(xn-1) + f(xn), where

Δx = (b-a)/n

Substitute the given values in above formula to get Δx value.

Δx = 1-0/5 = 1/5

Divide the interval [0,1] into n=5 subintervals of length Δx=1/5, with the following endpoints:

a = 0, 1/5, 2/5, 3/5, 4/5, 1= b

Evaluate the function at these end points:

f(x0) = f(a) = f(0) = √(1+sin3(0) = 1

2f(x1) = 2f(1/5) = 2√(1+sin3(1/5) = 2.00782606791279

2f(x2) = 2f(2/5) = 2√(1+sin3(2/5) = 2.05820697233265

2f(x3) = 2f(3/5) = 2√(1+sin3(3/5) = 2.17257446116512

2f(x4) = 2f(4/5) = 2√(1+sin3(4/5) = 2.34021475342487

f(x5) = f(1) = 2√(1+sin3(1) = 1.26325897447473

Δx/2 = 1/10

Finally sum up the above values and multiply by Δx/2

= ⅒ (1 + 2.00782606791279 + 2.05820697233265 + 2.17257446116512 + 2.34021475342487 + 1.26325897447473)

= 1.08420812293102

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

FAQs on Trapezoidal Rule Calculator

1. What is meant by Trapezoid Rule?

Trapezoid Rule is to find the exact value of a definite integral using a numerical method. This rule is based on the Newton-Cotes formula which states that one can get the exact value of the integral as an nth order polynomial. Trapezium rule works by approximating the region under the graph of function as a trapezoid and calculating its area.

2. Where do we use Trapezoid Rule?

Trapezoid Rule is a rule that is used to determine the area under the curve. In this method, the area under the curve by dividing the total area into smaller trapezoids instead of dividing into rectangles. Integration method works by approximating the area under the graph of a function as a trapezoid and it calculates the area.

3. What is the Trapezoid Rule Formula?

Trapezoidal Rule formula is mentioned here:

∫ab f(x)dx ≈ Δx/2 [f(x0) + 2f(x1) + 2f(x2)+. . . +2f(xn-1) + f(xn),

where

Δx = (b-a)/n

4. Approximate the integral ∫01 x3 dx using the Trapezoidal Rule with n = 2 subintervals.

Trapezoidal Rule formula with n = 2 subintervals is

T = Δx/2 [f(x0) + 2f(x1) + f(x2)]

Δx = (b-a)/n

=1-0/2 = 1/2

f(x0) = f(0) = 0

f(x1) = f(1/2) = (1/2)3 = 1/8

f(x2) = f(1) = 13 = 1

So,

∫01 x3 dx ≈ 1/4 [0+ 2x(1/8) + 1] = 1/4 x 5/4 = 5/16

Second Order Differential Equation Calculator | Second ODE Calculator

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Second Order Differential Equation Calculator

Free online Second Order Differential Equation Calculator is designed to check the second order differential of the given expression and display the result within seconds. Provide your equation as the input value and hit the calculate button to get the second order derivatives along with work. Must Read: MGL Pivot Point Calculator

Second Order Differential Equation Calculator: Second order differential equation is an ordinary differential equation with the derivative function 2. Go to the below sections to know the step by step process to learn the Second Order Differential Equation with an example. The Handy Calculator tool provides you the result without delay.

Second Order Differential Equation is represented as d^2y/dx^2=f”’(x)=y’’. Have a look at the following steps and use them while solving the second order differential equation.

  • Take any equation with second order differential equation
  • Let us assume dy/dx as an variable r
  • Substitute the variable r in the given equation
  • It will form a binomial equation
  • Solve the equation and find its factors
  • Find the value of y

Example:

Question: Solve d^2y/dx^2-10dy/dx+25y=0?

Answer:

Given equation is

d2y/dx2-10dy/dx+25y=0

Let us take y=erx then

dy/dx=rerx

d2y/dx2=r2erx

Substitute these values in the equation

r2erx-10rerx+25erx=0

erx (r2-10r+25)=0

r2-10r+25=0

r2-5r-5r+25=0

r(r-5)-5(r-5)=0

(r-5)(r-5)=0

r=5

So, we can say that y=e5x

dy/dx=5e5x

d2y/dx2=25e5x

So,

d2y/dx2-10dy/dx+25y

=25e5x-10*5e5x+25e5x

=25e5x-50e5x+25e5x

=0

So, in this case our solution is

y=Ae5x+Bxe5x

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

FAQs on Second Order Differential Equation Calculator

1. How many solutions does a second order differential equation have?

To construct the general solution for a second order equation, we need to take two independent solutions. So, it has 2 solutions.

2. How do you solve a second order differential equation?

Consider any variable for the derivative and substitute that value in the equation. Find the roots of that variable and substitute the values in the given equation.

3. How do you write a second order differential equation?

The standard form of a second order differential equation is pd2y/dx2+qdx/dy+r=0. The mathematical operator can be either plus or minus.

4. What is the difference between first and second order differential equations?

An equation having only first derivatives is known as a first order differential equation and an equation containing a second derivative is called a second order differential equation. First order differential equation is represented as dy/dx while the second order differential equation representation is d2y/dx2.

Parabola Calculator | Calculator to solve Parabola Equation

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Parabola Calculator

Use this user friendly Parabola Calculator tool to get the output in a short span of time. You just need to enter the parabola equation in the specified input fields and hit on the calculator button to acquire vertex, x intercept, y intercept, focus, axis of symmetry, and directrix as output.

Parabola Calculator: Are you trying to solve the parabola equation? If yes, this is the right spot for you. From here you will be going to learn the process of calculating parabola equation and finding vertex, focus, x and y intercepts, directrix and axis of symmetry values. By checking the below sections, you will get a good knowledge on the parabola equation concept and you will also obtain a handy calculator tool that gives result in fraction of seconds.

How to Solve the Parabola Equation?

We can find the x intercept, y intercept, vertex, focus, directrix, axis of symmetry using any parabola equation in the form of y = ax2 + bx + c. In the following sections, we are providing the simple steps to find all those parameters of parabola equation. Follow them while solving the equation.

