Explore topic-wise InterviewSolutions in Current Affairs.

A line parallel to the straight line $2x-y=0$ is tangent to the hyperbola

$\frac{x^2}{4}-\frac{y^2}{2}=1$ at the point $(x_1,y_1)$. Then $x_1^2+5y_1^2$ is equal to :

Consider the matrix $A=\left[\begin{array}{ccc}1& 4& 3\\ 7& 6& 9\\ 2& 5& 8\end{array}\right].$ Then cofactor of element $9$ in matrix $A$ is



[2 marks]

A class has $15$ students whose ages are $14,17,15,14,21,17,19,20,16,18,20,17,16,19$ and $20$ years. One student is selected in such a manner that each has the same chance of being chosen and the age $X$ of the selected student is recorded. Then standard deviation is:

A possible value of $\tan \left(\frac{1}{4}{\sin }^{-1}\frac{\sqrt{63}}{8}\right)$ is

If $y=(1+x)(1+2x)(1+3x),$ then the value of $\frac{dy}{dx}$ at $x=0$ is



[1 mark]

The range of values of 'a' such that the angle $\theta$ between the pair of tangents drawn from (a, 0) to the circle $x^2+y^2=1$ satisfies $\frac{\pi }{2}<\theta <\pi$, is

If
are
mutually perpendicular vectors of equal magnitudes, show that the
vector
is
equally inclined to
and.

If possible, find the sum of the matrices A and B, where:

A = $\left[\begin{array}{c}\sqrt{3}1\\ 23\end{array}\right]$ and B = $\left[\begin{array}{c}xyz\\ abc\end{array}\right]$

If $b$ is any positive integer and $a=7$, applying Euclid’s division lemma $(b=aq+r)$, the value of $r$ can be:​

Let a matrix $A=\left[\begin{array}{cc}2{\sin }^{2}x& {\cos }^{2}x\\ -2& 1\end{array}\right]$ is such that sum of elements in $\text{Adj}\left(A\right)$ is equal to $\frac{11}{4}.$ Then the value of $x$ can be

A real valued function $f\left(x\right)$ satisfies the function equation $f(x-y)=f\left(x\right)f\left(y\right)-f(a-x)f(a+y)$ where a is a given constant $f\left(0\right)=1,f(2a-x)$ is equal to

For any quadratic expression $f\left(x\right)=a{x}^2+bx+c;a<0$, having zeros as $\alpha ,\beta$ and if $k$ is any real number such that $k<\beta <\alpha ,$ then select the correct statement(s).

If a line along a chord of the circle $4x^2+4y^2+120x+675=0,$ passes through the point $(-30,0)$ and is tangent to the parabola $y^2=30x,$ then the length of this chord is

The differential equation of all straight lines passing through the point (1,-1)is

[MP PET 1994]

If $\left|{\cos }^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right|<\frac{\pi }{3}$, then

A company manufactures two types of sweaters type A and type B. It costs Rs 360 to make a type A sweater and Rs 120 to make a type B seater. The company can make atmost 300 sweaters and spend atmost Rs 72000 a day. The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100. The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.

Formulate this problem as a LPP to maximise the profit to the company.

If $A=[a_{ij}{]}_{3\times 3}$ such that
$a_{ij}=\{\begin{array}{cc}3& \text{when}i=j\\ \left[\frac{i}{j}\right]& \text{when}j>i\\ \left[\frac{j}{i}\right]& \text{when}i>j\end{array}$
then $\left\{\frac{det\left(adj\right(adjA)}{8}\right\}$ is
(where $\{.\}$ represents fractional part function and [.] represents greatest integer function)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

If $a,b>0$ and $\underset{0}{\overset{\infty }{\int }}\frac{\ln \left(bx\right)}{x^2+a^2}dx=\frac{\pi }{2a},$ then the value of $ab$ is

Classify the following as scalar and vector quantities:
(i) Velocity

If $3\text{and}4$ lies between the roots of the equation $x^2+2kx+9=0$ then $k$ lies in the interval

Let the mean and variance of the frequency distribution

$\begin{array}{ccccc}x:& x_1=2& x_2=6& x_3=8& x_4=9\\ f:& 4& 4& \alpha & \beta \end{array}$

be $6$ and $6.8$ respectively. If $x_3$ is changed from $8$ to $7$, then the mean for the new data will be

Solve the inequality 6 ≤ –3(2x – 4) < 12

In a $\Delta ABC$ which of the following is true:

Integrate the rational functions.
$\int \frac{1}{x^4-1}dx$

Using method of integration find the area bounded by the curve |x| + |y| = 1.

Choose the quadratic equation(s) whose difference and product of roots are given as $3$ and $28,$ respectively.

If the distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is

The relation "less than” in the set of natural numbers is

The value of $\underset{0}{\overset{3}{\int }}\mathrm{sgn}({\tan }^{-1}x+e^x)dx$ is

If a, 4, b are in A.P., and a, 2, b are in G.P., then a,1, b are in: