Explore topic-wise InterviewSolutions in Current Affairs.

Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

Let U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4}, B = {2,4,6,8} and C = {3,4,5,6}. Find :

(i) $A^{\prime }$ (ii) $B^{\prime }$ (iii) $(A\cap C{)}^{\prime }$

(iv) $(A\cup B{)}^{\prime }$ (v) ${\left(A^{\prime }\right)}^{\prime }$ (vi) $(B-C{)}^{\prime }$

The point of concurrency of the altitudes drawn from the vertices $A(a{t}_1{t}_2,a(t_1+t_2\left)\right),B(a{t}_2{t}_3,a(t_2+t_3\left)\right)$ and $C(a{t}_3{t}_1,a(t_3+t_1\left)\right)$ of the triangle $ABC$ (where $t_1\ne t_2\ne t_3)$ is

The sum of an infinite geometric series is $3$. When the common ratio of the series is doubled, then the sum becomes $5$. The first term of the series is

If x < 4 , x^2 < 16 and x is a natural number. Prove that there are only three values which satisfy all the given equations simultaneously.

In the parabola $y^2=4ax$, the length of the chord passing through the vertex and inclined to the axis at $\frac{\pi }{4}$ is

If $y=\cot \theta ({\sin }^2\theta +\sin \theta \cos \theta )$, then

If a + b + c = 0, the correct statements for the equation $a{x}^2+bx+c=0$ are

Chose the correct answer.

The line y=x+1 is a tangent to the curve $y^2=4x$ at the point

(a) (1,2) (b) (2,1) (c) (1,-2) (d) (-1,2).

Find the number of ways in which one can post 5 letters in 7 letter boxes.

$Find\frac{d}{dx}(si{n}^{m}x.co{s}^{n}x)$

Fractional part of $\frac{2^{78}}{31}$ is

If two circles $(x-1{)}^2+(y-3{)}^2=r^{2}and{x}^2+y^2-4x-4y+4=0$ intersect in two distinct point then

If x $\in (0,\pi )$ and $sinx.co{s}^{3}x>cosx.si{n}^{3}x$ then complete set of values of x is

Let $\sum _{k=1}^{10}f(a+k)=16(2^{10}-1)$, where the function $f$ satisfies $f(x+y)=f\left(x\right)+f\left(y\right)$ for all natural numbers $x,y$ and $f\left(1\right)=2$. Then the natural number '$a$' is:

The value of a for which one root of the quadratic equation.$(a^2-5a+3)x^2+(3a-1)x+2=0$ is twice as large as other, is

Does the expansion of ${(2x^2-\frac{1}{x})}^{20}$ contain any term involving $x^9?$

How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I ?

If R is a relation from a fininte set A having m elements to a fininte set B having n elements, then the number of relations from A to B is

Find the equation of the straight line upon which the length of the perpendicular from the origin is 2 and the slope of this perpendicular is $\frac{5}{12}.$

If $2^{7}co{s}^3\theta si{n}^5\theta =asin8\theta -bsin6\theta +csin4\theta +dsin2\theta$ and $\theta$ is real then the value of $\frac{a^4+b^4+c^4+d^4}{1329}$ is___

Let $P_n$ denote the number of ways in which three people can be selected out of n people sitting in a row, if no two of them are consecutive. If, $P_{n+1}-P_n=15$, then the value of n, is___.

If the line y=mx+1 touches the hyperbola $\frac{x^z}{9}-\frac{y^z}{2}$ = 1 then m =

Write $\left(i^{25}\right)$ in polar form.

Which of the following statements are true ? Give reason to support your answer.

(i) For any two sets A and B either A $\subseteq$ B or B $\subseteq$ A.

(ii) Every subset of an infinite set is infinite.

(iii) Every subset of a finite set is finite.

(iv) Every set has a proper subset.

(v) {a,b,a,b,a,b....} is an infinite set.

(vi) {a, b, c} and {1, 2, 3} are equivalent sets.

(vii) A set can have infinitely many subsets.

Binary operation 'subtraction' on integers is

Value of the expression $\frac{1}{\sqrt{2}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{8}}+\frac{1}{\sqrt{11}+\sqrt{8}}+...n$ terms, is

The coefficient of $\frac{1}{x}$ in the expansion of $(1+x{)}^n{(1+\frac{1}{x})}^n$ is

The coefficient of $x^{50}$ in the expansion of $(1+x{)}^{1000}+2x(1+x{)}^{999}+3x^2(1+x{)}^{998}+.....+1001x^{1000}$

A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is

[MP PET 1989]

Which of the following is the general equation of plane ?

The middle term in the expansin of ${(\frac{2x^2}{3}+\frac{3}{2x^2})}^{th}$ is

Let the mean of $n$ terms be $\overline{x}$, if the first term is increased by $1$, second term is increased by $2$ and so on, then the new mean is

The equations of the directrices of the hyperbola $16x^2-9y^2=-144$ are:

If the cube roots of unity be $1,\omega ,{\omega }^2$ then the roots of the equation $(x-3{)}^2+8=0$ are

A number x is selected at random from the set {1,2,3,..............99). A number y is selected from the same set.The probability that the number: $7^X+5^Y$ last digit is 8.

The number of two digit numbers n such that the difference of n and the number formed by reversing the digits of n, is prime, is

Equation of the circle passing through the focii of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having centre at $(0,3)$ is

Prove that:
(i) $\frac{n!}{(n-r)!}$
= n(n-1)(n-2)...(n-(r-1))
(ii) $\frac{n!}{(n-r)!r!}+\frac{n!}{(n-r+1)!(r-1)!}$
= $\frac{(n+1)!}{r!(n-r+1)!}$

$x^2-2x+\frac{3}{2}=0$

If tangent to the circle $x^2+y^2=5$ at $(1,-2)$ also touches the circle $x^2+y^2-8x+6y+20=0$ at point $(h,k),$ then the value of $h+k$ is