List of practice Questions

The area of the shaded portion

is:

Area of the region bounded by \(y=-1, y=2, x=y^3 \space and \space x=0\) is:

The differential equation whose solution is Ax²+By²=1 where A and B are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below:

Integrating factor of the differential equation \((1-y²) \frac{dx}{dy} + xy = ay\) is:

Let \(\overrightarrow a = 4\hat i -\hat j + 3\hat k\) and \(\overrightarrow b = -2\hat i + \hat j-2\hat k\). Then
(A) \(\overrightarrow a\) is a unit vector
(B) \(\overrightarrow a\times \overrightarrow b=-\hat i + 2\hat j + 2\hat k\)
(C) \(\overrightarrow a\) and \(\overrightarrow b\) are parallel vectors
(D) \(\overrightarrow a\) and \(\overrightarrow b\)are neither parallel nor perpendicular vectors
Choose the correct answer from the options given below :

Let \(\overrightarrow a\) and \(\overrightarrow b\) be two unit vectors. If the vectors \(\overrightarrow c=5\overrightarrow a-4\overrightarrow b\) and \(\overrightarrow d = \overrightarrow a+2\overrightarrow b\) perpendicular to each other, then the angle between \(\overrightarrow a\) and \(\overrightarrow b\) is:

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:

If the straight lines \(x=1+s, y = -3-s, z=1+λs\) and \(x = \frac{t}{2},y=1+t, z=2-t\) with parameters s and t respectively, are coplanar, then \(λ\) is equal to:

Match List I with List II

Choose the correct answer from the options given below:

If in a binomial distribution n=4, P(X=0)=\(\frac{16}{81}\), then P(X = 4) equals :

A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B, if A starts first:

The inverse of the function f: R→R given by f(x) = 2x +7 is:

If f(x) =\(\begin{cases}\frac{x^2-9}{x-3}, x≠3 \\ 5, x=3 \end {cases}\) then f(x):

The integral \(\int_0^1x(1-x)^n dx\) is equal to :

The set of value of \(x\) for which the angle between the \(\overrightarrow a = 2x²\hat i + 4x \hat j + \hat k\) and \(\overrightarrow b =7\hat i-2\hat j + x\hat k\) is obtuse is :

The shortest distance between the lines \(\frac{x + 3}{1} = \frac{y-2}{2} = \frac{z+4}{3} \space and \space  \frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-6}{4}\) is: =

If x is the least positive integer satisfying 100 ≡ x(mod 6), then (2x+1) is equal to :

The quantity of water that must be added to 36 litres of milk at 2 ½ litres for ₹120 so as to have mixture worth ₹36 for a litre is:

In a partnership, A invests one-fourth of the capital for one-third of the time, B invests one-third of the capital for one-fourth of the time and C invests the rest of the capital for the whole time. Out of a profit of ₹3,500, A's share is:

Match List I with List II

Choose the correct answer from the options given below:

If \(\begin{bmatrix}3& 2x + 5y &-2 \\x + 4y  &7 &-5\end{bmatrix}=\begin{bmatrix}3 &10&-2\\ 2&7&-5\end{bmatrix}\) Then the values of x and y are:

If A is a square matrix of order 3 and |A|=5, then |adj(adjA)| is:

If the matrix \(A =\begin{bmatrix}x&-2 &-5y\\ 2&0& -9 \\10& 3z &0\end{bmatrix}\)is skew-symmetric, then the value of \((2x-3y+4z)\) is:

If \(y = log(\frac{x^5}{e^5})\), then \(\frac{d^2y}{dx^2}\) is,

The point on the curve y²=16x for which the y-coordinate is changing 2 times as fast as the x-coordinate is: