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

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

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

(a)

1

(b)

3

(c)

4

(d)

2

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

(a)

4

(b)

5

(c)

6

(d)

7

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 total number of 9 digit number which have all different digit is ________.

(a)

10!

(b)

9!

(c)

9\(\times\)9!

(d)

10\(\times\)10!

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

(a)

7!

(b)

3!

(c)

8!

(d)

5!

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 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

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

(a)

2

(b)

-2

(c)

4

(d)

-4

The double ordinate passing through the focus is _______.

(a)

focal chord

(b)

latus rectum

(c)

directrix

(d)

axis

The value of \(\sin15^o\) is ______.

(a)

\(\frac{\sqrt{3}+1}{2\sqrt{2}}\)

(b)

\(\frac{\sqrt{3}-1}{2\sqrt{2}}\)

(c)

\(\frac{\sqrt3}{\sqrt2}\)

(d)

\(\frac{\sqrt3}{2\sqrt2}\)

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

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

(a)

x²

(b)

x

(c)

1

(d)

x² + x + 1

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 = e^x intersect the y-axis at _______.

(a)

(0,0)

(b)

(1,0)

(c)

(0,1)

(d)

(1,1)

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

(a)

1

(b)

\(\infty\)

(c)

\(-\infty\)

(d)

\(\theta\)

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

(a)

x²

(b)

1

(c)

-x²

(d)

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

The technology matrix of an economic system of two industries is \(\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}\). Test whether the system is viable as per Hawkins-Simon conditions.

Using the property of determinant, evaluate \(\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.\)

Expand the following by using binomial theorem.\(\left( x+\frac { 1 }{ y } \right) ^{ 7 }\)

Find the angle between the pair of lines represented by the equation 3x²+10xy+8y²+14x+22y+15=0.

Find the value of \(\cos\left(\frac{5\pi}{12}\right)\)

Show that the functions f(x) = 5x - \(\left| x \right| \) is continuous at x = 0

Differentiate \({ x }^{ \frac { 2 }{ 3 } }\) from first principles

Solve: 2x + 5y = 1 and 3x + 2y = 7 using matrix method.

Find the equation of the circle which touches the line x = 0, y = 0 and x = a.

Differentiate the following with respect to x (ax² + bx + c)ⁿ

Differentiate the following with respect to x.  \(\frac { { e }^{ x } }{ 1+x } \)

Differentiate the following with respect to x. cos³x

If e^y (x + 1) = 1, show that \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }\)

Differentiate: \(\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\)

Evaluate:\(\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}\)

If \(A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right] \), then show that A^TA^-1 = \(\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .\)

By the principle of mathematical induction, prove the following.
aⁿ - bⁿ is divisible by a - b, for all \(n\in N\) .

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Show that the given lines 3x - 4y - 13 = 0, 8x - 11y = 33 and 2x - 3y - 7 = 0 are concurrent and find the concurrent point.

If cosec A + sec A = cosec B + sec B, prove that cot\(\left( \frac { A+B }{ 2 } \right) \) = tanA tanB

Differentiate: \(\frac { sinx+cosx }{ sinx-cosx } \)with respect to 'x'