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Questions:

Multiple Choice Question

50 x 1 = 50

If y = log x then y₂ = ________.

(a)

\(\frac{1}{x}\)

(b)

\(-\frac{1}{x^2}\)

(c)

\(-\frac{2}{x^2}\)

(d)

e²

If y = e^2x then \(\frac{d^2y}{dx^2}\) at x = 0 is ________.

(a)

(b)

(c)

(d)

If y = x and z = \(\frac{1}{x}\) then \(\frac{dy}{dz}=\)________.

(a)

x²

(b)

(c)

-x²

(d)

\(-\frac{1}{x^2}\)

The graph of f(x) = e^x is identical to that of ________.

(a)

f(x) = a^x, a > 1

(b)

f(x) = a^x, a < 1

(c)

f(x) = a^x, 0 < a < 1

(d)

y = ax +b, a \(\ne\) 0

f(x) = - 5 , for all \(x\in R\), is a ________.

(a)

an identity function

(b)

modulus function

(c)

exponential function

(d)

constant function

Which of the following function is neither even nor odd?

(a)

f(x) = x³ + 5

(b)

f(x) = x⁵

(c)

f(x) = x¹⁰

(d)

f(x) = x²

The minimum value of the function f(x) = |x| is _______.

(a)

(b)

-1

(c)

(d)

\(-\infty \)

The graph of the line y = 3 is _______.

(a)

Parallel to x-axis

(b)

Parallel to y-axis

(c)

Passing through the origin

(d)

Perpendicular to x-axis

If \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\) then f(0) is _______.

(a)

(b)

(c)

-1

(d)

10.

If \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\), then f(5) is _______.

(a)

-1

(b)

(c)

(d)

11.

If p sec 50^o= tan 50^o then p is _______.

(a)

cos 50^o

(b)

sin 50^o

(c)

tan 50^o

(d)

sec 50^o

12.

\(\tan\left(\frac{\pi}{4}-x\right)\) is _______.

(a)

\(\left(\frac{1+\tan x}{1-\tan x}\right)\)

(b)

\(\left(\frac{1-\tan x}{1+\tan x}\right)\)

(c)

1-tan x

(d)

1+tan x

13.

The value of \(cosec^{-1}\left(\frac{2}{\sqrt{3}}\right)\) is ________.

(a)

\(\frac{\pi}{4}\)

(b)

\(\frac{\pi}{2}\)

(c)

\(\frac{\pi}{3}\)

(d)

\(\frac{\pi}{6}\)

14.

The value of \(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}}\) is _______,

(a)

\(\frac{1}{\sqrt3}\)

(b)

\(\frac{1}{2}\)

(c)

\(\frac{\sqrt3}2\)

(d)

\(\frac{1}{\sqrt2}\)

15.

The value of \(\frac{2\tan30^o}{1+tan^230}\) is _____.

(a)

\(\frac12\)

(b)

\(\frac{1}{\sqrt3}\)

(c)

\(\frac{\sqrt{3}}{2}\)

(d)

\(\sqrt3\)

16.

The value 4cos³40^o- 3cos40^o is ________.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(\frac{-1}{2}\)

(c)

\(\frac{1}{2}\)

(d)

\(\frac{1}{\sqrt2}\)

17.

The value of cos²45^o- sin²45^o is_______.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(\frac{1}{2}\)

(c)

(d)

\(\frac{1}{\sqrt{2}}\)

18.

The value of sec A sin(270^o + A) is ______.

(a)

-1

(b)

cos² A

(c)

sec² A

(d)

19.

The value of \(\sin 28^o\cos 17^o+\cos 28^o\sin 17^o\) is _______.

(a)

\(\frac{1}{\sqrt2}\)

(b)

(c)

\(\frac{-1}{\sqrt2}\)

(d)

20.

The degree measure of \(\frac{\pi}{8}\) is ______.

(a)

20^o60^'

(b)

22^o30^'

(c)

20^o60^'

(d)

20^o30^'

21.

The equation of directrix of the parabola y² = - x is _______.

(a)

4x+ 1 =0

(b)

4x - 1 = 0

(c)

x - 4=0

(d)

x + 4 = 0

22.

The equation of the circle with centre (3,-4) and touches the x - axis is _______.

(a)

(x - 3)² +(y - 4)² = 4

(b)

(x - 3)² +(y + 4)² = 16

(c)

(x-3)²+ (y- 4)²= 16

(d)

x²+y²= 16

23.

If the perimeter of the circle is 8π units and centre is (2, 2) then the equation of the circle is _______.

