The maximum value of \((1/x)^x\) is

\((1/e)^e\)

\(e^{1/e}\)

\(e^e\)

\(e\)

The contrapositive of the converse of the statement “If x is a prime number then x is odd” is

If x is not a prime number then x is not an odd

If x is a prime number then it is not odd.

If x is not an odd number then x is not a prime number.

If x is not a prime number then x is odd

The simplified form of \(\large i^n+i^{n+1}+i^{n+2}+i^{n+3}\)  is

i

-1

1

0

The coefficient of variation of two distributions are 60 and 70. the standard deviation are 21 and 16 respectively, then their mean is

22.85

28.25

23

34

The slope of the tangent to the curve \(x =t^2+3t-8 ,y=2t^2-2t-5\) at the point (2, -1) is

\(-{6/7}\)

7/6

6/7

22/7

Suppose \(\vec{a}+\vec{b}+\vec{c}=0 ,|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7\)  then  the angle between    \(\vec{a}\) & \(\vec{b}\)   is

π/4

π/3

π/2

π

Let * be a binary operation defined on R by a * b = \(\frac{a+b}4\forall a,b\) \(\in R\) then the operation * is

 Neither Associative nor commutative

Associative but not commutative

 Commutative but not Associative

 Commutative and Associative

if \(X^mY^n=(X+Y)^{m+n}\) then \(\frac{dY}{dX}\) is equal to

\(\frac YX\)

0

XY

\(\frac{X+Y}{XY}\)

If \(\Large Y=e^{sin^{-1}(t^2-1)}\) & \(\Large X=e^{sec^{-1}(\frac 1{t^2-1})}\) then \(\large \frac{dY}{dX}\) is equal to

\(\frac{-X}Y\)

\(\frac YX\)

\(\frac {-Y}X\)

\(\frac XY\)

If \(1+sin\theta+sin^2\theta+....upto \, \infty\) \(=2\sqrt3 +4 \) then \(\theta\) =____

3π/4

π/3

π/4

π/6

The order and degree of the differential equation \([1+(\frac{dY}{dX})^2+sin(\frac{dY}{dX})]^{3/4} = \frac {d^2Y}{dX^2}\)

order=2

degree= not defined

order=2

degree=\(\frac 34\)

order=2

degree=4

order=2

degree=3

The value of \(sin^{-1}(cos\frac{53\pi}5)\) is

\(\large \frac{-\pi}{10}\)

\(\large \frac \pi{10}\)

\(\large \frac{-3\pi}5\)

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

If a=3,b=4,c=5 each one of \(\vec a,\vec b \,and \, \vec c\) is perpendicular to   the sum of the remaining then \(|\vec a +\vec b+\vec c|\) is equal to

\(\sqrt5\)

\(5\sqrt2\)

\(\frac2{\sqrt5}\)

\(\frac5{\sqrt2}\)

The real part of \((1-cos\theta+i\,sin\theta)^{-1}\) is

\(\large cot\frac\theta2\)

\(\large tan\frac\theta2\)

\(\large \frac 1{1+cos\theta}\)

\(\large \frac12\)

Area lying between the curves  \(y^2=\) 2x  and y = x is

\(\large \frac34\) sq.units

\(\large \frac14\) sq.units

\(\large \frac13\) sq.units

\(\large \frac23\) sq.units

If the straight lines 2x+ 3y- 3=0  and x+ky+7= 0 are perpendicular, then the value of k is

 -3/2

 -2/3

3/2

2/3

If A=\(\frac{1}{\pi}\begin{bmatrix}sin^{-1}(\pi x)&tan^{-1}(\frac{x}{\pi})\\sin^{-1}(\frac{x}{\pi})& cot^{-1}(\pi x)\end{bmatrix}\),B=\(\frac{1}{\pi}\begin{bmatrix}-cos^{-1}(\pi x)&tan^{-1}(\frac{x}{\pi})\\sin^{-1}(\frac{x}{\pi})& -tan^{-1}(\pi x)\end{bmatrix}\) then A-B is equal to

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

2I

0

I

The set A has 4 elements and the set B has 5 elements then the number of injective mappings that can be defined from A to B is

120

60

72

144

Integrating factor of \(X\frac{dY}{dX}-Y=X^4-3X\) is

-X

\(\frac1X\)

logX

X

If A=\(\begin{bmatrix}3&1\\-1&2\end{bmatrix}\)then \(A^{2}-5A\) is equal to

-7I

7I

-I

I

Two cards are drawn at random from a pack of 52 cards. The probability of these two being “Aces” is

