If |adj(adj A)| = |A|⁹, then the order of the square matrix A is

(a)

3

(b)

4

(c)

2

(d)

5

The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is ____________

(a)

0

(b)

1

(c)

2

(d)

infinitely many

iⁿ+iⁿ⁺¹+iⁿ⁺²+iⁿ⁺³ is

(a)

0

(b)

1

(c)

-1

(d)

i

A zero of x³ + 64 is

(a)

0

(b)

4

(c)

4i

(d)

-4

For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has ________

(a)

one solution

(b)

two solution

(c)

at least two solution

(d)

no solution

The value of sin^-1 (cos x), \(0\le x\le\pi\) is

(a)

\(\pi-x\)

(b)

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

(c)

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

(d)

\(x-\pi\)

\(cot\left( \frac { \pi }{ 4 } -{ cot }^{ -1 }3 \right) \)

(a)

7

(b)

6

(c)

5

(d)

none

The equation of the circle passing through (1, 5) and (4, 1) and touching y-axis is x² + y² − 5x − 6y + 9 + \(\lambda\)(4x + 3y − 19) = 0 where λ is equal to

(a)

\(0,-\frac { 40 }{ 9 } \)

(b)

0

(c)

\(\frac { 40 }{ 9 } \)

(d)

\(\frac { -40 }{ 9 } \)

The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is ____________

(a)

x² + y² = 4

(b)

x² +y² = 9

(c)

x² +y² = 45

(d)

x² +y² = 14

If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

(a)

2

(b)

-1

(c)

1

(d)

0

The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +\overset { \wedge }{ 4k } \) is ____________

(a)

4

(b)

2\(\sqrt { 3 } \)

(c)

4\(\sqrt { 3 } \)

(d)

5\(\sqrt { 3 } \)

The angle between the planes 2x + y - z = 9 and x + 2y + z = 7 is_____________

(a)

cos^-1 (5/6)

(b)

cos^-1 (5/36)

(c)

cos^-1 (1/2)

(d)

cos^-1 (1/12)

The volume of a sphere is increasing in volume at the rate of 3 πcm³ / sec. The rate of change of its radius when radius is \(\frac { 1 }{ 2 } \) cm

(a)

3 cm/s

(b)

2 cm/s

(c)

1 cm/s

(d)

\(\cfrac { 1 }{ 2 } cm/s\)

The statement "If f has a local extremum at c and if f'(c) exists then f'(c) = 0" is ________

(a)

the extreme value theorem

(b)

Fermat's theorem

(c)

Law of mean

(d)

Rolle's theorem

A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is

(a)

0.2%

(b)

0.4%

(c)

0.04%

(d)

0.08%

If u = log (x³ + y³ + z³ - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) = _____________

(a)

\(\frac { 3 }{ x+y+z } \)

(b)

x+y+z

(c)

\(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

(d)

\(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

The value of \(\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx } \) is

(a)

\(\pi\)

(b)

\(2\pi\)

(c)

\(3\pi\)

(d)

\(4\pi\)

The solution of \(\frac{d y}{d x}+p(x) y=0\) is

(a)

\(y={ ce }^{ \int { pdx } }\)

(b)

\(y={ ce }^{ -\int { pdx } }\)

(c)

\(x={ ce }^{ -\int { pdy } }\)

(d)

\(x={ce }^{ \int { pdy } }\)

The solution of \(\frac{dy}{dx}+y\) cot x = sin 2x is ___________

(a)

y sin x = \(\frac{2}{3}\)sin³x+c

(b)

y sec x = \(\frac{x^2}{2}+c\)

(c)

y sin x = c+x

(d)

2y sin x = sin x - \(\frac{sin\ 3x}{3}+c\)

The population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

(a)

\(\frac{dp}{dt}=\frac{k}{p}\)

(b)

\(\frac{dp}{dt}=kt\)

(c)

\(\frac{dp}{dt}=kp\)

(d)

\(\frac{dp}{dt}=-kp\)

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
\(f(x)= \begin{cases}\frac{1}{l} & 0
The mean and variance of the shorter of the two pieces are respectively.

(a)

\(\frac { l }{ 2 } ,\frac { { l }^{ 2 } }{ 3 } \)

(b)

\( \frac { l }{ 2 } ,\frac { { l }^{ 2 } }{ 6 } \)

(c)

\(l,\frac { { l }^{ 2 } }{ 12 } \)

(d)

\(\frac { l }{ 2 } ,\frac { { l }^{ 2 } }{ 12 } \)

If \(f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0 is the p.d.f, of x then c is _____________

(a)

\(\frac { 1 }{ 3 } \)

(b)

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

(c)

\(\frac { 8 }{ 3 } \)

(d)

\(\frac { 3 }{ 8 } \)

A binary operation on a set S is a function from

(a)

S ⟶ S

(b)

(SxS) ⟶ S

(c)

S⟶ (SxS)

(d)

(SxS) ⟶ (SxS)

Which of the following is a contradiction?

(a)

p v q

(b)

p ∧ q

(c)

q v ~ q

(d)

q ∧ ~ q

Which of the following is a statement?

(a)

7+2<10

(b)

Wish you all success

(c)

All the best

(d)

How old are you?