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NCERT Solutions for class 12 Maths | Chapter 5 - Continuity and Differentiability

Questions
1 If x = et sin t, y = etcos t, t is a parameter, then dy/dx at (1, 1) is equal to
A –1/2
B –1/4
C 0
D 1/2

Answer:0
2 If y = e3x+n, then the value of dy/dx|x=0 is
A 1
B 0
C -1
D 3e7

Answer:0
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3 If x =Class 12 Maths Chapter 5 Continuity and Differentiability is equal to dx
A –y/x
B y/x
C –x/y
D x/y

Answer:–x/y
4 The derivative of y = (1 – x) (2 – x)…. (n – x) at x = 1 is equal to
A 0
B (-1) (n – 1)!
C n ! – 1
D (-1)n-1 (n – 1)!

Answer:(-1) (n – 1)!
5 xy. yx = 16, then the value of dy/dx at (2, 2) is
A -1
B 0
C -1
D None of these

Answer:-1
6 If y = Class 12 Maths Chapter 5 Continuity and Differentiability then dy/dx is equal to
A 1/2 sec² x
B sec² x
C sec x tan x
D e1/2 log(1+tan²x)

Answer:sec x tan x
7 If x sin (a + y) = sin y, then dy/dx is equal to
A sin2(a+y)/sina
B sina/sin2(a+y)
C sin(a+y)/sina
D sina/sin(a+y)

Answer:sin2(a+y)/sina
8 The derivative of cos-1 (2x² – 1) w.r.t cos-1 x is
A 2
B
C 2x
D 1 – x²

Answer:2
9 If f(x) = x² sin1/x, where x ≠ 0, then the value of the function f(x) at x = 0, so that the function is continuous at x = 0 is
A 0
B -1
C 1
D None of these

Answer:0
10 The function f(x) = Class 12 Maths Chapter 5 Continuity and Differentiability is
A discontinuous at only one point at x = 0
B discontinuous at exactly two points
C discontinuous at exactly three points
D None of these

Answer:discontinuous at only one point at x = 0
11 The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval [o, √3] is
A 1
B -1
C 3/2
D 1/3

Answer:1
12 If ax² + 2hxy + by² = 1, then dy/dx equals
A hx+by/ax+by
B ax+by/hx+by
C ax+hy/hx+hy
D −(ax+hy)/hx+by

Answer:−(ax+hy)/hx+by
13 If y = sin-1 Class 12 Maths Chapter 5 Continuity and Differentiability then dy/dx is equal to
A 1
B 0
C π/2
D None of these

Answer:0
14 If y = aex+ be-x + c Where a, b, c are parameters, they y’ is equal to
A aex – be-x
B aex + be-x
C -(aex + be-x)
D aex – bex

Answer:aex – be-x
15 If x = a cos4 θ, y = a sin4 θ. then dy/dx at θ = 3π/4 is
A -1
B 1
C -a²
D a²

Answer:-1
16 Let y = t10 + 1 and x = t8 + 1, then  d2y/dx2 , is equal to
A d2y/dx2
B 20t8
C 5/16t6
D None of these

Answer:None of these
17 If x = sin-1 (3t – 4t³) and y = cos-1 Class 12 Maths Chapter 5 Continuity and Differentiability then dy/dx is equal to
A 1/2
B 2/5
C 3/2
D 1/3

Answer:1/3
18 If y = log Class 12 Maths Chapter 5 Continuity and Differentiability then dy/dx is equal to
A 7
B 3/x−2
C 3/(x−1)
D None of these

Answer:None of these
19 The derivative of sin-1 with respect to cos-1 is
A -1
B 1
C 2
D 4

Answer:1
20 If xy = ex-y then dy/dx is
A 1+x/1+logx
B 1−logx/1+logy
C not defined
D −y/(1+logx)2

Answer:−y/(1+logx)2

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