  • At first, take any parabola equation.
  • Find out a, b, c values in the given equation
  • Substitute those values in the below formulae
  • Vertex v (h, k).
  • h = -b / (2a), k = c – b2 / (4a).
  • Focus of the x coordinate is -b/2a.
  • Focus of the y coordinate is c – (b2 – 1)/ (4a)
  • Then, focus is (x, y)
  • Directrix equation y = c – (b2 + 1) / (4a)
  • Axis of symmetry is -b/ 2a.
  • Solve the y intercept by keeping x = 0 in the parabola equation.
  • Perform all mathematical operations to get the required values.

Examples

Question 1: Find vertex, focus, y-intercept, x-intercept, directrix, and axis of symmetry for the parabola equation y = 5x2 + 4x + 10?

Solution:

Given Parabola equation is y = 5x2 + 4x + 10

The standard form of the equation is y = ax2 + bx + c

So, a = 5, b = 4, c = 10

The parabola equation in vertex form is y = a(x-h)2 + k

h = -b / (2a) = -4 / (2.5)

= -2/5

k = c – b2 / (4a)

= 10 – 42 / (4.5)

= 10- 16 / 20 = 10*20 – 16 / 20

= 184/ 20 = 46/5

y = 5(x-(-2/5))2 + 46/5

= 5(x+2/5)2 + 46/5

Vertex is (-2/5, 46/5)

The focus of x coordinate = -b/ 2a = -2/5

Focus of y coordinate is = c – (b2 – 1)/ (4a)

= 10 – (16 – 1) / (4.5)

= 10 – 15/20

= 37/4

Focus is (-2/5, 37/4)

Directrix equation y = c – (b2 + 1) / (4a)

= 10 – (42 + 1) / (4.5)

= 10 – 17 / 20

=200 – 17 / 20

=183/20

Axis of Symmetry = -b/ 2a = -2/5

To get y-intercept put x = 0 in the equation

y = 5(0)2 + 4(0) + 10

y = 10

To get x-intercept put y = 0 in the equation

0 = 5x2 + 4x + 10

No x-intercept.

Question 2: Find the equation, focus, axis of symmetry, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the parabola that passes through the points (1,4), (2,9), (−1,6)?

Solution:

Given points are (1,4), (2,9), (−1,6)

The standard form of the equation of the parabola is y = ax2 + bx + c

When the parabola passes through the point (1,4) then, 4 = a+b+c

when the parabola passes through the point (2,9), then 9 = a(2)2 + b(2) + c = 4a + 2b + c

when the parabola passes through the point (-1,6), then 6 = a – b + c

Solve first and third equation

a + b+ c = 4

a – b + c = 6

2(a + c) = 10

a + c = 10/2 = 5

substitute a + c = 5 in first equation

5 + b = 4

b = 4-5

b = -1

Put a = 5-c, b = -1 in second equation

4(5- c) -2 + c = 9

20 – 4c -2 +c = 9

18 – 3c = 9

18-9 = 3c

c = 3

Substitute b = -1 c = 3 in the third equation

a +1 + 3 = 6

a + 4 = 6

a = 2

Put a =2, b = -1, c = 3 in the standard form of parabola equation

y = 2x2 – x + 3

The parabola equation in vertex form is y = a(x-h)2 + k

h = -b / (2a) = 1/4

k = c – b2 / (4a) = 3 – 1 / 8 = 23/8

y = 2(x-1/4)2 + 23/8

Vertex is (1/4, 23/8)

The focus of x coordinate = -b/ 2a = 1/4

Focus of y coordinate is = c – (b2 – 1)/ (4a)

= 3 – (1 – 1) / (4.2)

= 3/8

Focus is (1/4, 3/8)

Directrix equation y = c – (b2 + 1) / (4a)

= 3 – (1 + 1) / (4.2)

= 3-2/8

=24-2/8 = 22/8 = 11/4

Axis of Symmetry = -b/ 2a = 1/4

To get y-intercept put x = 0 in the equation

y = 2(0)2 – 0 + 3

y = 3

y intercept (0, 3)

To get x-intercept put y = 0 in the equation

0 = 2x2 – x + 3

No x-intercept.

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FAQs on Parabola Calculator

1. What is meant by parabola?

Parabola is a curve where any point is at an equal distance from a fixed point (focus) and a fixed straight line (directrix).

2. Where is parabola used in real life?

Parabola can be seen in nature or in man made items. From the paths of thrown baseballs, to fountains, even functions, to satellite, and radio waves.

3. Where is the focus of a parabola?

A parabola is set of all points in a plane which are equal distance from a given point and given line. The point is called parabola focus and the line is known as directrix of parabola. The focus lies on the axis of symmetry of the parabola.

4. What is a parabola used for?

The parabola has many important applications, from a parabolic microphone or parabolic antenna to automobile headlight reflectors and the design of ballistic missiles. They are frequently used in engineering, physics and other areas.

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Radius of Convergence Calculator | Online Calculator Tool

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Radius of Convergence Calculator

Free online Radius of Convergence Calculator tool evaluates the radius of a convergence of a power series. Simply enter your function and variable range in the given input sections and tap on the calculate button to get the instant output along with a detailed procedure.

Radius of Convergence Calculator: If you want to know the radius of convergence of a power series equation and need any help? Then we are here you to assist for any kind of math solutions. Have a look at the Radius of Convergence Calculator to solve the power series function within seconds. This article gives a detailed description of steps to solve the radius of convergence manually and we will explain it with few examples.

Method to Calculate Radius of Convergence of a Power Series

Follow these simple steps to find out the radius of convergence of a power series

  • Take a power series
  • Consider the value of x for which the power series will converge
  • To get the radius of convergence, find out ratio test
  • And evaluate the function as per the ratio test
  • Ratio test will gives you the limit value
  • Substitute the limit value to get the R i.e Radius of Convergence

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

Example

Question: Find the Radius of Convergence for the power series Sigma n=to infinity 2n/nx(4x-8)n

Solution:

Let us take Cn=2n/nx(4x-8)n

We know that this power series will converge for x=2

For the above power series, the ratio test will be

L=Cn+1/Cn

L=lim n to infinity 2n+1(4x-8)n+1/n+1*n/2n(4x-8)n

lim n to infinity 2n(4x-8)/n+1

(4x-8) lim n to infinity 2n/n+1

=2(4x-8)

So we will get the below convergence info from this

2(4x-8)<1

x-aR

8(x-2)<1

(x-2)<⅛

8(x-2)>1

(x-2)>1/8

So, the radius of convergence for the power series is R=1/8

FAQs on Radius of Convegence

1. What is the Radius of Convergence?

Radius of Convergence of a power series is the radius of the largest disk in which the series converges. It will be non negative real number or infinity. In the positive case, the power series converges absolutely.

