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

If \(\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}\) then \(\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}\) is ________.

(a)

\(\triangle\)

(b)

-\(\triangle\)

(c)

3\(\triangle\)

(d)

-3\(\triangle\)

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

(a)

abc

(b)

0

(c)

a²b²c²

(d)

-abc

If A is square matrix of order 3, then |kA| is________.

(a)

k|A|

(b)

-k|A|

(c)

k³|A|

(d)

-k³|A|

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

(a)

1

(b)

3

(c)

4

(d)

2

The inventor of input-output analysis is ________.

(a)

Sir Francis Galton

(b)

Fisher

(c)

Prof. Wassily W. Leontief

(d)

Arthur Caylay

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

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

The value of n, when nP₂ = 20 is _______.

(a)

3

(b)

6

(c)

5

(d)

4

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

For all n > 0, nC₁ + nC₂ + nC₃ + ... +nC_n is equal to _______

(a)

2n

(b)

2ⁿ- 1

(c)

n²

(d)

n² - 1

The last term in the expansion of (3 +\(\sqrt{2}\) )⁸ is ________

(a)

81

(b)

16

(c)

8\(\sqrt{2}\)

(d)

27\(\sqrt{3}\)

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 

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

(a)

2⁶-2

(b)

2⁵-1

(c)

2⁸

(d)

2⁷

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

(a)

715

(b)

78

(c)

286

(d)

13

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)

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

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

(a)

3

(b)

2

(c)

1/3

(d)

1/2

If kx² + 3xy - 2y² = 0 represent a pair of lines which are perpendicular then k is equal to _______.

(a)

1/2

(b)

-1/2

(c)

2

(d)

-2

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

(a)

(1,1)

(b)

(-1,-1)

(c)

(-1,1)

(d)

(1, -1)

The equation of the circle with centre on the x axis and passing through the origin is _______.

(a)

x² - 2ax + y = 0

(b)

y² - 2ay + x² = 0

(c)

x²+y²=a²

(d)

x² - 2ay + y = 0

In the equation of the circle x² + y² = 16 then y intercept is (are) _______.

(a)

4

(b)

16

(c)

±4

(d)

±16

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

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

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 double ordinate passing through the focus is _______.

(a)

focal chord

(b)

latus rectum

(c)

directrix

(d)

axis

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

(a)

20^o60^'

(b)

22^o30^'

(c)

20^o60^'

(d)

20^o30^'

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

(a)

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

(b)

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

(c)

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

(d)

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

The value of \(\cos(-480^o)\) is ________.

(a)

\(\sqrt3\)

(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 cos²45^o - sin²45^o is_______.

(a)

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

(b)

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

(c)

0

(d)

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

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 \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\) then tan(2A + B) is equal to ______.

(a)

1

(b)

2

(c)

3

(d)

4

\(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is _____.

(a)

\(\frac{3}{5}\)

(b)

\(\frac{5}{3}\)

(c)

\(\frac{4}{5}\)

(d)

\(\frac{5}{4}\)

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

(a)

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

(b)

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

(c)

\(\sqrt2\)

(d)

\(-\sqrt2\)

\(\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}\) is _______.

(a)

cos²x-sin²x

(b)

sin²x-cos²x

(c)

1

(d)

0

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

If f(x) = \(\frac{1-x}{1+x}\) then f(-x) is equal to _______.

(a)

-f(x)

(b)

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

(c)

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

(d)

f(x)

If f(x) = 2^x and get g(x) = \(\frac{1}{2^x}\) then (fg)(x) is ________.

(a)

1

(b)

0

(c)

4^x

(d)

\(\frac{1}{4^x}\)

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

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

(a)

an identity function

(b)

modulus function

(c)

exponential function

(d)

constant function

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

(a)

(0, \(\infty \))

(b)

(0, \(\infty \))

(c)

(-\(\infty \), \(\infty \))

(d)

(1, \(\infty \))

If f(x) = x² and g(x) = 2x + 1 then (fg)(0) is ________.

(a)

0

(b)

2

(c)

1

(d)

4

\(\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =\)________.

(a)

1

(b)

\(\infty\)

(c)

\(-\infty\)

(d)

\(\theta\)

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

(a)

-2

(b)

1

(c)

2

(d)

-1

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

(a)

x²

(b)

1

(c)

-x²

(d)

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