Explore topic-wise InterviewSolutions in Current Affairs.

We are given y = ln(x+1). Find x in terms of y

The integral $\underset{\pi /6}{\overset{\pi /3}{\int }}{\sec }^{2/3}x{cosec}^{4/3}xdx$ is equal to :

$1.3+3.5+5.7+....+(2n-1)(2n+1)=\frac{n(4n^2+6n-1)}{6}$

Using mathematical induction, the numbers $a_n^{\prime }s$ are defined by, $a_0=1,a_{n+1}=3n^2+n+a_n(n\ge 0).$ Then $a_n=$

The slope of the line touching both the parabolas $y^2=4x$ and $x^2=-32y$ is

If $I_n=\int (lnx{)}^{n}dxthen{I}_n+n{I}_{n-1}$

The value of the integral, $\underset{1}{\overset{3}{\int }}[x^2-2x-2]dx,$ where $\left[x\right]$ denotes the greatest integer less than or equal to $x,$ is

If $tanx=\frac{2b}{a-c}(a\ne c),y=aco{s}^{2}x+2bsinxcosx+csi{n}^{2}xandz=asi{n}^{2}x-2bsinxcosx+co{s}^{2}x,$ then

If the focus of the parabola $(y-\beta {)}^2=4(x-\alpha )$ always lies between the lines $x+y=1$ and $x+y=3$ then

If a line makes angles ${90}^{\circ },$ ${60}^{\circ }$ and ${30}^{\circ }$ with positive direction of $x,y$ and $z-$axis respectively, then direction cosines of the line respectively, are



[2 marks]

The interval in which

is increasing is

(A) (B) (−2,
0) (C) (D) (0,
2)

Let $a,b(b>a)$ are the roots of the quadratic equation $(k+1)x^2-(20k+14)x+91k+40=0;$ where $k>0$, then which among the following option(s) is/are correct for the roots

The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.

The integer n for which $\underset{x\to 0}{\text{lim}}\frac{(\cos x-1)(\cos x-e^x)}{x^n}$ is a finite non-zero number is

The distance of origin from the plane passing through points $A(3,-2,-2),B(1,2,-3)$ and $C(2,1,-1),$ is $\frac{p}{\sqrt{62}},$ the value of $p$ is

The position vector of the point which divides the join of points given by position vectors $2\overrightarrow{a}-3\overrightarrow{b}$ and $3\overrightarrow{a}-2\overrightarrow{b}$ internally in the ratio 2:3 is

The values of a for which $2x^2$ - 2 (2a + 1)x + a (a + 1) = 0 may have one root less than a and other root greater than a are given by

A biased coin has a property that probability of occurence of head is twice that of tail. What is the probability that if the coin is tossed twice then the head occurs atleast once?

In triangle $ABC,AD$ is the altitude from $A.$ If $b>c,$ $\angle C={23}^{\circ },andAD=\frac{abc}{b^2-c^2},\text{then}\angle B=$

Match the following by appropriately matching the lists based on the information given in Column I and Column II​​​​​​

$\begin{array}{cccc}& ColumnI& & ColumnII\\ a.& \text{If}a,b,c\text{are in}G.P.,\text{then}& \text{p.}& A.P.\\ & {\log }_{a}10,{\log }_{b}10,{\log }_{c}10\text{are in}& & \\ b.& \text{If}\frac{a+b{e}^x}{a-b{e}^x}=\frac{b+c{e}^x}{b-c{e}^x}=\frac{c+d{e}^x}{c-d{e}^x},& \text{q.}& H.P.\\ & \text{then}a,b,c,d& & \\ c.& \text{If}a,b,c\text{are in}A.P.;& \text{r.}& G.P.\\ & a,x,b\text{are in}G.P.\text{and}& & \\ & b,y,c\text{are in}G.P.,& & \\ & \text{then}{x}^2,b^2,y^2\text{are in}& & \end{array}$

Which of the following relations is incorrect for solutions with respect to their colligative properties?

If the graph of y = f(x) is

Find the graph of $|y|=f\left(x\right)$?

A function f(x) defined on [a,b] will have a local minimum at x = b if -

Ifare
such thatis
perpendicular to,
then find the value of λ.