2. What is the radius of convergence is 0?

The radius of convergence R =0 tells that the distance between the center of a power series interval of convergence and its endpoints.

3. Can the radius of convergence be negative?

No, the radius of convergence can never be a negative number.

4. What is the ratio test for convergence?

The ratio test defines that: if L<1 then the series is convergent or if L>1 then the series is divergent. In case L=1, tes is inclusive, because it satisfies both convergent and divergent.

ATUL Pivot Point Calculator

Hindi Essay (Hindi Nibandh) | 100 विषयों पर हिंदी निबंध लेखन – Essays in Hindi on 100 Topics

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Hindi Essay (Hindi Nibandh) 100 विषयों पर हिंदी निबंध लेखन

हिंदी निबंध: हिंदी हमारी राष्ट्रीय भाषा है। हमारे हिंदी भाषा कौशल को सीखना और सुधारना भारत के अधिकांश स्थानों में सेवा करने के लिए बहुत महत्वपूर्ण है। स्कूली दिनों से ही हम हिंदी भाषा सीखते थे। कुछ स्कूल और कॉलेज हिंदी के अतिरिक्त बोर्ड और निबंध बोर्ड में निबंध लेखन का आयोजन करते हैं, छात्रों को बोर्ड परीक्षा में हिंदी निबंध लिखने की आवश्यकता होती है।

निबंध – Nibandh In Hindi – Hindi Essay Topics

हिन्दी निबंध – Essay in Hindi – Hindi Nibandh
शिक्षा पर निबंध
खेल पर निबंध
विज्ञान और तकनीकी पर निबंध
भारत पर निबंध
सामाजिक मुद्दे और सामाजिक जागरूकता पर निबंध
विभिन्न उत्सवों पर निबंध
महान व्यक्तियों पर निबंध
रिश्तों पर निबंध
नैतिक मूल्य पर निबंध
पर्यावरण के मुद्दें और जागरूकता पर निबंध
स्वास्थ्य और तंदुरुस्ती पर निबंध
प्रकृति पर निबंध
लोकोक्ति पर निबंध
स्मारकों पर निबंध

इसलिए, यह जानना और समझना बहुत महत्वपूर्ण है कि विषय के बारे में संक्षिप्त और कुरकुरा लाइनों के साथ एक आदर्श हिंदी निबन्ध कैसे लिखें। साथ ही, कक्षा 1 से 10 तक के छात्र उदाहरणों के साथ इस पृष्ठ से विभिन्न हिंदी निबंध विषय पा सकते हैं। तो, छात्र आसानी से स्कूल और प्रतियोगी परीक्षाओं के लिए हिंदी में निबन्ध कैसे लिखें, इसकी तैयारी कर सकते हैं। इसके अलावा, आप हिंदी निबंध लेखन की संरचना, हिंदी में एक प्रभावी निबंध लिखने के लिए टिप्स आदि के बारे में कुछ विस्तृत जानकारी भी प्राप्त कर सकते हैं। ठीक है, आइए हिंदी निबन्ध के विवरण में गोता लगाएँ।

हिंदी निबंध लेखन – स्कूल और प्रतियोगी परीक्षाओं के लिए हिंदी में निबन्ध कैसे लिखें?

प्रभावी निबंध लिखने के लिए उस विषय के बारे में बहुत अभ्यास और गहन ज्ञान की आवश्यकता होती है जिसे आपने निबंध लेखन प्रतियोगिता या बोर्ड परीक्षा के लिए चुना है। छात्रों को वर्तमान में हो रही स्थितियों और हिंदी में निबंध लिखने से पहले विषय के बारे में कुछ महत्वपूर्ण बिंदुओं के बारे में जानना चाहिए। हिंदी में पावरफुल निबन्ध लिखने के लिए सभी को कुछ प्रमुख नियमों और युक्तियों का पालन करना होगा।

हिंदी निबन्ध लिखने के लिए आप सभी को जो प्राथमिक कदम उठाने चाहिए उनमें से एक सही विषय का चयन करना है। इस स्थिति में आपकी सहायता करने के लिए, हमने सभी प्रकार के हिंदी निबंध विषयों पर शोध किया है और नीचे सूचीबद्ध किया है। एक बार जब हम सही विषय चुन लेते हैं तो विषय के बारे में सभी सामान्य और तथ्यों को एकत्र करते हैं और अपने पाठकों को संलग्न करने के लिए उन्हें अपने निबंध में लिखते हैं।

तथ्य आपके पाठकों को अंत तक आपके निबंध से चिपके रहेंगे। इसलिए, हिंदी में एक निबंध लिखते समय मुख्य बिंदुओं पर ध्यान केंद्रित करें और किसी प्रतियोगिता या बोर्ड या प्रतिस्पर्धी जैसी परीक्षाओं में अच्छा स्कोर करें। ये हिंदी निबंध विषय पहली कक्षा से 10 वीं कक्षा तक के सभी कक्षा के छात्रों के लिए उपयोगी हैं। तो, उनका सही ढंग से उपयोग करें और हिंदी भाषा में एक परिपूर्ण निबंध बनाएं।

हिंदी भाषा में दीर्घ और लघु निबंध विषयों की सूची

हिंदी निबन्ध विषयों और उदाहरणों की निम्न सूची को विभिन्न श्रेणियों में विभाजित किया गया है जैसे कि प्रौद्योगिकी, पर्यावरण, सामान्य चीजें, अवसर, खेल, खेल, स्कूली शिक्षा, और बहुत कुछ। बस अपने पसंदीदा हिंदी निबंध विषयों पर क्लिक करें और विषय पर निबंध के लघु और लंबे रूपों के साथ विषय के बारे में पूरी जानकारी आसानी से प्राप्त करें।

विषय के बारे में समग्र जानकारी एकत्रित करने के बाद, अपनी लाइनें लागू करने का समय और हिंदी में एक प्रभावी निबन्ध लिखने के लिए। यहाँ प्रचलित सभी विषयों की जाँच करें और किसी भी प्रकार की प्रतियोगिताओं या परीक्षाओं का प्रयास करने से पहले जितना संभव हो उतना अभ्यास करें।

