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

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

If A = \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)such that ad - bc \(\neq\) 0 then A^-1 is ________.

(a)

\({{1}\over{ad-bc}}\begin{pmatrix} d & b \\-c & a\end{pmatrix}\)

(b)

\({{1}\over{ad-bc}}\begin{pmatrix} d & b \\c & a\end{pmatrix}\)

(c)

\({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\-c & a\end{pmatrix}\)

(d)

\({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\c & a\end{pmatrix}\)

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)

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

If A and B are non-singular matrix then, which of the following is incorrect?

(a)

A² = I Iimplies A^-1 = A

(b)

I^-1 = I

(c)

If AX = B, then X = B^-1 A

(d)

If A is square matrix of order 3 then |adj A|= |A|²

The value of \(\begin{vmatrix} x & x^2 & -yz & 1 \\ y & y^2 & -zx & 1 \\ z & z^2 & -xy &1 \end{vmatrix}\) is ________.

(a)

1

(b)

0

(c)

-1

(d)

-xyz

If A = \(\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix},\) then |2A| is equal to ________.

(a)

4 cos 2 \(\theta\)

(b)

4

(c)

2

(d)

1

If \(\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}\) and A_ij is cofactor of a_ij, then value of \(\triangle\) is given by ________.

(a)

a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃

(b)

a₁₁ A₁₁ + a₁₂ A₂₁ + a₁₃ A₃₁

(c)

a₂₁ A₁₁ + a₂₂ A₁₂ + a₂₃ A₁₃

(d)

a₁₁ A₁₁ + a₂₁ A₂₁ + a₃₁ A₃₁

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)

0

If nC₃ = nC₂, then the value of nC₄ is _______.

(a)

2

(b)

3

(c)

4

(d)

5

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

(a)

4!

(b)

20

(c)

25

(d)

5

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

(a)

4

(b)

5

(c)

6

(d)

7

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is ________.

(a)

2

(b)

6

(c)

20

(d)

24

If n is a positive integer, then the number of terms in the expansion (x + a)ⁿ is _______.

(a)

n

(b)

n + 1

(c)

n-1

(d)

2n

The middle term in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\) is _______.

(a)

10C₄\(\left( \frac { 1 }{ x } \right) \)

(b)

10C₅

(c)

10C₆

(d)

10C₇x⁴

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

(a)

9

(b)

11

(c)

5

(d)

7

The number of 3 letter words that can be formed from the letters of the word number when the repetition is allowed are ________.

(a)

206

(b)

133

(c)

216

(d)

300

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

(a)

18

(b)

12

(c)

9

(d)

6

The value of (5C₀ + 5C₁) + (5C₁ + 5C₂) + (5C₂ + 5C₃) + (5C₃ + 5C₄) + (5C₄ + 5C₅ ) is ________.

(a)

2⁶-2

(b)

2⁵-1

(c)

2⁸

(d)

2⁷

Sum of Binomial co-efficient in a particular expansion is 256, then number of terms in the expansion is ________.

(a)

8

(b)

7

(c)

6

(d)

9

Sum of the binomial coefficients is ________.

(a)

2ⁿ

(b)

n²

(c)

2n

(d)

n + 17

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)

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)

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

The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is _______.

(a)

x+2y+2 = 0

(b)

x - 2y + 1 = 0

(c)

2x - y + 2 = 0

(d)

3x + y + 1 = 0

Length of the latus rectum of the parabola y² = - 25x is _______.

(a)

25

(b)

-5

(c)

5

(d)

-25

If the centre of the circle is (-a, -b) and radius is \(\sqrt{a^2-b^2}\), then the equation of circle is _______.

(a)

x²+y²+2ax+2by+2b² = 0

(b)

x²+y²+2ax +2by-2b² = 0

(c)

x² +y² - 2ax - 2by - 2b² = 0

(d)

x² + y - 2ax - 2by + 2b² = 0

Combined equation of co-ordinate axes is _______.

(a)

x²-y² = 0

(b)

x²+y² = 0

(c)

xy = c

(d)

xy = 0

If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is _______.

(a)

6

(b)

3

(c)

12

(d)

4

The distance between directrix and focus of a parabola y² = 4ax is _______.

(a)

a

(b)

2a

(c)

4a

(d)

3a

The radian measure of 37^o30^' is ______.

(a)

\(\frac{5\pi}{24}\)

(b)

\(\frac{3\pi}{24}\)

(c)

\(\frac{7\pi}{24}\)

(d)

\(\frac{9\pi}{24}\)

If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is _______.

(a)

\(\frac{1}{\sqrt6}\)

(b)

\(\frac{-1}{\sqrt6}\)

(c)

\(\frac{\sqrt5}{\sqrt6}\)

(d)

\(\frac{-\sqrt5}{\sqrt6}\)

The value of \(\sin(-420^o)\) is _______.

(a)

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

(b)

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

(c)

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

(d)

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

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

(a)

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

(b)

1

(c)

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

(d)

0

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

(a)

-1

(b)

cos² A

(c)

sec² A

(d)

1

The value of 1 - 2sin²45^o is _______.

(a)

1

(b)

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

(c)

\(\frac14\)

(d)

0

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

(a)

\(\frac12\)

(b)

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

(c)

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

(d)

\(\sqrt3\)

If \(\sin A=\frac{1}{2}\) then \(4\cos^3A-3\cos A\) is ________.

(a)

1

(b)

0

(c)

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

(d)

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

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)

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

If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is  _____.

(a)

\(\frac{16}{15}\)

(b)

0

(c)

\(\frac{56}{65}\)

(d)

\(\frac{64}{65}\)

The value of \(\frac{1}{cosec(-45^o)}\) is _______.

(a)

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

(b)

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

(c)

\(\sqrt2\)

(d)

\(-\sqrt2\)

If f(x) = x² - x + 1, then f (x + 1) is _______.

(a)

x²

(b)

x

(c)

1

(d)

x² + x + 1

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)

2

(b)

5

(c)

-1

(d)

0

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

The graph of y = 2x² is passing through _______.

(a)

(0,0)

(b)

(2,1)

(c)

(2,0)

(d)

(0,2)

Which one of the following functions has the property f (x) = \(f\left( \frac { 1 }{ x } \right) \), provided \(x \neq 0\)

(a)

\(f\left( x \right) =\frac { { x }^{ 2 }-1 }{ x } \)

(b)

\(f\left( x \right) =\frac { 1-{ x }^{ 2 } }{ x } \)

(c)

f(x) = x

(d)

\(f\left( x \right) =\frac { { x }^{ 2 }+1 }{ x } \)

The range of f(x) = |x|, for all \(x\in R\), is ________.

(a)

(0, \(\infty \))

(b)

(0, \(\infty \))

(c)

(-\(\infty \), \(\infty \))

(d)

(1, \(\infty \))

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

For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?

(a)

-2

(b)

1

(c)

2

(d)

-1

\(\frac{d}{dx}(\frac{1}{x})\) is equal to ________.

(a)

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

(b)

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

(c)

log x

(d)

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

If y = log x then y₂ = ________.

(a)

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

(b)

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

(c)

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

(d)

e²