C++ FILE FOR BOARDS CLASS 12

						MATHS DIFF. CAL. (MOCK PH. TEST)
									MAINS PATTERN
		⎛	+	y		2x −		⎞
	1.	If f ⎜ 2x			,		y	⎟	= xy, then f(x, y) + f (y, x) =
				8			8
		⎝						⎠
		(A) 1							(B) 0
		(C) 2							(D) 3

2.The domain of definition of f(x) = sec-1(cos2x) is

		(A) mπ , m ∈I						(B) π/2
		(C) π/4						(D) none of these
	3.	If f : R → R is		the	function defined by f(x) =			ex2	− e−x2	, then
								ex2	+ e−x2
		(A) f(x)	is an	increasing function				(B) f(x) is a decreasing function
		(C) f(x)	is onto					(D) none of these.
	4.	The function f(x) =			1 + sin x − cos x		is not defined at x = 0. The value of f(0) so that
					1 − sin x − cos x
		f(x) is continuous at x = 0, is
		(A) 1						(B) −1
		(C) 0						(D) none of these

5.lim π − cos−1 x is

+x + 1x→−1

(A)

1

(B)

1

2

2π

(C)

1

(D) none of these

π

The function f(x) =

cos x − sin x

is not defined at x =

π

⎛

π ⎞

6.

. The value of

f ⎜

⎟ so that

cos2x

4

⎝

4 ⎠

f(x) is continuous is

(A) 1

(B) −1

(C)

(D)

1

2

2

7.The set of all points where the function f (x) = x|x| is differentiable is

(A) (–∞, ∞)	(B) (–∞, 0) ∪ (0, ∞)
(C) (0, ∞)	(D) [0, ∞]

8.Let f: R → R be a function defined by f(x) = max (x, x3). The set of all points where f(x) is not differentiable is

		(A) {−1, 1}			(B) {−1, 0}
		(C) {0, 1}			(D) {−1, 0, 1}
		If x = sin−1 (3t − 4t3 ) and y = cos−1			dy	is equal to
	9.		1− t2 , then
					dx

(A)1/2

(C)3/2

10.Which of the following function are bijective:

(A)f : Z → Z defined by y = x + 2

(C)f : Z → R defined by y = √x

11.Period of |sin 2x| + |cos 8x| is

(A)π2

(C) 16π

12.The range of the function sin–1(x2 + 2x), x > 0 is

	⎡		π		,	π ⎤
(A) ⎢−						⎥
	⎣		2			2 ⎦
(C)	⎡	π		,		π ⎤
	⎢					⎥
	⎣	3				2 ⎦

−

13.If f(x) = 3x − 1, then ∑f(r) is equal ton 1

r =0

(B)2/5

(D)1/3

(B)f : Z → Z defined by y = 2x

(D)f : R → R defined by y = x + |x|

(B)π8

(D) none of these

(B)	⎛	0,	π ⎤
	⎜		⎥
	⎝		2 ⎦

(D) none of these

	(A) 3n − 1			(B)	3n	− 1
					2
	(C)	3n − 2n − 1		(D) none of these
		2

14.If f(x) = sin–1x and g(x) = x , the domain of composite function fog(x) is :

	(A) [–1, 1]							(B) [–2, 1]
	(C) [0, –1]	(D) [0, 1]
							− 3	is equal to
15.	If f (9) = 9, f′ (9) = 4, then lim			f	(x)
		x→9			x − 3
	(A) 9							(B) 4
	(C) 3							(D) 2

16.The function f (x) = 1 + |sin x| is

	(A) continuous nowhere	(B) continuous everywhere
	(C) differential nowhere	(D) differentiable at x = 0
17.	⎪⎧x +1,	x ≤ 1
	f(x) = ⎨
	⎩⎪3 − ax2 ,	x > 1
	Value of ‘a’ for which f(x) is continuous, is
	(A) 1	(B) 2
	(C) –1	(D) –2

⎛ x2 + 5x + 3

⎞x

18.

If f (x) = ⎜

⎟

, then lim f (x) is

x2 + x

+ 2

⎝

⎠

x→∞

(A) e4

(B) e3

(C) e2

(D) 24

19.

If f(x) =

1

,

then the points of discontinuity of the composite function y =

(2 − x )

f(f(f(x))) are

(A) 2, 3/4

(B) 1, 2

(C) 2, 3

(D) 2, 3/2, 4/3

⎛

+ 1

⎞

⎛

−1

⎞

dy

−

x

−

x

20.

y = sec 1

⎜

⎟ + sin

1

⎜

⎟ , then the value of

is

⎜

x −1

⎟

⎜

x + 1

⎟

dx

⎝

⎠

⎝

⎠

(A) 0

(B) 1

(C) – 1

(D) – ½

21.

If f(x) = a sin

x

+ be

x

is differential at x = 0, then

(A) a = 0

(B) b = 0

(C) a – b = 0

(D) a + b = 0

If 2x + 2y = 2x + y, then the value of

dy

22.

at x = y = 1 is

dx

(A) 0

(B) – 1

(C) 1

(D) 2

23.

If f (x) =

1

, x ≠ 0, 1 then the graph of the function y = f{f (f (x))}, x > 1 is

1 − x

(A) a circle

(B) an ellipse

(C) a straight line

(D) a pair of straight line

⎛

π ⎞

⎛

π ⎞

⎛ 5

⎞

24.

If f(x) = sin2x + sin2

⎜ x +

⎟

+ cos x cos ⎜ x +

⎟ and g ⎜

⎟ = 1, then (g of) (x)

⎝

3 ⎠

⎝

3 ⎠

⎝ 4

⎠

is equal to

(A) 2

(B) 1

(C) 3

(D) 4

25.Which of the following functions is inverse of itself

		(A) f(x) =	1	− x			(B) f(x) = log x
			1	+ x
		(C) f(x) = 2x(x - 1)					(D) none of these
	26.	Value of f (1) so that function f (x) =				ex − e	is continuous at x = 1 is
						x − 1
		(A) 0					(B) e2
		(C) e					(D)	e
							2

	27.	lim	sin xn	(m < n) is equal to
			(sin x)m
		x→0
		(A) 1		(B) 0
		(C) n/m		(D) none of these

28.Let f(x) = sinx + [x]x (where [.] denotes greatest integer function), 1 ≤ x ≤ 3 has

(A)3 points of discontinuity

(B)3 points of non – differentiability

(C)2 points of non – differentiability

(D)1 points of non – differentiability

29.Let f (x) = xp cos⎛⎜ 1 ⎞⎟ , when x ≠ 0 and f(x) = 0 when x = 0. Then f(x) will be

⎝x ⎠

	differentiable at x = 0, if
	(A) p > 0				(B) p > 1
	(C) 0 < p < 1				(D)	1	< p < 1
				2
30.	The derivative of f(x) = 3		2 + x		at the point x0 = - 3 is
	(A) 3				(B) – 3
	(C) 0				(D) does not exist

Answers:

1.B

2A

3D

4B

5B

6. D

7.A

8D

9.D

10A

11A

12. B

13C

14D

15.B

16.B

17A

18A

19.D

20.A

21D

22.B

23C

24B

25A

26C

27.B

28.C

29B

30. B