हिंदी निबंधों की संरचना

Hindi Essay Parts

उपरोक्त छवि आपको हिंदी निबन्ध की संरचना के बारे में प्रदर्शित करती है और आपको निबन्ध को हिन्दी में प्रभावी ढंग से रचने के बारे में कुछ विचार देती है। यदि आप स्कूल या कॉलेजों में निबंध लेखन प्रतियोगिता में किसी भी विषय को लिखते समय निबंध के इन हिस्सों का पालन करते हैं तो आप निश्चित रूप से इसमें पुरस्कार जीतेंगे।

इस संरचना को बनाए रखने से निबंध विषयों का अभ्यास करने से छात्रों को विषय पर ध्यान केंद्रित करने और विषय के बारे में छोटी और कुरकुरी लाइनें लिखने में मदद मिलती है। इसलिए, यहां संकलित सूची में से अपने पसंदीदा या दिलचस्प निबंध विषय को हिंदी में चुनें और निबंध की इस मूल संरचना का अनुसरण करके एक निबंध लिखें।

हिंदी में एक सही निबंध लिखने के लिए याद रखने वाले मुख्य बिंदु

अपने पाठकों को अपने हिंदी निबंधों के साथ संलग्न करने के लिए, आपको हिंदी में एक प्रभावी निबंध लिखते समय कुछ सामान्य नियमों का पालन करना चाहिए। कुछ युक्तियाँ और नियम इस प्रकार हैं:

  • अपना हिंदी निबंध विषय / विषय दिए गए विकल्पों में से समझदारी से चुनें।
  • अब उन सभी बिंदुओं को याद करें, जो निबंध लिखने शुरू करने से पहले विषय के बारे में एक विचार रखते हैं।
  • निबंध लेखन के मूल प्रारूप का पालन करें और निबंध को तीन भागों में विभाजित करें।
    • पहला भाग: परिचय
    • दूसरा भाग: विषय का शारीरिक / विस्तार विवरण
    • तीसरा भाग: निष्कर्ष / अंतिम शब्द
  • एक निबंध लिखते समय सुनिश्चित करें कि आप एक सरल भाषा और शब्दों का उपयोग करते हैं जो विषय के अनुकूल हैं और एक बात याद रखें, वाक्यों को जटिल न बनाएं,
  • जानकारी के हर नए टुकड़े के लिए निबंध लेखन के दौरान एक नए पैराग्राफ के साथ इसे शुरू करें।
  • अपने पाठकों को आकर्षित करने या उत्साहित करने के लिए जहाँ कहीं भी संभव हो, कुछ मुहावरे या कविताएँ जोड़ें और अपने हिंदी निबंध के साथ संलग्न रहें।
  • विषय या विषय को बीच में या निबंध में जारी रखने से न चूकें।
  • यदि आप संक्षेप में हिंदी निबंध लिख रहे हैं तो इसे 200-250 शब्दों में समाप्त किया जाना चाहिए। यदि यह लंबा है, तो इसे 400-500 शब्दों में समाप्त करें।
  • महत्वपूर्ण हिंदी निबंध विषयों का अभ्यास करते समय इन सभी युक्तियों और बिंदुओं को ध्यान में रखते हुए, आप निश्चित रूप से किसी भी प्रतियोगी परीक्षाओं में कुरकुरा और सही निबंध लिख सकते हैं या फिर सीबीएसई, आईसीएसई जैसी बोर्ड परीक्षाओं में।

हिंदी निबंध लेखन पर अक्सर पूछे जाने वाले प्रश्न

1. मैं अपने हिंदी निबंध लेखन कौशल में सुधार कैसे कर सकता हूं?
अपने हिंदी निबंध लेखन कौशल में सुधार करने के सर्वोत्तम तरीकों में से एक किताबों और समाचार पत्रों को पढ़ना और हिंदी में कुछ जानकारीपूर्ण श्रृंखलाओं को देखना है। ये चीजें आपकी हिंदी शब्दावली में वृद्धि करेंगी और आपको हिंदी में एक प्रेरक निबंध लिखने में मदद करेंगी।

2. CBSE, ICSE बोर्ड परीक्षा के लिए हिंदी निबंध लिखने में कितना समय देना चाहिए?
हिंदी बोर्ड परीक्षा में एक प्रभावी निबंध लिखने पर 20-30 का खर्च पर्याप्त है। क्योंकि परीक्षा हॉल में हर मिनट बहुत महत्वपूर्ण है। इसलिए, सभी वर्गों के लिए समय बनाए रखना महत्वपूर्ण है। परीक्षा से पहले सभी हिंदी निबन्ध विषयों से पहले अभ्यास करें और परीक्षा में निबंध लेखन पर खर्च करने का समय निर्धारित करें।

3. हिंदी में निबंध के लिए 200-250 शब्द पर्याप्त हैं?
200-250 शब्दों वाले हिंदी निबंध किसी भी स्थिति के लिए बहुत अधिक हैं। इसके अलावा, पाठक केवल आसानी से पढ़ने और उनसे जुड़ने के लिए लघु निबंधों में अधिक रुचि दिखाते हैं।

4. मुझे छात्रों के लिए सर्वश्रेष्ठ औपचारिक और अनौपचारिक हिंदी निबंध विषय कहां मिल सकते हैं?
आप हमारे पेज से कक्षा 1 से 10 तक के छात्रों के लिए हिंदी में विभिन्न सामान्य और विशिष्ट प्रकार के निबंध विषय प्राप्त कर सकते हैं। आप स्कूलों और कॉलेजों में प्रतियोगिताओं, परीक्षाओं और भाषणों के लिए हिंदी में इन छोटे और लंबे निबंधों का उपयोग कर सकते हैं।

5. हिंदी परीक्षाओं में प्रभावशाली निबंध लिखने के कुछ तरीके क्या हैं?
हिंदी में प्रभावी और प्रभावशाली निबंध लिखने के लिए, किसी को इसमें शानदार तरीके से काम करना चाहिए। उसके लिए, आपको इन बिंदुओं का पालन करना चाहिए और सभी प्रकार की परीक्षाओं में एक परिपूर्ण हिंदी निबंध की रचना करनी चाहिए:

