The proposition p ∧ (¬p ∨ q) is

Which one is the inverse of the statement (pVq)➝(pΛq)?

Which one of the following statements has truth value F?

If a * b=\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \) on the real numbers then * is

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

Which one of the following is a binary operation on N?

A binary operation on a set S is a function from

The value of \(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }x\ cos \ x \ dx } \) is

For any value of \(n \in \mathbb{Z}, \int_{0}^{\pi} e^{\cos ^{2} x} \cos ^{3}[(2 n+1) x] d x\) is

\(\text { The value of } \int_{0}^{\frac{2}{3}} \frac{d x}{\sqrt{4-9 x^{2}}} \text { is }\)

The value of \(\int _{ 0 }^{ 1 }{ { ({ sin }^{ -1 }x) }^{ 2 } } dx\) is

The volume of solid of revolution of the region bounded by y² = x(a − x) about x-axis is

The value of \(\int _{ 0 }^{ \infty }{ { e }^{ -3x }{ x }^{ 2 }dx } \) is

The value of  \(\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx } \) is

If f(x,y, z) = xy +yz +zx, then f_x - f_z is equal to

If w (x, y, z) = x² (y - z) + y² (z - x) + z²(x - y), then \(\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z } \) is

The value of \(\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3x\ dx }\ is\)

The area between y² = 4x and its latus rectum is

If \(f(x)=\int_{0}^{x} t \cos t d t, \text { then } \frac{d f}{d x}=\)

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

The approximate change in the volume V of a cube of side x metres caused by increasing the side by 1% is

If w (x, y) = x^y, x > 0, then \(\frac { \partial w }{ \partial x } \) is equal to

If \(u(x, y)=e^{x^{2}+y^{2}}\),then \(\frac { \partial u }{ \partial x } \) is equal to

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

If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is

The probability mass function of a random variable is defined as:

x	-2	-1	0	1	2
f(x)	k	2k	3k	4k	5k

Then E(X ) is equal to: 

Suppose that X takes on one of the values 0, 1, and 2. If for some constant k, \(P(X=i)=k P(X=i-1) \text { for } i=1,2 \text { and } P(X=0)=\frac{1}{7}\) , then the value of k is

The random variable X has the probability density function 
\(f(x)=\left\{\begin{array}{lr} a x+b & 0<x<1 \\ 0 & \text { otherwise } \end{array}\right.\) and \(E(X)=\frac { 7 }{ 12 } \), then a and b are respectively

If P(X = 0) = 1 − P(X = 1). If E(X) = 3Var(X), then P(X = 0).

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k², where k is the face that comes up k = {1, 2, 3, 4, 5}.
The expected amount to win at this game in Rs. is

Let X be random variable with probability density function
\(f(x)=\left\{\begin{array}{ll} \frac{2}{x^{3}} & x \geq 1 \\ 0 & x<1 \end{array}\right.\)
Which of the following statement is correct 

If the solution of the differential equation \(\frac{d y}{d x}=\frac{a x+3}{2 y+f}\)represents a circle, then the value of a is

The population P in any year t is such that the rate of increase in the population is proportional to the population. Then

The number of arbitrary constants in the particular solution of a differential equation of third order is

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

The solution of the differential equation \(\frac { dy }{ dx } =2xy\) is

If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\) When

The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

The solution of the differential equation \(2x\frac{dy}{dx}-y=3\) represents

The general solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } \) is

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

The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters,is

The point of inflection of the curve y = (x - 1)³ is

The maximum product of two positive numbers, when their sum of the squares is 200, is

The maximum slope of the tangent to the curve y = e^x sin x, x ∈ [0, 2π] is at

The number given by the Rolle's theorem for the functlon x³ - 3x², x ∈ [0, 3] is

What is the value of the limit \(\lim _{x \rightarrow 0}\left(\cot x-\frac{1}{x}\right) \text { is }\) 

The abscissa of the point on the curve \(f\left( x \right) =\sqrt { 8-2x } \) at which the slope of the tangent is -0.25 ?

The position of a particle moving along a horizontal line of any time t is given by s(t) = 3t² -2t- 8. The time at which the particle is at rest is