\(\large \frac{1}{13}\)

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

\(\large \frac{1}{221}\)

\(\large \frac{1}{26}\)

The value of \(\large \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}sin^{103}x. cos^{101}x dx\) is

0

2

\((\large \frac{\pi}{4})^{101}\)

\((\large \frac{\pi}{4})^{103}\)

\(\large \lim_{x\to 0} \frac{xe^{x}-sin \,x}{x}\) is equal to

2

0

1

3

If x = 2 + 3 \(cos\,\theta\) and y = 1 - 3 \(sin \,\theta\) represent a  circle then the centre and radius is

(-2,-1),3

\((1,2),\frac13\)

(2,1),3

(2,1),9

If \(\large sin^{-1}X + sin^{-1}Y=\frac{\pi}{2}\) then \(X^{2}\) is equal to

\(\sqrt{1-Y}\)

0

\(Y^2\)

\(1-Y^2\)

The value of the \(Sin1^{\circ}+sin2^{\circ}+....sin359^{\circ}\) is  equal to

180

-1

1

0

The 11th term in the  expansion of \((X+\frac1{\sqrt X})^{14}\) is

\(\frac X{1001}\)

i

\(\frac{1001}X\)

\(\frac{999}X\)

If A is a matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, the order of the matrix B is

m × n

n×m

n×n

m×m

The differential coefficient of \(log_{10}X\) with respect  to \(log_X10\)  is

\(\frac {X^2}{100}\)

\((log_X10)^2\)

\(-(log_{10}X)^2\)

1

The two curves \(X^3-3XY^2+2=0 \) and \(3X^2Y-Y^3=2\)

Cut at an angle of π/4

Cut at an angle of π/3

 Cut each other at right angle

Touch each other

If \(tan^{-1}(X^2+Y^2)=\alpha\) then \(\frac{dY}{dX}\)is equal to

 -XY

\(\frac XY\)

XY

\(\frac {-X}Y\)

The rate of change of area of a circle with respect to its radius at r = 2 cms is

4π

2

2π

4

\(\large\int_{0}^{\pi/2} \frac{sin^{1000}Xdx}{sin^{1000}X+cos^{1000}X}\)is equal to

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

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

1

1000

The value of \(tan\frac{\pi}{8}\) is equal to

\(1-\sqrt2\)

\(\frac1{\sqrt2+1}\)

\(\sqrt2+1\)

\(\frac12\)

The solution for the differential equation \(\frac{dy}y+\frac{dx}x=0\) is

 x + y =c

x y = c

log x. log y = c

\(\frac1x+\frac1y=c\)

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 5y + 8 = 0

\((0,\frac{-8}5,0)\)

\((\frac8{25},0,0)\)

\((0,\frac85,0)\)

\((0,-\frac{18}5,2)\)

The simplified from of \(tan^{-1}(\frac XY)-tan^{-1}(\frac{X-Y}{X+Y})\) is equal to

\(\pi\)

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

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

0

If \(A=\begin{bmatrix} Cos2\theta& -sin2\theta \\ sin2\theta&cos2\theta\end{bmatrix}\)and A+\(A^T\)=I Where I is the unit matrix of 2 ×2  & \(A^T\) is the transpose of A, then the value of \(\theta\) is equal to

3π/2

π

\({\pi}/3\)

π/6

The value of \(\Large \int\frac{e^{6logX}-e^{5logX}}{e^{4logX}-e^{3logX}}\) dx is equal to

\(\frac1X\)

\(\frac3{X^3}\)

\(\frac{ X^3}3\)

0

If \(3tan^{-1}X+cot^{-1}X=\pi\) then X equal to

1/2

-1

1

0

The value of \(\int\frac{e^X(X^2 tan^{-1}X+tan^{-1}X+1)}{X^2+1}dX\) is equal to

\(e^{tan^{-1}X}+C\)

\(tan^{-1}(X^C)+C\)

\(tan^{-1}(e^X)+C\)

\(e^Xtan^{-1}X+C\)

The value of x if x \((\hat{I}+\hat J+\hat K)\) is a unit vector is

\(\large\pm\frac13\)

\(\pm -3\)

\(\large\pm\sqrt3\)