  • एक पंच-लाइन की शुरुआत।
  • बहुत सारे विशेषणों का उपयोग करें।
  • रचनात्मक सोचें।
  • कठिन शब्दों के प्रयोग से बचें।
  • आंकड़े, वास्तविक समय के उदाहरण, प्रलेखित जानकारी दें।
  • सिफारिशों के साथ निष्कर्ष निकालें।
  • निष्कर्ष के साथ पंचलाइन को जोड़ना।

निष्कर्ष
हमने एक टीम के रूप में हिंदी निबन्ध विषय पर पूरी तरह से शोध किया और इस पृष्ठ पर कुछ मुख्य महत्वपूर्ण विषयों को सूचीबद्ध किया। हमने इन हिंदी निबंध लेखन विषयों को उन छात्रों के लिए एकत्र किया है जो निबंध प्रतियोगिता या प्रतियोगी या बोर्ड परीक्षाओं में भाग ले रहे हैं। तो, हम आशा करते हैं कि आपको यहाँ पर सूची से हिंदी में अपना आवश्यक निबंध विषय मिल गया होगा।

यदि आपको हिंदी भाषा पर निबंध के बारे में अधिक जानकारी की आवश्यकता है, तो संरचना, हिंदी में निबन्ध लेखन के लिए टिप्स, हमारी साइट LearnCram.com पर जाएँ। इसके अलावा, आप हमारी वेबसाइट से अंग्रेजी में एक प्रभावी निबंध लेखन विषय प्राप्त कर सकते हैं, इसलिए इसे अंग्रेजी और हिंदी निबंध विषयों पर अपडेट प्राप्त करने के लिए बुकमार्क करें।

Laplace Transform Calculator | Quick & Easy Process

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Laplace Transform Calculator

Laplace Transform Calculator: If you are interested in knowing the concept to find the Laplace Transform of a function, then stay on this page. Here, you can see the easy and simple step by step procedure for calculating the laplace transform.

This Laplace Transform Calculator handy tool is easy to use and shows the steps so that you can learn the topic easily. We are providing the best examples so that you can understand the concept. Make your calculations faster with the help of our free online tool.

Solve Laplace Transform of a Function

We all know that calculating Laplace Transform is a little bit tough when compared with other mathematical operations. Have a look at the detailed step by step procedure that is helpful in solving the Laplace Transform of any kind of equation.

  • Take a fiction or an equation to which you want to perform the operation.
  • Perform the integration operation on the given function.
  • Do all mathematical calculations to the solution.
  • Substitute the values in the obtained equation to get the result.

Standard Form

The standard form to represent the Laplace Transform is

F(s)=L(f(x))= Integration 0 to infinity e^-stf(t)dt

where f(t) is a function

s is the complex number frequency parameter

Example:

Question: What is the Laplace Transform of 3sinh(2t)+3sin(2t)?

Solution:

Let us take the functions f(t), g(t)

f(t)=sinh(2t)

g(t)=sin(2t)

Use the linearity property of Laplace Transform

L[a.f(t)+b.g(t)]=a.L[f(t)]+b.L[g(t)]

L[sinh(2t)]=2/s2-4

Lsin(2t)]=2/s2+4

L[3sinh(2t)+3sin(2t)]=3×2/s2-4+3×2/s2+4

=6/s2-4+6/s2+4=6x{1/s2-4+1/s2+4}

=6x{s2+4+s2-4/s4-16}

=6x{2s2/s4-16}

=12s2/s4-16

The Laplace Transform of 3sinh(2t)+3sin(2t) is 12s2/s4-16.

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

Frequently Asked Questions on Laplace Transforms

1. What is the purpose of Laplace Transform?

The purpose of the Laplace Transform is to transform ordinary differential equations into algebraic equations. Like the Fourier transform, it is used for solving the integral equations.

2. What are the applications of the Laplace Transform?

The applications of Laplace Transform are Circuit Analysis, Signal Processing, and Communication Systems.

3. Is Laplace Transform linear?

Yes, Laplace Transform is linear.

4. What is the difference between Laplace and Fourier Transform?

The fourier transform doesn’t care about changing the magnitudes of a signal. But the laplace transform cares both changing magnitudes and oscillation parts. Actually, the Fourier Transform is a subset of the Laplace Transform.

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ML Aggarwal Solutions

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ML Aggarwal ICSE Solutions for Class 6 to 10

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Indigo Summary in English by Louis Fischer

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Indigo Summary in English by Louis Fischer

Indigo Summary in English and Hindi Pdf. Indigo is written by Louis Fischer.

Learncram.com has provided indigo questions and answers, indigo chapter summary pdf, indigo class 12 line by line explanation, class 12 english chapter indigo summary in hindi, indigo class 12 pdf, indigo important questions and answers pdf, message of chapter indigo. Refer more: INDIGO pivots calculator

Students can also check the English Summary to revise with them during exam preparation.

Indigo Summary in English by Louis Fischer

Indigo by Louis Fischer About the Author

Louis Fischer (29 February 1896 – 15 January 1970) was an American journalist. He wrote the biography of Mahatma Gandhi entitled The Life of Mahatma Gandhi. ‘Indigo’ is an excerpt from this book widely acknowledged as one of the best books written on Gandhi.

Author Name Louis Fischer
Born 29 February 1896, Philadelphia, Pennsylvania, United States
Died 15 January 1970, Princeton, New Jersey, United States
Education Central High School, South Philadelphia High School
Awards National Book Award for History and Biography (Nonfiction)
Nationality American
Louis Fischer - indigo summary in english class 12
Louis Fischer

Indigo Theme

The chapter ‘Indigo’ emphasizes the fact that an effective leadership can solve any kind of problem without any harm to anybody. This chapter deals with the way Mahatma Gandhi solved the problem of poor sharecroppers of Champaran in a non-violent way.

Indigo Theme Summary in English

Indigo Summary in English

‘Indigo’ details numerous events in the life of Gandhi which he witnessed in Champaran, Bihar. It was in 1916 that Gandhi was approached by a peasant, Rajkumar Shukla, from Champaran. He wanted Gandhi to visit Champaran and do something for the condition of peasants there. Due to his persistent efforts, he was successful in bringing Gandhi to Champaran after a few months. On the way to Champaran from Calcutta, Gandhi, in order to understand the problems of the sharecroppers, decided to meet a lawyer, Rajendra Prasad, in Patna and Professor J.B. Kriplani at Muzzafarpur.