(a)

(x - 2)² + (y - 2)² = 4

(b)

(x - 2)² + (y - 2)² = 16

(c)

(x - 4)² + (y - 4)² = 2

(d)

x² + y² =4

24.

ax² + 4xy + 2y² = 0 represents a pair of parallel lines then 'a' is _______.

(a)

(b)

-2

(c)

(d)

-4

25.

The centre of the circle x² + y - 2x + 2y - 9 = 0 is _______.

(a)

(1,1)

(b)

(-1,-1)

(c)

(-1,1)

(d)

(1, -1)

26.

The length of the tangent from (4,5) to the circle x² + y² = 16 is _______.

(a)

(b)

(c)

(d)

27.

The locus of the point P which moves such that P is at equidistance from their coordinate axes is _______.

(a)

\(y={1\over x}\)

(b)

y = -x

(c)

y = x

(d)

\(y=-{1\over x}\)

28.

The x-intercept of the straight line 3x + 2y - 1 = 0 is _______.

(a)

(b)

(c)

1/3

(d)

1/2

29.

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is _______.

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

30.

The angle between the pair of straight lines x² - 7xy + 4y² = 0 _______.

(a)

\(tan^{-1}\left(1\over 3\right)\)

(b)

\(tan^{-1}\left(1\over 2\right)\)

(c)

\(tan^{-1}\left(\sqrt{33}\over 5\right)\)

(d)

\(tan^{-1}\left(5\over\sqrt{33}\right)\)

31.

Sum of the binomial coefficients is ________.

(a)

2ⁿ

(b)

n²

(c)

(d)

n + 17

32.

Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is _____.

(a)

(b)

(c)

(d)

33.

Thirteen guests has participated in a dinner. The number of handshakes happened in the dinner is __________.

(a)

715

(b)

(c)

286

(d)

34.

There are 10 true or false questions in an examination. Then these questions can be answered in ______.

(a)

240 ways

(b)

120 ways

(c)

1024 ways

(d)

100 ways

35.

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is _________.

(a)

(b)

(c)

(d)

36.

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to _______.

(a)

(b)

(c)

(d)

37.

The term containing x³ in the expansion of (x - 2y)⁷ is _________.

(a)

3^rd

(b)

4^th

(c)

5^th

(d)

6^th

38.

The number of diagonals in a polygon of n sides is equal to _______.

(a)

nC₂

(b)

nC₂ - 2

(c)

nC₂ - n

(d)

nC₂ - 1

39.

If nP_r = 720 (nC_r), then r is equal to ______.

(a)

(b)

(c)

(d)

40.

The number of ways selecting 4 players out of 5 is _______.

(a)

(b)

(c)

(d)

41.

If \(\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5\) then value of \(\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}\) is ________.

(a)

-5

(b)

-125

(c)

-25

(d)

42.

If \(\begin{vmatrix} x & 2 \\ 8 &5 \end{vmatrix}=0\) then the value of x is ________.

(a)

\({{-5}\over{6}}\)

(b)

\({{5}\over{6}}\)

(c)

\({{-16}\over{5}}\)

(d)

\({{16}\over{5}}\)

43.

If A is 3 \(\times\) 3 matrix and |A| = 4, then |A^-1| is equal to ________.

(a)

\({{1}\over{4}}\)

(b)

\({{1}\over{16}}\)

(c)

(d)

44.

If A is an invertible matrix of order 2, then det (A^-1) be equal to ________.

(a)

det (A)

(b)

\({{1}\over{det(A)}}\)

(c)

(d)

45.

If A \(=\begin{pmatrix} -1 & 2 \\ 1 & -4 \end{pmatrix}\) then A (adj A) is ________.

(a)

\(\begin{pmatrix} -4 & -2 \\ -1 & -1 \end{pmatrix}\)

(b)

\(\begin{pmatrix} 4 & -2 \\ -1 & 1 \end{pmatrix}\)

(c)

\(\begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}\)

(d)

\(\begin{pmatrix} 0 & 2 \\ 2 & 0 \end{pmatrix}\)

46.

The inverse matrix of \(\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}\) is ________.

(a)

\(\begin{pmatrix} 2 & -1 \\-5 & 3 \end{pmatrix}\)

(b)

\(\begin{pmatrix} -2 & 5 \\1 & -3 \end{pmatrix}\)

(c)

\(\begin{pmatrix} 3 & -1 \\-5 & -3 \end{pmatrix}\)

(d)

\(\begin{pmatrix} -3 & 5 \\1 & -2 \end{pmatrix}\)

47.

The number of Hawkins-Simon conditions for the viability of an input - output analysis is ________.

(a)

(b)

(c)

(d)

48.

adj (AB) is equal to ________.

(a)

adj A adj B

(b)

adj A^T adj B^T

(c)

adj B adj A

(d)

adj B^T adj A^T

49.

