Explore topic-wise InterviewSolutions in .

If sin $\theta$ = $-\frac{1}{\sqrt{2}}$ and tan $\theta$ = 1, then $\theta$ lies in which quadrant.

Function f(x) is defined in [a, b]. If the function is continuous throughout the interval [a, b] then which among the following are correct

Find the coefficient of $x^{90}$ in $(x+x^2+x^3+..........{)}^2(x^5+x^6+...........{)}^9$

If $|z|\le 4$, then maximum value of $|iz+3-4i|$ is equal to:

If $|z-\frac{1}{z}|$ = 1, then:

If tan A + tan B + tan C = tan A tan B tan C. Find the minimum value of tan A . tan B . tan C?

The equation,$\frac{x^2}{10-a}+\frac{y^2}{4-a}=1$ represents an ellipse if

Find equation of the line through the point (0, 2) making an angle $\frac{2\pi }{3}$ with the positive x - axis. Also, find the equation of line parallel to it and crossing the y - axis at a distance of 2 units below the origin.

Which of the following is not a real valued function?

In any $\Delta ABC,$ prove that

$acosA+bcosB+ccosC=2asinBsinC.$

If |$\frac{a+ib}{c+id}$| = |4+3i| , then the value of |$\frac{a^2+b^2}{c^2+d^2}$| is _________

A box has 7 red and 4 blue balls. Two balls are drawn at random with replacement and an event is defined as '2 red balls are drawn. Find number of favorable outcomes.

Let the $n^{th}$ terms of an A.P., G.P. and H.P. be $a,b,c$ respectively. If the first and the $(2n-1{)}^{th}$ terms of the A.P., G.P. and H.P. are equal, then which of the following is/are correct?

The locus of the midpoint of the portion between the axes of
$xcos\alpha +ysin\alpha =p,$ where p is a constant, is

Let a be a complex number such that |a|<1 and $z_1$,$z_2$,...... be vertices of a polygon such that $z_k$=1+a+$a^2$+.....+$a^{k-1}$. Then the vertices of the polygon lie within a circle

The term independent of x in ${(2x^{\frac{1}{2}}-3x^{\frac{-1}{3}})}^{20}$

If a,b,cϵ R and 1 is a root of the equation a$x^2$ + bx + c = 0 then the equation 4 a$x^2$+ 3 bx + 2c = 0, c ≠ 0 has roots which are :

A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are, respectively, $p$, $q$ and $1/2$. if the probability that the student is successful is $1/2$, then $p(1+q)=$

If $\sin x+\cos x=a,$ then $1+2\sin x\cos x=$

The domain of the function $\sqrt{\left(lo{g}_{0.5}x\right)}$ is

If the middle points of the sides of a triangle be (-2, 3), (4, -3) and (4, 5), then the centroid of the triangle is

$\text{Derivatie of}{e}^{si{n}^{-1}x}w.r.t.si{n}^{-1}is$

Which of the following is the possible value of |x| if $|x{|}^2$ - 6|x| + 8 = 0

The value of $\frac{e^{i\theta }+e^{-i\theta }}{2}$ is

Which of the following is the empty set

In any $\Delta ABC,$ prove that

$a^{3}sin(B-C)+b^{3}sin(C-A)+c^{3}sin(A-B)=0.$

Let $T_n$ denote the number of triangles which can be formed using the vertices of a

regular polygon of n sides. If $T_{n+1}-T_n=21$ , then n equals

If ∝, β are the roots of $x^2$ + px + 1 = 0, γ, δ the roots of $x^2$ + qx + 1 = 0, then (∝ - γ)( β -γ)(∝+ δ)( β +δ) =

If {x} denotes the fractional part of x then the value of $\left\{\frac{2^{2003}}{17}\right\}$ is

The number of ordered pair (a,x) satisfying the equation $se{c}^2$(a + 2)x + $a^2$ - 1 = 0; -$\pi$ < x < $\pi$ is

The probability that a student will pass the final examination in both english and Hindi is 0.5 and the probability of passing neither is 0.1. I fthe probability of passing the English examination is 0.75, What is the probability of passing he HINDI examination?

Find the set of real values of x for which ${\log }_{12}$ ($x^2$ - x) < 1.

If ${\left(\frac{1+cos\theta +isin\theta }{1+cos\theta -isin\theta }\right)}^4$ = cosn$\theta$+isinn$\theta$ , then n is

equal to

If $w=\alpha +i\beta ,where\beta \ne 0andz\ne 1,$ satisfies the condition that $\left(\frac{w-\overline{w}z}{1-z}\right)$ is purely real, then the set of values of z is

In the binomial expansion of $(a-b{)}^n,n\ge 5,$ the sum of the $5^{th}and{6}^{th}$ terms is zero. Then a/b equals

If the origin is the centroid of the triangle with vertices P(2z, 2, 6), Q(-4,3b, -10) and R(8, 14, 2c) find the values of a, b and c.

The domain of f(x) is (0, 1). Then the domain of $f\left(e^x\right)+f\left(ln|x|\right)$ is

If $x=\sum _{n=0}^{\infty }(-1{)}^n{\tan }^{2n}\theta$ and $y=\sum _{n=0}^{\infty }{\cos }^{2n}\theta ,$ where $0<\theta <\frac{\pi }{4},$ then:

If $x^4$ occurs in the $r^{th}$ term in the expansion of $(x^4+\frac{1}{x^3}{)}^{15}$, then r =