By the time Gandhi reached Champaran, the news of his mission had spread like wildfire. After reaching Champaran, Gandhi learnt that arable areas were divided into large estates, owned by the Englishmen, and worked by the peasants. Indigo was the main commercial crop of the area as the landlords forced all the tenants to grow indigo on 15% of their land and surrender the entire crop as rent. When the landlords learnt that synthetic indigo had been developed by the Germans, they asked the tenants to pay them compensation for releasing them from 15% arrangement that they had signed. This brought misery to the peasants and they wanted Gandhi to help them.

Gandhiji, first of all, collected all the facts and information. He also dealt with the resistance of the British. While going to investigate the maltreatment of a peasant in a village near Motihari, Gandhi was ordered to return midway and was served a summons to report to the court the following morning. The peasants came in huge numbers outside the court to support Gandhi and the officials were unable to control the crowd. As a result, the trial was postponed and so allowed Gandhi to move around freely.

All the prominent lawyers, including Rajendra Prasad, Brij Kishor Babu, Maulana Mazharul Huq arrived in Champaran to support Gandhi and decided to go to jail with Gandhi if he was sent to jail. But Gandhi received a written communication that the Lieutenant Governor had dropped the case. This was the beginning of the triumph of civil disobedience in India.

Gandhi, along with his team of lawyers, continued his investigation and met the Lieutenant Governor four times. Finally, an official inquiry was ordered. Gandhi accepted 25% of the money offered to the farmers as refund. This instilled courage among the farmers and marked their victory over injustice and exploitation.

After this, Gandhi worked for the economic and cultural development of the area. With the help of Mahadev Desai and Narhari Parikh, their wives, his wife and son, Gandhi opened schools and taught cleanliness and sanitation. A volunteer doctor came to improve the appalling state of health services.

Gandhi taught a lesson of self-reliance to his followers by refusing the idea of keeping Charles Freer Andrews in India to help him. As per Gandhi, it was a sign of weakness to seek the help of an Englishman to bolster their efforts.
Thus, Champaran became a symbol of self-reliance and Indian Independence.

Indigo Summary in English

Ghadari Babas in Kalapani Jail Summary

Business Studies MCQs for Class 12 with Answers Chapter 11 Marketing

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Business Studies MCQs for Class 12 with Answers Chapter 11 Marketing

Free PDF Download of CBSE Business Studies Multiple Choice Questions for Class 12 with Answers Chapter 10 Financial Market. Business Studies MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Business Studies Financial Market MCQs Pdf with Answers to know their preparation level.

Financial Market Class 12 Business Studies MCQs Pdf

1. Which of the following statements is not true with regard to the concept of product?
(a) It is a bundle of utility.
(b) It is a source of satisfaction.
(c) It is confined to physical product.
(d) All of the above.

Answer/Explanation

Answer: c
Explanation:
(c) It includes both tangible and intangible attributes

Business Studies MCQs with Questions and Answers

2. In order to promote the sales of the company, Mukund Limited has decided to offer consumer durable products at 0% finance. Identify the type of marketing factor being described in the above line.
(a) Controllable factor
(b) Non-controllable factor
(c) Environmental factor
(d) None of the above

Answer/Explanation

Answer: a
Explanation:
(a) It is promotion

Marketing with Questions and Answers

3. Harshit is planning a start up a venture for offering mobile pet care services at door step. He has decided to charge ?1000 for heated hydrobath & blow dry of a pet and ?500 for shampoo and conditioning. Identify the element of marketing mix which is not being described in the above case.
(a) Product
(b) Place
(c) Price
(d) None of the above

Answer/Explanation

Answer: d
Explanation:
(d) It is promotion

4. Guneet went to a shop and expressed her desire to buy a copper water bottle only of Prestige company. Identify the component related to branding being described in the above case.
(a) Trademark
(b) Generic name
(c) Brand name
(d) Brand mark

Answer/Explanation

Answer: c
Explanation:
(c) Prestige is a brand name

5. The term ‘market’ may be understood in which of the following contexts?
(a) Geographical area covered
(b) Type of buyers
(c) Quantity of goods transacted
(d) All of the above

Answer

Answer: d

6. According to the modem marketing concept, which of the following statements is true?
(a) It refers to the group of people who do not have the ability but willingness to buy a particular product.
(b) It refers to only the set of people who have the purchasing power to buy a particular product.
(c) It refers to the set of actual and potential buyers for a product.
(d) It refers only to the people who show interest in a particular product.

Answer

Answer: c

7. Which of the following is a feature of marketing process?
(a) Satisfying needs and wants of the consumers
(b) Creating a market offering
(c) Developing an exchange mechanism
(d) All of the above

Answer

Answer: d

8. Which of the following statements does not reflect a condition to be satisfied for an exchange to take place?
(a) Involvement of at least two parties- the buyer and the seller- is mandatory.
(b) Each party should be capable of offering something of value to the other.
(c) Exchange can take place if the buyers and sellers are not able to communicate with each other.
(d) Each party should have freedom to accept or reject other party’s offer.

Answer

Answer: c

9. Which of the following can be marketed?
(a) Red Cross society persuading to donate blood.
(b) Kerala Tourism persuading people to visit Kerala for health tourism.
(c) Political parties persuading to vote for a particular candidate.
(d) All of the above

Answer

Answer: d

10. Karam Limited is offering a travel package for 15 destinations worldwide with a free insurance on the bookings for the month of December, 2019. Identify the feature of marketing being described in the above lines.
(a) Needs and wants
(b) Creating a market offering
(c) Customer value
(d) Exchange mechanism

Answer

Answer: c

11. Agile Limited has launched a new range of air conditioners in order to add value to the usability of the product. The new range of air conditioners have an inbuilt air purifier and are available in attractive colours. Identify the type of marketing philosophy being described in the above lines.
(a) Product concept
(b) Production concept
(c) Marketing concept
(d) Societal marketing concept

Answer

Answer: a

12. In order to promote the habit of health and hygiene among weaker sections of the society, Abhyas Limited has launched low cost packs of hand wash. Identify the type of marketing philosophy being adopted by the company.
(a) Product concept
(b) Production concept
(c) Marketing concept
(d) Societal marketing concept

