Explore topic-wise InterviewSolutions in Current Affairs.

The equation of curve passing through (1, 1) in which the sub-tangent is always bisected at the origin cannot be

If $\alpha ,\beta$ are the two roots of the quadratic equation $4x^2-26x+34=0$ such that $\alpha >\beta ,$ then $\alpha =$

If $f\left(x\right)=\frac{t+3x-x^2}{x-4},$ where $t$ is a parameter and $f\left(x\right)$ has exactly one minimum and one maximum, then the range of values of $t$ is

Patients are recruited onto the two arms $(0-\text{control,}1-\text{treatment})$ of a clinical trail. The probability that an adverse outcome occurs on the control arm is $p_0$ and is $p_1$ for treatment arm. Patients are allocated alternatively onto the two arms, and their outcomes are independent. The probability that the first adverse event occurs on the control arm, is

If $\tan A$ and $\tan B$ are the roots of the quadratic equation, $3x^2-10x-25=0,$ then the value of $3{\sin }^2(A+B)-10\sin (A+B)\cdot \cos (A+B)-25{\cos }^2(A+B)$ is :

If $A={\int }_1^{sin\theta }\frac{tdt}{1+t^2}dt,B={\int }_1^{cosec\theta }\frac{1}{t(1+t^2)}dt$ then

$\left|\begin{array}{ccc}A& A^2& B\\ e^{A+B}& B^2& -1\\ 1& A^2+B^2& -1\end{array}\right|=?$

A vetor $\overrightarrow{a}$ has components $3p$ and $1$ with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If with respect to new system, $\overrightarrow{a}$ has components $p+1$ and $\sqrt{10},$ then a value of $p$ is equal to:

The range of the function $f\left(x\right)=\ln \left({\sin }^{-1}\right(x^2+x\left)\right),$ is

If $\overrightarrow{a}{}^{\prime }=\hat{i}+\hat{j},\overrightarrow{b}{}^{\prime }=\hat{i}+\hat{j}+2\hat{k}$ and $\overrightarrow{c}{}^{\prime }=2\hat{i}+\hat{j}-\hat{k}$. Then altitude of the parallelopiped formed by the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ having base formed by $\overrightarrow{b}$ and $\overrightarrow{c}$ is $(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ and ${\overrightarrow{a}}^{\prime },{\overrightarrow{b}}^{\prime },{\overrightarrow{c}}^{\prime }$ are reciprocal system of vectors)

If ${}^n{C}_r={}^5{C}_5$, find the value of n.

Find the mean deviation about the mean for the data

The expression $\frac{{\int }_0^n\left[x\right]dx}{{\int }_0^n\left\{x\right\}dx}$ where [x] and {x} are integral and fractional part of x and $nϵN$ is equal to

If $f\left(x\right)=1+nx+\frac{n(n-1)}{2}{x}^2+\frac{n(n-1)(n-2)}{6}{x}^3+\cdots +x^n$, where $n\in N,$ then $f^{\prime \prime }\left(1\right)$ is equal to

Show that
the relation R in the set R of real numbers, defined as

R = {(a,
b): a ≤ b²}
is neither reflexive nor symmetric nor transitive.

The total number of ways in which a beggar can be given at least one rupee from two $1$ rupee coins, three $50$ paisa coins and four $25$ paisa coins is

Let $f\left(x\right)=(1-x{)}^2{\sin }^{2}x+x^2$ for all $x\in R,$ and let $g\left(x\right)=\underset{1}{\overset{x}{\int }}(\frac{2(t-1)}{t+1}-\ln t)f\left(t\right)dt$ for all $x\in (1,\infty )$

Consider the statements:

$P:\text{There exists some}x\in IR\text{such that}f\left(x\right)+2x=2(1+x^2)$

$Q:\text{There exists some}x\in IR\text{such that}2f\left(x\right)+1=2x(1+x)$

Then

Differentiate the following functions with respect to x :

$\frac{acosx+bsinx+c}{sinx}$

For some real number $c,$ the graphs of the equation $y=|x-20|+|x+18|$ and the line $y=x+c$ intersect at exactly one point. Then $c$ is

A sequence $b_0,b_1,b_2,\cdots$ is defined by letting $b_0=5$ and $b_k=4+b_{k-1}$ for all natural numbers $k.$ Then which of the following is/are correct?

(Solve using mathematical induction)

A company has two plants to manufacture television. Plant $1$ manufactures $70\%$ of televisions and plant $2$ manufactures $30\%$. At plant $1$, $80\%$ of the televisions are rated as of standard quality and at plant $2$, $90\%$ of the televisions are rated as of standard quality. A television is chosen at random and is found to be of standard quality. The probability that it has come from plant $2$ is:

The value of $\left|\begin{array}{ccc}1& bc& a(b+c)\\ 1& ac& b(a+c)\\ 1& ab& c(a+b)\end{array}\right|$ is, $($where $a\ne b\ne c)$

The value of integral $\int \frac{\tan \sqrt{x}{\sec }^2\sqrt{x}}{\sqrt{x}}dx$ is

(where $C$ is constant of integration)

The value of $2^{2010}\frac{\underset{0}{\overset{1}{\int }}{x}^{1004}{(1-x)}^{1004}dx}{\underset{0}{\overset{1}{\int }}{x}^{1004}{(1-x^{2010})}^{1004}dx}$ is equal to

The equation of reflection of $y^2=x$ about $y-$axis is

Let the observations $x_i(1\le i\le 10)$ satisfy the equations, $\sum _{i=1}^{10}(x_i-5)=10$ and $\sum _{i=1}^{10}(x_i-5{)}^2=40$. If $\mu$ and $\lambda$ are the mean and the variance of observations, $(x_1-3),(x_2-3),...,(x_{10}-3)$, then the correct option(s) is/are

Examine the consistency of the system of equations

$2x-y=5,x+y=4$

If the $2^{\text{nd}},3^{\text{rd}}$ and $4^{\text{th}}$ terms in the expansion of $(x+a{)}^n$ are $240,720$ and $1080$ respectively, then the value of least term in the expansion is

If
U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}.
Verify that

(i) (ii)

${lim}_{x\to \infty }\frac{\sqrt{x^2+a^2}-\sqrt{x^2+b^2}}{\sqrt{x^2+c^2}-\sqrt{x^2+d^2}}$

An equilateral triangle is inscribed in the parabola $y^2=4ax,$ such that one vertex of this triangle coincides with the vertex of the parabola. Side length of this triangle is

Given that $f\left(0\right)=0$ and $\underset{x\to 0}{lim}\frac{f\left(x\right)}{x}$ exists, say $L$. Here $f^{\prime }\left(0\right)$ denotes the derivative of $f$ w.r.t. $x$ at $x=0$. Then $L$ is :