\(\large\pm\frac1{\sqrt3}\)

If \(cos\alpha,cos\beta ,cos\gamma\) are the direction cosines of a vector \(\vec a\) , then \(cos2\alpha+cos2\beta+cos2\gamma\) is equal to

0

-1

3

2

If A is any square matrix of order 3×3  then |3A| is equal to

9|A|

27|A|

\(\frac13|A|\)

3|A|

 If x y z are not equal and ≠0≠1 the value of \(\left|\begin{array}{cc} logx & logy& logz \\log2x &log 2y &log2z\\log3x &log3y&log3z\end {array}\right|\) is equal to

log (x+y+z)

0

log(6xyz)

log(xyz)

The function f ( x )=[x] where [x] the greatest integer function is continuous at

-2

1

4

1.5

If \(2\vec a.\vec b=|\vec a|.|\vec b|\) then the angle between \({\vec a } \)&\(\vec b\) is

60°

90°

45°

30°

The length of latus rectum of the parabola 4\(y^2\) +3x +3y +1 =0 is

3/4

12

7

4/3

If \(P(A\cap B)=7/10 ,P(B)=17/20,\) , where P stands for probability then P(A|B)  is equal to

1/8

14/17

17/20

7/8

If x y z are all different and not equal to zero and \(\left| \begin{array}{cc} {1+X} &1&1\\1&1+Y& 1 \\1&1&1+Z\end {array}\right|=0\) then the value of \(X^{-1}+Y^{-1}+Z^{-1}\) is equal to

-1

-X-Y-Z

\(X^{-1}Y^{-1}Z^{-1}\)

XYZ

The value of \(\large\int\frac{e^X(1+X)dx}{cos^2(e^X.X)}\) is equal to

\(cot (e^X)+c\)

\(tan(e^X)+c\)

\(tan(e^X.X)+c\)

\(-cot(e.X^X)+c\)

Two dice are thrown simultaneously, the probability of obtaining a total score of 5 is

\(\large\frac16\)

\(\large\frac19\)

\(\large\frac1{12}\)

\(\large\frac1{18}\)

If \(\vec a\)  and \(\vec b\)  are unit vectors then what is the angle between \(\vec a \)  and \(\vec b\) for \(\sqrt3\vec a-\vec b\)  to be unit vector?

90°

60°

45°

30°

The general solution of \(cot\theta+tan\theta=2\) is

\(\large\theta=n\pi+(-1)^n\pi/8\)

\(\large\theta=\frac {n\pi}2+(-1)^n\pi/6\)

\(\large\frac{n\pi}2+(-1)^n\pi/4\)

\(\large\theta=\frac{n\pi}2+(-1)^n\pi/8\)

The vector equation of the plane which is at a distance of \(3/\sqrt{14}\) from the origin and the normal from the origin is \(2\hat I-3\hat J+\hat K\) is

\(\vec r.(2\hat I+\hat K)=3\)

\(\vec r.(\hat I+2\hat J)=3\)

\(\vec r.(\hat I+\hat J+\hat K)=9\)

\(\vec r.(2\hat I-3\hat J+\hat K)=3\)

The value of \(\int_2^8\frac{\sqrt{10-X}}{\sqrt X+\sqrt{10-X}}dX\) is

3

0

8

10

The sum of 1st n terms of the series \(\frac{1^2}1+\frac{1^2+2^2}{1+2}+\frac{1^2+2^2+3^2}{1+2+3}+...\)

\(\frac{n(n-2)}6\)

\(\large\frac{n(n-2)}3\)

\(\large\frac{n(n+2)}3\)

\(\large\frac{(n+2)}3\)

If \(X^Y=e^{X-Y}\) then \(\frac{dY}{dX}\) is equal to

\(\frac1Y-\frac1{X-Y}\)

\(\frac {logX}{(1+logX)^2}\)

\(\frac{e^X}{X^{X-Y}}\)

\(\frac{logX}{log(X-Y)}\)

Let f : R → R be defined by f (x)=2x+6 which is a bijective mapping then \(f^{-1}(X)\)  is given by

6x + 2

x - 3

2x + 6

\(\frac X2-3\)

The equation of the normal to the curve \((1+X^2)=2-X\) where the tangent crosses x - axis is

 x +5y+ 10 =0

5x+y+10=0

x -5y -10 =0

 5x-y-10=0