If (AB)^-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A^-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B^-1 = 

(a)

\(\left[ \begin{matrix} 2 & -5 \\ -3 & 8 \end{matrix} \right] \)

(b)

\(\left[ \begin{matrix} 8 & 5 \\ 3 & 2 \end{matrix} \right] \)

(c)

\(\left[ \begin{matrix} 3 & 1 \\ 2 & 1 \end{matrix} \right] \)

(d)

\(\left[ \begin{matrix} 8 & -5 \\ -3 & 2 \end{matrix} \right] \)

If 0 ≤ θ  ≤ π and the system of equations x + (sinθ)y - (cosθ)z = 0, (cosθ)x - y +z = 0, (sinθ)x + y - z = 0 has a non-trivial solution then θ is

(a)

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

(b)

\(\frac { 3\pi }{ 4 } \)

(c)

\(\frac { 5\pi }{ 6 } \)

(d)

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

If \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to 

(a)

0

(b)

1

(c)

2

(d)

3

The principal argument of \(\cfrac { 3 }{ -1+i } \) is

(a)

\(\cfrac { -5\pi }{ 6 } \)

(b)

\(\cfrac { -2\pi }{ 3 } \)

(c)

\(\cfrac { -3\pi }{ 4 } \)

(d)

\(\cfrac { -\pi }{ 2 } \)

If α, β and γ are the zeros of x³ + px² + qx + r, then \(\Sigma \frac { 1 }{ \alpha } \) is

(a)

\(-\frac { q }{ r } \)

(b)

\(-\frac { p }{ r } \)

(c)

\(\frac { q }{ r } \)

(d)

\(-\frac { q }{ p } \)

\(\sin ^{-1} \frac{3}{5}-\cos ^{-1} \frac{12}{13}+\sec ^{-1} \frac{5}{3}-\operatorname{cosec}^{-1} \frac{13}{12}\) is equal to

(a)

2\(\pi\)

(b)

\(\pi\)

(c)

0

(d)

tan^-1\(\frac{12}{65}\)

\(\sin ^{-1}\left(\tan \frac{\pi}{4}\right)-\sin ^{-1}\left(\sqrt{\frac{3}{x}}\right)=\frac{\pi}{6}\). Then x is a root of the equation

(a)

x²−x−6 = 0

(b)

x²−x−12 = 0

(c)

x²+x−12 = 0

(d)

x²+x−6 = 0

The centre of the circle inscribed in a square formed by the lines x² − 8x − 12 = 0 and y² − 14y + 45 = 0 is

(a)

(4, 7)

(b)

(7, 4)

(c)

(9, 4)

(d)

(4, 9)

The locus of a point whose distance from (-2,0) is \(\frac { 2 }{ 3 } \) times its distance from the line x = \(\frac { -9 }{ 2 } \) is

(a)

a parabola

(b)

a hyperbola

(c)

an ellipse

(d)

a circle

If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between \(\vec { a } \ and \ \vec { b } \) is

(a)

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

(b)

\(\frac { 3\pi }{ 4 } \)

(c)

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

(d)

\( { \pi }\)

If the length of the perpendicular from the origin to the plane 2x + 3y + λz =1, λ > 0 is \(\frac{1}{5}\), then the value of λ is

(a)

\(2\sqrt { 3 } \)

(b)

\(3\sqrt { 2 } \)

(c)

0

(d)

1

The slope of the line normal to the curve f(x) = 2cos 4x at \(x=\cfrac { \pi }{ 12 } \) is

(a)

\(-4\sqrt { 3 } \)

(b)

-4

(c)

\(\cfrac { \sqrt { 3 } }{ 12 } \)

(d)

\(4\sqrt { 3 } \)

The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

(a)

\(\frac{1}{31}\)

(b)

\(\frac15\)

(c)

5

(d)

31

If \(\frac{\Gamma(n+2)}{\Gamma(n)}=90\) then n is 

(a)

10

(b)

5

(c)

8

(d)

9

The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

(a)

2

(b)

3

(c)

4

(d)

1

The solution of the differential equation \(\frac{d y}{d x}=\frac{y}{x}+\frac{\phi\left(\frac{y}{x}\right)}{\phi^{\prime}\left(\frac{y}{x}\right)}\) is

(a)

\(x\phi \left( \frac { y }{ x } \right) =k\)

(b)

\(\phi \left( \frac { y }{ x } \right) =kx\)

(c)

\(y\phi \left( \frac { y }{ x } \right) =k\)

(d)

\(\phi \left( \frac { y }{ x } \right) =ky\)

A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

(a)

1

(b)

2

(c)

3

(d)

4

Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day
II. The number of customers in a queue to buy train tickets at a moment.
III. The time taken to complete a telephone call.

(a)

I and II

(b)

II only

(c)

III only

(d)

II and III

The operation * defined by \(a * b =\frac{ab}{7}\) is not a binary operation on

(a)

Q⁺

(b)

Z

(c)

R

(d)

C

Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11

(a)

(a)	(b)	(c)	(d)
F	T	F	T

(b)

(a)	(b)	(c)	(d)
T	F	T	F

(c)

(a)	(b)	(c)	(d)
T	T	F	F

(d)

(a)	(b)	(c)	(d)
F	F	T	T