Explore topic-wise InterviewSolutions in .

Choose the correct answer in the following.

Area lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines x=0 and x=2

(a) $\pi$ (b) $\frac{\pi }{2}$

(c) $\frac{\pi }{3}$ (d) $\frac{\pi }{4}$

There are four parcels and five pos offices. In how many different ways can tl parcels be sent by registered post ?

1. 0.125

The direction ratios of two lines AB,AC are 1, -1, -1 and 2, -1,1. The direction ratios of the normal to the plane ABC are

The total number of divisors of the form $4n+2(n\ge 0)$ of integer $240$ is

The standard deviation and mean of a data set are $6.5$ and $12.5$ respectively. Then the coefficient of variation is

If (a+ib)(c +id)(e + if)(g + ih) = A + iB , then ( $a^2+b^2\left)\right(c^2+d^2\left)\right(e^2+f^2\left)\right(g^2+h^2)$ =

If $x\in [-5,3],$ then the correct option(s) is (are)

The approximate value of $(1.0002{)}^{3000}$ is equal to

Let $f\left(n\right)$ denotes the number of different ways in which the positive integer $n$ can be expressed as the sum of $1^{\prime }s$ and $2^{\prime }s$. For example $f\left(4\right)=5$, since

$4=2+2=2+1+1=1+2+1=1+1+2=1+1+1+1$.



Then which of the following(s) is (are) CORRECT ?

If $A=\text{diag}(13,26,39,52,65),$ then the trace of $A^2$ is equal to

Let $f,g$ and $h$ be three functions defined as

$f\left(x\right)=\{\begin{array}{cc}x& \text{for}\left|x\right|\le 1\\ 1& \text{for}\left|x\right|>1\end{array},$



$g\left(x\right)=\{\begin{array}{cc}\cos \left(\frac{\pi }{2}x\right)& \text{for}\left|x\right|\le 1\\ |x-1|& \text{for}\left|x\right|>1\end{array}$



and $h\left(x\right)=\{\begin{array}{cc}\frac{\left|x\right|-1}{{\log }_a\left|x\right|}& \text{for}\left|x\right|\ne 1\\ \ln a& \text{for}\left|x\right|=1\end{array}$ for $a>0$ and $a\ne 1$



If $l,m,n$ denote the number of points of discontinuity of the functions $f,g$ and $h$ in their domain respectively, over $R$, then $(l,m,n)$ is

An ellipse intersects the hyperbola $x^2-y^2=\frac{1}{2}$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. The axes of the ellipse are along the coordinate axes.

Match $\text{List I}$ with $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{The radius of the director circle of ellipse is equal to}& \text{(P)}& \sqrt{2}\\ \text{(B)}& \text{The length of latus rectum of ellipse is equal to}& \text{(Q)}& \sqrt{3}\\ \text{(C)}& \text{The distance between directrices of ellipse is equal to}& \text{(R)}& 2\\ \text{(D)}& \text{The square of radius of auxiliary circle of ellipse is equal to}& \text{(S)}& 4\\ & & \text{(T)}& 1\end{array}$



Which of the following is the only CORRECT combination?

The solution(s) of the equation $(3|x|-3{)}^2=|x|+7$ which belong to the domain of $\sqrt{x(x-3)}$ is/are

​​​​​​A circle $C_1$ with centre at the origin meets $x$-axis at $A$ and $B$ (where $A\&B$ lies on negative and positive $x-$axis respectively). Two points $P\left(a\right)$ and $Q\left(b\right)$ are on the circle such that $b-a$ is a constant, where $a$ and $b$ are the parametric angles of the points. $BP$ and $AQ$ meets at $R$. Locus of $R$ is a circle $C_2$.

Let $c$ be the radius of $C_1$ and $d$ be the radius of $C_2$.



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(1)}& \text{For}b-a=\frac{\pi }{2}\text{, the value of}\frac{d^2}{c^2}\text{is}& \text{(P)}& 0\\ \text{(2)}& \text{For}b-a=\frac{\pi }{2}\text{and}c=\sqrt{2}\text{, circle}{C}_2\text{intersects}& \text{(Q)}& 1\\ & \text{the coordinate axes at four points}L,M,N,O.& & \\ & \text{Let the area of the quadrilateral LMNO is}2\sqrt{2}p.& & \\ & \text{Then the value of}p\text{is}& & \\ \text{(3)}& \text{Let}{m}_1,m_2\text{be the slopes of the line BQ,AP}& \left(R\right)& 2\\ & \text{respectively.}\text{If}{m}_1{m}_2=-1\text{, then}\frac{a}{b}\text{is}& & \\ \text{(4)}& \text{Let}{m}_1,m_2\text{be the slopes of the line BQ,AP}& \left(S\right)& 3\\ & \text{respectively.}\text{If}{m}_1=m_2\text{, then}\frac{3|b-a|}{\pi }\text{is}& & \\ & & \left(T\right)& 4\end{array}$



Then the CORRECT option is :

The slope intercept form of the line $3x+7y+8=0$ is

रक्त
के
बहाव
को
रोकने
के
लिए
क्या
करना
चाहिए?

Question 6

The vertices of triangle ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that $\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}$. Calculate the area of triangle ADE and compare it with area of triangle ABC.

The range of $f\left(x\right)=\left|\begin{array}{ccc}-\sqrt{2}& \sin x& \cos x\\ 1& \cos x& \sin x\\ -1& \sin x& -\cos x\end{array}\right|,$ is

${\int }_0^{\frac{\pi }{2}}\frac{d\theta }{1+tan\theta }=$ [Roorkee 1980; MP PET 1996; DCE 1999]

If $y\left(\frac{\pi }{2}\right)=e,$ then the solution of $y^{\prime }\sin x=y\ln y$ is

Which of the follwing statements are correct ?

1. The coordinates of the point R which divides the line

segment joining two points $P(x_1,y_1,z_1)$ and $Q(x_2,y_2,z_2)$

externally in the ratio m:n are $(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n})$.

2. If R divides PQ internally in the ratio m:n, then its coordinates

are obtained by replacing n by -n in the statement 1.

In the grid given below, we wish to go from corner $A$ to corner $B$ moving up and right only one unit at a time. The number of paths that include an edge of the shaded square is


(correct answer + 2, wrong answer - 0.50)

न्यूटन
को
संस्कृत
मानव
कहने
के
पीछे
कौन
से
तर्क
दिए
गए
हैं?
न्यूटन
द्वारा
प्रतिपादित
सिद्धांतो
एवं
ज्ञान
की
कई
दूसरी
बारीकियों
को
जानने
वाले
लोग
भी
न्यूटन
की
तरह
संस्कृत
नहीं
कहला
सकते,
क्यों?

Let $f\left(x\right)=\{\begin{array}{cc}\frac{x^3-a{x}^2+2}{x^2-3x+2},& 0<x<1\\ b^2{x}^2+bx+1,& x=1\\ {(1+(\ln c)\cdot {\tan }^2(x-1\left)\right)}^{1/(\ln x{)}^2},& 1<x<2\end{array}$



be continuous at $x=1.$ Then which of the following relations can hold good?

How much time would it take to distribute one Avogadro number of wheat grains, if 10¹⁰ grains are distributed each second?