Answer

Answer: b

13. Sujhav Limited is a company dealing in various types of fire extinguishers. Considering the fact that people generally don’t buy fire extinguishers, the company undertakes aggressive sales promotion efforts in order to create and maintain demand for the product. Identify the type of marketing philosophy being described in the given case,
(a) Product concept
(b) Selling concept
(c) Marketing concept
(d) Societal marketing concept

Answer

Answer: b

14. Madhubala is planning to launch an online education portal. In order to understand the varied needs of the students, she conducted an online survey. Based on the feedback of the survey, she has decided to offer educational packages to the prospective buyers. Identify the type of marketing concept being described in the given lines.
(a) Product concept
(b) Production concept
(c) Marketing concept
(d) Societal marketing concept

Answer

Answer: c

15. Pragati Limited has chalked out an action plan in order to increase its market share in the international market by 20% in the next one year. The action plan contains the details about how the production levels will be increased, promotional activities will be carried out and so on. Identify the type of marketing function being described in the given lines.
(a) Gathering and analysing market information
(b) Marketing planning
(c) Product designing and development
(d) Packaging and labelling

Answer

Answer: b

16. In order to improve upon its competitive edge, Khushboo Limited has change the packaging of its hair care products. They are now available in a consumer friendly design, which has a nozzle attached to the lid so that at the time of usage, the consumer doesn’t need to open the cap of the bottle. Name the marketing function being explained in the given lines.
(a) Product designing and development
(b) Customer support services
(c) Promotion
(d) Physical distribution

Answer

Answer: a

17. In order to get feedback about its new product launch, Taggi Limited conducted an online survey through a short questionnaire. Identify the marketing function being mentioned in the given line.
(a) Gathering and analysing market information
(b) Marketing planning
(c) Product designing and development
(d) Packaging and labelling

Answer

Answer: a

18. Gabbar is a wholesaler of food grains. He categorises his stock into different groups on the basis of their quality and also fixes up the prices accordingly. Identify the type of marketing function being mentioned in the given line.
(a) Physical distribution
(b) Transportation
(c) Warehousing
(d) Standardisation and grading

Answer

Answer: d

19. In order to enhance the easy marketability of the products, Dev, a producer gets the home furnishing products manufactured in confirmation to the predetermined specifications. Identify the type of marketing function being described in the given case.
(a) Physical distribution
(b) Standardisation and grading
(c) Transportation
(d) Warehousing

Answer

Answer: b

20. Good Health Limited has decided to launch a new range of water bottles with in-built water purifier. Instead of marketing the product by is generic name, the company has decided to call it Turifiere’. Identify the type of marketing function being described in the given lines.
(a) Packaging and labelling
(b) Branding
(c) Pricing
(d) Promotion

Answer

Answer: b

21. Drishti Limited is a chain of trusted optical centers for prescription & fashion eyewear. It caters to affluent people with a range of premium sunglasses for men, women and kids. In order to raise the level of buyers’ satisfaction, the company has decided to create a special section in each of its outlets for handling customer complaints and adjustment requirements. Identify the type of marketing function described in the given lines.
(a) Product designing and development
(b) Customer support services
(c) Promotion
(d) Physical distribution

Answer

Answer: b

22. Ecofriend Limited has decided to launch solar jackets, which will have an inbuilt solar charger as well. In order to make its product competitive, the company has decided to offer it for sale within the range of ^1500 to ^4000. Identify the related function of marketing being mentioned in the given case.
(a) Packaging and labelling
(b) Branding
(c) Pricing
(d) Promotion

Answer

Answer: c

23. Keeping in view the recent trends of sales regression, Sona Limited has decided to offer a flat 15% discount on all its products. Identify the related function of marketing being described in the given lines.
(a) Packaging and labelling
(b) Branding
(c) Pricing
(d) Promotion

Answer

Answer: d

24. BeCool Limited has decided to market its products through the conventional network of manufacturer-wholesaler-retailer-consumer. Identify the function of marketing being described in the above line.
(a) Physical distribution
(b) Transportation
(c) Warehousing
(d) Standardisation and grading

Answer

Answer: a

25. While reading the label of a pack of aluminium foil, Reshma discovered that the product was manufactured at Hyderabad but was available for sale in many states across the country. Identify the function of marketing which has made this possible.
(a) Physical distribution
(b) Standardisation and grading
(c) Transportation
(d) Warehousing

Answer

Answer: c

26. Ranjan’s business is being adversely affected due to the delay in delivery on account of poor weather conditions. Identify the marketing function which will be helpful to him in this regard.
(a) Physical distribution
(b) Standardisation and grading
(c) Transportation
(d) Warehousing

Answer

Answer: d

27. Champ Limited is a company providing online education to school children of all the classes. Over the years, it has established a good reputation and a market share of 75%. However, in past 2 months, due to the entry of a new competitor in the same segment, the market share of the company has reduced by 20%. Identify the type of marketing factor which has adversely affected the sales of the company.
(a) Controllable factors
(b) Environmental factors
(c) Marketing mix
(d) None of the above

Answer

Answer: b

28. Identify the component of branding being depicted below.
Business Studies MCQs for Class 12 with Answers Chapter 11 Marketing 1
(a) Brand name
(b) Brand mark
(c) Trademark
(d) Generic name

Answer

Answer: b

29. What does the symbol given below denote?
Business Studies MCQs for Class 12 with Answers Chapter 11 Marketing 2
(a) Brand name
(b) Brand mark
(c) Trademark
(d) Generic name

Answer

Answer: c

30. Pranav has decided to start a business of manufacturing crockery and cutlery items. In order to give a unique identification to his products, he has decided to assign the brand name ‘Elegan’ as it will enable the firm to secure and control the market for its products. Identify the relative advantage of branding to the marketers being described in the above case.
(a) Facilitates differential pricing
(b) Ease in the launching of new products
(c) Facilitates product differentiation
(d) Assists in advertising and display programmes

Answer

Answer: c

31. Srijan is fond of a particular brand of stationery. Every time he buys his favourite brand stationery products, he does not need make a close inspection of that product. Identify the relative advantage of branding to the customers being described in the given case.
(a) Supports in product identification
(b) Certifies quality
(c) Considered to be a status symbol
(d) None of the above

