CUET Mathematics - Calculus - Application Of Derivatives | Free Questions - Page 12

Q1:

2022: 23 Aug Shift 1

Calculus

>

Application of Derivatives

Easy

Core

A student Sumit is running on a playground along the curve given by $y = x^2 + 7$ . Another student Amit standing at a point with co-ordinates $(3, 7)$ on the playground wants to hit Sumit by paper ball, when Sumit is nearest to him.

Based on the above information answer the following.

If D is the distance between Sumit and Amit, then the value of $x$ for which D is minimum, is :

$3$

$5$

$1$

$2$

Correct Answer

Option 3

Correct Answer

Explanation

Q2:

2022: 23 Aug Shift 1

Calculus

>

Application of Derivatives

Easy

Core

A student Sumit is running on a playground along the curve given by $y = x^2 + 7$ . Another student Amit standing at a point with co-ordinates $(3, 7)$ on the playground wants to hit Sumit by paper ball, when Sumit is nearest to him.

Based on the above information answer the following.

The position of Sumit when Amit will hit the paper ball is :

$(5, 32)$

$(1, 8)$

$(3, 7)$

$(3, 16)$

Correct Answer

Option 2

Correct Answer

Explanation

Q3:

2022: 23 Aug Shift 1

Calculus

>

Application of Derivatives

Easy

Core

A student Sumit is running on a playground along the curve given by $y = x^2 + 7$ . Another student Amit standing at a point with co-ordinates $(3, 7)$ on the playground wants to hit Sumit by paper ball, when Sumit is nearest to him.

Based on the above information answer the following.

Minimum value of D is :

$5$

$\sqrt{5}$

$3$

$1$

Correct Answer

Option 2

Correct Answer

Explanation

Q4:

2022: 25 May Shift 1

Calculus

>

Application of Derivatives

Easy

Common

Match List I with List II

LIST I	LIST II
A. Maximum value of $f(x) = -\lvert x+1 \rvert + 3$	I. 6
B. Minimum value of $f(x) = (2x-1)^2 + 5$	II. 5
C. Maximum value of $f(x) = 6 - x^2$	III. no maximum value
D. Maximum value of $f(x) = x^3 + 1$	IV. 3

Choose the correct answer from the options given below:

A-IV, B-II, C-I, D-III

A-III, B-IV, C-I, D-II

A-I, B-II, C-III, D-IV

A-II, B-III, C-IV, D-I

Correct Answer

Option 1

Correct Answer

Explanation

Q5:

2022: 25 May Shift 1

Calculus

>

Application of Derivatives

Medium

Common

If $f(x) = \frac{1}{1-x}$ , then for $x > 1, f(x)$ is:

decreasing

constant

increasing

neither decreasing nor increasing

Correct Answer

Option 3

Correct Answer

Explanation

Q6:

2022: 25 May Shift 1

Calculus

>

Application of Derivatives

Easy

Core

The approximate volume of a cube of side a meters on increasing the side by 4% is:

$1.04 a^3$ m $^3$

$1.004 a^3$ m $^3$

$1.12 a^3$ m $^3$

$1.12 a^2$ m $^3$

Correct Answer

Option 3

Correct Answer

Explanation

Q7:

2022: 25 May Shift 1

Calculus

>

Application of Derivatives

Medium

Core

The maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$ is:

0

12

16

32

Correct Answer

Option 2

Correct Answer

Explanation

Q8:

2022: 25 May Shift 1

Calculus

>

Application of Derivatives

Medium

Core

The equation of the tangent, to the curve $y = x^2 - 2x - 3$ which is perpendicular to the line $x + 2y + 3 = 0$ , is

$4x - 2y = 7$

$2x - y = 7$

$2x - y = 5$

$4x - 2y = 5$

Correct Answer

Option 2

Correct Answer

Explanation

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