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Calculus MCQ's

The document contains 26 multiple choice questions regarding calculus concepts such as: - Properties of one-to-one, onto, and bijective functions - Limits, including the limit as x approaches infinity of 1/x - Continuity and differentiability of the absolute value function - Increasing and decreasing functions defined by their derivatives - Concavity and critical points of functions - Integration techniques including the integrating factor, Simpson's rule, and finding antiderivatives - Partial derivatives and directional derivatives of multivariable functions

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479 views4 pages

Calculus MCQ's

The document contains 26 multiple choice questions regarding calculus concepts such as: - Properties of one-to-one, onto, and bijective functions - Limits, including the limit as x approaches infinity of 1/x - Continuity and differentiability of the absolute value function - Increasing and decreasing functions defined by their derivatives - Concavity and critical points of functions - Integration techniques including the integrating factor, Simpson's rule, and finding antiderivatives - Partial derivatives and directional derivatives of multivariable functions

Uploaded by

SADANAND KALE
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CALCULUS MCQ’s

1 A function is said to be ______________ if and only if f(a) = f(b)


implies that a = b for all a and b in the domain of f.
(A) One-to-many (B) One-to-one
(C) Many-to-many (D) Many-to-one

2 A function is said to be Bijective if it is ______.


(A) One - One (B) onto
(C) Injective (D) both one-One and Onto

3 Inverse of function exist if function is _______.


(A) One - One (B) Onto
(C) Injective (D) Bijective

4 If Range(f) = Co-domain of function f, then f is said to be ________.


(A) One - One (B) Onto
(C) Injective (D) Bijective

5 lim 1/𝑥 = _____.


𝑥→∞
(A) 1 (B) 0
(C) 2 (D) 3

6 f(x) = |x| is _______ at x = 0.


(A) continuous (B) differentiable
(C) discontinuous (D) not defined

7 A function f: I → R is an increasing function if _____ order derivative


of f(x) is greater than 0, for all x ∈ I.
(A) first (B) second
(C) third (D) fourth

8 A function f: I → R is a decreasing function if 𝑓 ′ (x) ____ 0.


(A) < (B) >
(C) = (D) ≥

9 For which interval for which y = x3 is concave up?


(A) (0,∞) (B) (0,1)
(C) (-∞, 0) (D) [0,1]

10 Find the maximum profit that a company can make, if the profit
function is given by P(x) = 41 + 24x – 18x2.
(A) 25 (B) 50
(C) 45 (D) 49

11 Critical points of function given by f(x) = 41 + 24x – 18x2 is/are ____.


(A) 1,2 (B) 2/3
(C) -1,2 (D) 0

12 Solution of given differential equation: dy/dx = y. (y >0) is _______.


(A) logy = x + c (B) y = x + c
(C) y = x (D) y = 1

13 Solution of given differential equation: dy/dx = 1. is _______.


(A) logy = x + c (B) y = x + c
(C) y = x (D) y = 1

14 ʃ sin2x dx = _______,
(A) cosx (B) -cosx + c
(C) -cos2x/2 + c (D) sinx
15 What is the integrating factor of 4dy/dx + 8xy = xex?
2
(A) x (B) 𝑒 𝑥
(C) y (D) e2x

16 The area of region bounded by the curve y = sinx and lines x = 0 to x =


𝜋/2 is ______.
(A) 1 (B) 2/3
(C) -2 (D) 0
17 ∫𝑏 𝑓(𝑥)𝑑𝑥 , f(x) stand for _____.
𝑎
(A) lower limit (B) upper limit
(C) integrand (D) limit of integral

18 ∫𝑎 𝑓(𝑥)𝑑𝑥 = ____.
𝑎
(A) 1 (B) 2/3
(C) -2 (D) 0
19 Which of the following shapes is generally preferred in case of
application of Simpson’s rule?
(A) square (B) triangle
(C) trapezoid (D) rectangle

20 _____ order differential equation can be solved by Euler's method.


(A) first (B) second
(C) third (D) fourth

21 fx (x, y) = ______ of given function f(x, y) = x2 + y2 .


(A) 2x (B) 2x + 2y
(C) 2y (D) 0
22 ∇f (x, y) = ______ of given function f(x, y) = x2 + y2 .
(A) 2x (B) 2x + 2y
(C) 2y (D) (2x, 2y)

23 If lim f (x, y) = 4 and lim g (x, y) = 3 as (x, y) tends to (a, b), then
lim [f (x, y) + g (x, y)] = ___.
(A) 4 (B) 3
(C) 7 (D) not defined

24 Find directional derivative of given function f(x,y) = x2 + y2 at point


(1,1) in the direction of the vector A = i + 0j.
(A) 4 (B) 3
(C) 7 (D) 2
25 Find critical point of given function f(x,y) = x2 + y2 .
(A) (1, 1) (B) (0, 0)
(C) both of these (D) none of these
26 f (x, y, z) = xyz is function of ____ variable.
(A) 1 (B) 2
(C) 3 (D) 4

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