Answer

Answer: a

32. Karan had started the business of producing exclusive home decor items under the brand name ‘Eleganza’ 15 years back. Over the years, he has diversified into new segments like home furnishing, furniture and kitchenware. However, all the products are being sold under the same brand name ‘Eleganza’, as it appears to be apt for all of them. Identify the relative feature of a good brand name being described in the given case.
(a) Short and easy to pronounce, spell and remember
(b) Reflects the functions of the product
(c) Distinctive/easily identifiable
(d) Versatile, can be used for brand extension

Answer

Answer: d

33. Sugandha purchased a pack of crayons for her daughter from a nearby stationery shop. She noticed that the crayons were packed in a portable transparent plastic bag. Identify the level of packaging being described in the above lines.
(a) Primary package
(b) Secondary packaging
(c) Transportation packaging
(d) None of the above

Answer

Answer: a

34. Lavanya runs a Play School from her residence. Recently, she placed an order online for 200 chalk boxes. The boxes were delivered to her in a corrugated box. Identify this level of packaging which facilitated movement of the product.
(a) Primary package
(b) Secondary packaging
(c) Transportation packaging
(d) None of the above

Answer

Answer: c

35. In an inter school quiz competition, the participants were shown empty bottles of soft drinks and were asked to identify the brands. All the participants were able to do so. Identify the related point highlighting the importance of packaging which is being described in the given case.
(a) Rising standards of health and sanitation
(b) Facilitates product differentiation
(c) Innovative packaging adds value to a product.
(d) Useful in self service outlets

Answer

Answer: b

36. When Reema had sent her servant to the market to buy a pack of chips, she asked him specifically to bring the yellow coloured packet of chips of a particular brand. Identify the function of packaging being described in the above line.
(a) Helps in product identification
(b) Provides protection to the product
(c) Facilitates the use of product
(d) Assists in promotion of the product

Answer

Answer: a

37. On visiting a supermarket to buy a pack of moisturizer, Harsha noticed that the packaging of most of the beauty products exhibited a photograph of a celebrity. Identify the related function of packaging being described in the given case.
(a) Facilitates the use of product
(b) Assists in promotion of the product
(c) Helps in product identification
(d) Provides protection to the product

Answer

Answer: b

38. The labelling of a pack of oats cookies explains how the product is beneficial in adding fibre to the diet and the other related health benefits. Identify the related function of labelling being described in the given case.
(a) Describes the product and specifies its content
(b) Identification of the product or brand
(c) Grading of products
(d) Helps in promotion of the products

Answer

Answer: d

39. Identify the component of promotion mix being described in the given exhibit?
Business Studies MCQs for Class 12 with Answers Chapter 11 Marketing 3
(a) Advertising
(b) Sales Promotion
(c) Public relation
(d) Personal selling

Answer

Answer: b

40. Identify the related function of labelling being depicted below as given on the pack of the chips.
Business Studies MCQs for Class 12 with Answers Chapter 11 Marketing 4
(a) Describes the product and specifies its content
(b) Grading of products
(c) Helps in promotion of the products
(d) Identification of the product or brand

Answer

Answer: c

41. Ria refused to buy an insulated lunch box for ?1200 as she felt that the real worth of the product was much less than its monetary value. Identify the factor related to pricing decision being described in the given case.
(a) Cost of the product
(b) The utility and demand
(c) Government and legal regulations
(d) Pricing objectives

Answer

Answer: b

42. A salesman of a company dealing in pet foods is paid a fixed salary of ?20000 per month and furthermore, ?20 extra per unit of the product sold beyond the target sales. Identify the type of cost being described in the given example.
(a) Fixed cost
(b) Variable cost
(c) Semi-variable cost
(d) None of the above

Answer

Answer: c

43. Under which of the following conditions is a marketer not likely to fix the price of his products at higher end?
(a) When he faces high degree of competition
(b) When he wants to attain market share leadership
(c) When the product is unique in terms of packaging, product difference and product differentiation
(d) When the demand for the product is low

Answer

Answer: c

44. Under which of the following situations is a company not likely to fix a lower price for its product?
(a) When the competition has introduced a substitute product
(b) If the demand for a product is inelastic
(c) When the company wants to attain market share leadership
(d) When the demand for the product is low

Answer

Answer: b

45. Nooper Limited is marketing its products online. Identify the channel of distribution being adopted by the company.
(a) Zero level channel
(b) One level channel
(c) Two level channel
(d) Three level channel

Answer

Answer: a

46. Kannu has decided to sell her range of organic food products through her own retail outlets. Identify the channel of distribution being adopted by the company.
(a) Zero level channel
(b) One level channel
(c) Two level channel
(d) Three level channel

Answer

Answer: a

47. Srijan Limited sells its products through the company approved retailers. Identify the channel of distribution being adopted by the company.
(a) Zero level channel
(b) One level channel
(c) Two level channel
(d) Three level channel

Answer

Answer: b

48. Hena is planning to set up a small manufacturing unit for manufacturing eco-friendly packaging material. She has decided to market her products through the conventional channel of distribution, which involves wholesalers and retailers. Identify the channel of distribution being adopted by the company.
(a) Zero level channel
(b) One level channel
(c) Two level channel
(d) Three level channel

Answer

Answer: c

49. Under which of the following conditions will the company not be able to provide high level of customer services?
(a) When it maintains high level of inventory
(b) When it maintains low level of inventory
(c) When it owns large number of warehouses
(d) None of the above

Answer

Answer: b

50. Under which of the following conditions does a business need not maintain high level of inventory?
(a) When higher level of customer services need to be provided
(b) When high degree of accurate sales forecast can be made
(c) When the responsiveness of the distribution system is low
(d) All of the above

Answer

Answer: b

51. Mehak Limited has hired 300 salesmen who will be assigned the task of contacting prospective buyers and creating awareness about the new range of organic incenses introduced by the company. Identify the element of promotion been described in the given lines.
(a) Advertising
(b) Sales promotion
(c) Personal selling
(d) Public relation

Answer

Answer: c

52. Within 2 years of it’s inception, Bhavishya Limited has created a very positive reputation about itself and its products in the eyes of general public by participating extensively in various social welfare programs. Identify the component of promotion mixing described in the given lines.
(a) Advertising
(b) Personal selling
(c) Public relation
(d) Sales promotion

Answer

Answer: c

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