Explore topic-wise InterviewSolutions in Current Affairs.

The expansion of $\frac{1}{(4-3x{)}^{\frac{1}{2}}}$ binomial theorem will

be valid, if

If $A=\left[\begin{array}{cc}2& -3\\ -4& 1\end{array}\right],\text{then}adj(3A^2+12A)$ is equal to

Find the probability that a leap year will have 53 Fridays or 53 Saturdays.

If the vectors $\overrightarrow{a}=\left(clo{g}_{2}x\right)\hat{i}-6\hat{j}+2\hat{k}$ and $\overrightarrow{b}=\left(lo{g}_{2}x\right)\hat{i}+2\hat{j}+3\left(clo{g}_{2}x\right)\hat{k}$ make an obtuse angle for any $x\in (0,\infty )$ then c belongs to

${lim}_{x\to 2}\frac{x^2-x-2}{x^2-2x+sin(x-2)}$

In a horse race the odds in favour of three horses are , .The probability that one of the horse will win the race is

Q54. In how many ways can 10 identical red balls and one white ball be symmetrically arranged on a circular table?

कितने तरीकों से एक सामान 10 लाल गेंदों और एक सफे़द गेंद को एक वृत्ताकार मेज़ पर क्रमानुसार व्यवस्थित किया जा सकता है?

Tangents are drawn from the point $(-8,0)$ to the parabola $y^2=8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola, then the area of the triangle $PFQ$ (in sq. units) is equal to

If the circles $x^2+y^2=9$ and $x^2+y^2++8y+c=0$
touch each other, then c is equal to

How many different words can be formed with the letters of the word $ORDINARY$ such that the vowels occupy odd places?

Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle $\alpha$ with x-axis such that $sin\alpha =\frac{1}{3}.$

The point(s) which lies inside the region bounded by the curves $y^2=3x$ and $(x-2{)}^2=-4(y-4)$ is/are

A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to :

The differential equation of family of parobalas with foci at the origin and axis along the X- axis, is

One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

I want to take pie at right side. How should the equation look

π×1=180

Thanks

Sir in multiplication therom probability for more than two events is= P(E)P(F/E)P(G/EF)...let us asume G is differnt event ....(like both E and F are 2 king cards drawn and G is an ACE)...so G is not present in E and F..i,e P(G/EF) probability must be 0 right???

Two lines are parallel and inclined at an angle less than ${90}^{\circ }$ with the x-axis, then

If the equation of the tangent to the circle x=3+5$cos\theta$, $y$=$-1+5\sin \theta$ at the point (0,3) is $px+qy+r$ =0 and $p>0$ then p + q =

If $A$ is the area and $2s$ the sum of 3 sides of triangle then

The sides $a,b,c$ of a triangle satisfy the relations $c^2=2ab$ and $a^2+c^2=3b^2.$ Then the measure of $\angle BAC,$ in degrees, is

Let $E^c$ denotes the complement of an event E. If E, F, G are pairwise independent evens with P(G) > 0 and $P(E\cap F\cap G)=0.$ Then, $P(E^c\cap F^c|G)$ equals

If A, B and C are three sets such that $A\cap B=A\cap CandA\cup B=A\cup C$, then

If $a,b,c$ are three complex numbers such that $a^2+b^2+c^2=0$ and $\left|\begin{array}{ccc}{b}^2+c^2& ab& ac\\ ab& c^2+a^2& bc\\ ac& bc& a^2+b^2\end{array}\right|=k{a}^2{b}^2{c}^2$ then value of $k$ is -

The value of $sin\left(co{t}^{-1}\right(cos\left(ta{n}^{-1}x\right)\left)\right)$ is equal to

The solution of the equation
$\frac{dy}{dx}=\frac{3x-4y-2}{3x-4y-3}$ is

The solution of $(x+2y^3)\left(\frac{dy}{dx}\right)=y$ is (where c is arbitrary constant)

The order of the differential equation whose general solution is given by $y=c_{1}cos(2x+c_2)-(c_3+c_4)a^{x+c_5}+c_{6}sin(x-c_7)$, is

If sin $\alpha$, cos $\alpha$ are the roots of the equation a$x^2$ + bx + c = 0, then

The value of the limit $\underset{x\to 0}{lim}\{1^{1/si{n}^{2}x}+2^{1/si{n}^{2}x}+\dots \dots +n^{1/si{n}^{2}x}{\}}^{si{n}^{2}x}$ is

$\text{Given that y = a}sin\omega t+bt+c{t}^{2}cost\omega t.$

$\text{The unit of abc is same as that of}$

Let $p,q,r$ denote the arbitary statements then the logical equivalance of the statement $p\Rightarrow (q\vee r)$ is

The circle passing through the point $(-1,0)$ and touching the $y$-axis at $(0,2)$ also passes through the point:

The locus of the point of intersection of two tangents to the parabola $y^2=4ax$ which make an angle $\alpha$ with one another is

The ellipse $x^2+4y^2=4$ is inscribed in a rectangle touches its side and aligned with the coordinates axes, which is turn in inscribed in another ellipse which passes through that passes through the point $(4,0).$ Then , the equation of ellipse is

Let $A_n=\left(\frac{3}{4}\right)-{\left(\frac{3}{4}\right)}^2+{\left(\frac{3}{4}\right)}^3-...+(-1{)}^n{\left(\frac{3}{4}\right)}^n$ and $B_n=1-A_n$. Then, the least odd natural number $p$, so that $B_n>A_n$, for all $n\ge p$, is :

Prove that:
(i) $cos{55}^{\circ }+cos{65}^{\circ }+cos{175}^{\circ }=0$
(ii) $sin{50}^{\circ }-sin{70}^{\circ }+sin{10}^{\circ }=0$
(iii) $cos{80}^{\circ }+cos{40}^{\circ }-cos{20}^{\circ }=0$
(iv) $cos{20}^{\circ }+cos{100}^{\circ }+cos{140}^{\circ }=0$
(v) $sin\frac{5\pi }{18}-cos\frac{4\pi }{9}=\sqrt{3}sin\frac{\pi }{9}$
(vi) $cos\frac{\pi }{12}-sin\frac{\pi }{12}=\frac{1}{\sqrt{2}}$
(vii) $sin{80}^{\circ }-cos{70}^{\circ }=cos{50}^{\circ }$
(viii) $sin{51}^{\circ }-cos{81}^{\circ }=cos{21}^{\circ }$

${lim}_{x\to 0}\frac{e^{sinx}-1}{x}$

In a survey i was found that 21 persons liked product $P_1$, 26 liked product $P_2$ and 29 liked product $P_3$. If 14 persons liked products $P_{1}and{P}_2$ ; 12, persons liked prooduct $P_3$ and $P_1$; 14 persons liked products $P_2$ and $P_3$ and 8 liked all the three products. Find how many liked product $P_3$ only.