The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is ________.

(a)

abc

(b)

(c)

a²b²c²

(d)

-abc

50.

The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is_________.

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

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Answers Key:

Multiple Choice Question

50 x 1 = 50

\(y_1=\frac{1}{x}, y_2=\frac{-1}{x^2}\)

\(y_1=2 e^{2 x}, y_2=4 e^{2 x}, y_2=4 \text { at } x=0\)

\(\frac{d y}{d x}=1, \frac{d z}{d x}=\frac{-1}{x^2} \quad \frac{d y}{d z}=-x^2\)

(a)
f(x) = a^x, a > 1

(d)
constant function

f(-x) = -x³ + 5 ≠ f(x)

(a)
0

(a)
Parallel to x-axis

f(0) = 0 + 2 = 2

10.

f(5) = 5² - 4(5) = 5

11.

\(p =\frac{\tan 50^{\circ}}{\sec 50^{\circ}}=\frac{\sin 50^{\circ} / \cos 50^{\circ}}{1 / \cos 50^{\circ}} =\sin 50^{\circ}\)

12.

\(\tan (\pi / 4-x)=\frac{\tan \pi / 4-\tan x}{1+\tan \pi / 4 \tan x}=\frac{1-\tan x}{1+\tan x}\)

13.

14.

\(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}} =\tan 3(10) =\tan 30^{\circ}=\frac{1}{\sqrt{3}} \)

15.

\(\frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}} =\sin 2\left(30^{\circ}\right)=\sin 60^{\circ}=\frac{\sqrt{3}}{2} \)

16.

4cos³40^o- 3cos40^o = cos 3(40^o)
= cos 120^o
= cos (180^o - 60^o)
= -cos 60^o
\(= \frac{-1}{2}\)

17.

cos²45^o- sin²45^o = cos 2(45^o)
= cos 90^o = 0

18.

\(\sec A(-\cos A)=\frac{1}{\cos A}(-\cos A)=-1\)

19.

\(\sin (28+17)=\sin 45^{\circ}=\frac{1}{\sqrt{2}}\)

20.

\(\frac{\pi}{8}=\frac{180^{\circ}}{8}=22 \frac{1}{2}^{\circ}=22^{\circ} 30^{\prime}\)

21.

\(4 a=1 \Rightarrow a=\frac{1}{4}\)
Equation x = a
\(x=\frac{1}{4}\)

22.

(b)
(x - 3)² +(y + 4)² = 16

23.

\(2 n r=8 \pi\)
r = 4

24.

\(h^2-a b=0\)
\(4-2 a=0 \Rightarrow a=2\)

25.

C(- g, -f)

26.

\(\sqrt{4^2+5^2-16}=\sqrt{5^2}=5\)

27.

28.

On x axis y = 0
\(3 x=1 \Rightarrow x=\frac{1}{3}\)

29.

30.

31.

(a)
2ⁿ

32.

33.

(b)
78

34.

210 = 1024 (2.x 2... 10 terms)

35.

The number of parallelograms = 4C₂ x 3C₂

36.

Equality coefficient of x in the numerator
kx = 4 (2n) + 1 (x)
kx = 9x

37.

38.

39.

\(n P_r =720(\mathrm{nCr}) \)
\(\frac{n !}{(n-r) !} =720\left(\frac{n !}{r !(n-r) !}\right) \)
\(r ! =720 \)
\(r ! =6 ! \)
r = 6

40.

No. of ways = 5C₄ = 5C₁ = 5

41.

\(\left|\begin{array}{cc} 20 & 15 \\ 15 & 5 \end{array}\right|=5 \times 5\left|\begin{array}{ll} 4 & 3 \\ 3 & 1 \end{array}\right|\)
\(=5 \times 5 \times-5\)
\(=-125\)

42.

5x - 16 = 0
5x = 16
\(x=\frac{16}{5}\)

43.

(Since \(\left|A^{-1}\right|=\frac{1}{|A|}\))

44.

(b)
\({{1}\over{det(A)}}\)

45.

\(|A|=4-2=2\)
\(A(\operatorname{adj} A)=|A| I=\left(\begin{array}{ll} 2 & 0 \\ 0 & 2 \end{array}\right)\)

46.

\(|A|=6-5=1\)
\(A^{-1}=\left(\begin{array}{cc} 2 & -1 \\ -5 & 3 \end{array}\right)\)

47.

(d)
2

48.

49.

50.

\(\left|\begin{array}{lll} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{array}\right|=0 \Rightarrow-1\left[x^2-x\right]=0\)
\(\Rightarrow x(x-1)=0 \Rightarrow x=0,1\)