Explore topic-wise InterviewSolutions in Current Affairs.

$\frac{sec8A-1}{sec4A-1}$ is equal to

If $\alpha$ and $\beta$ are the roots of the quadratic equation $a{x}^2+bx+c=0$, then $\underset{x\to \frac{1}{\alpha }}{lim}\sqrt{\frac{1-\cos (c{x}^2+bx+a)}{2(1-\alpha x{)}^2}}=$

Let $S\left(x\right)=\int \frac{dx}{e^x+8e^{-x}+4e^{-3x}},R\left(x\right)=\int \frac{dx}{e^{3x}+8e^x+4e^{-x}}$ and $M\left(x\right)=S\left(x\right)-2R\left(x\right).$ If $M\left(x\right)=\frac{1}{2}ta{n}^{-1}\left(f\right(x\left)\right)+c$ then f(0)=

The points at which the function $f\left(x\right)=\frac{x+1}{x^2+x-12}$ is discontinuous, are

Find the torque about point $O$ and $A$. $\overrightarrow{F}$ = $5\sqrt{3}\hat{i}+5\hat{j}$

If the odds in favour of an event be 3 : 5, then the probability of non-occurrence of the event is

If $\alpha ,\beta$ are the roots of the equation $x^2-2x+3=0$, then the equation whose roots are $P={\alpha }^3-3{\alpha }^2+5\alpha -2$ and $Q={\beta }^3-{\beta }^2+\beta +5$ is

${lim}_{x\to 3}\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}$

$Find\frac{dy}{dx},ify=si{n}^{-1}x+si{n}^{-1}\sqrt{1-x^2},-1\le x,\le 1.$

Consider all the permutations of the word $BENGALURU$. The number of words in which vowels occur at even places is given as $A$ and the number of words in which the letters of the word $GLUE$ appear together in that order is given as $B$. Find the value of $A-B$

Let the given line intersect x-axis at R. If a line through R intersects the hyperbola at S and T, then the minimum value of (RS) (RT) is ________

If $a,b,c\in R^{+}$ are such that $2a,b,4c$ are in A.P. and $c,a,\text{and}b$ are in G.P., then

Number of real solution(s) of the $|x+2|={\log }_{0.5}x$ is

Find the following integrals.
$\int (a{x}^2+bx+c)dx.$

Write the distance between the vertex and focus of the parabola $y^2+6y+2x+5=0.$

The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21, from these numbers in that order, we obtain an A.P. Find the numbers.

The total number of solutions of the equation cosx.cos2x.cos3x=$\frac{1}{4}$ in [0, $\pi$] is

Represent to solution set of each of the following in equations graphically in two dimensional plane :

$x+2y\ge 6$

If $aϵ\{-1,2,3,4,5\}$ and $bϵ\{0,3,6\},$ write the set of all ordered pairs (a, b) such that a + b = 5.

Let $a,b,c$ are in AP and $a^2,b^2,c^2$ are in G.P. If $a<b<c$ and $a+b+c=\frac{3}{2}$ then $a=$

What is the value of 8.0 km in inches?

(1 m = 1.1 yards & 1 yard = 36 inches)

Find the equations of the tangent and normal to the given curves at the given points

(i) $y=x^4-6x^3+13x^2-10x+5at(0,5)$

(ii) $y=x^4-6x^3+13x^2-10x+5at(1,3)$

(iii) $y=x^{3}at(1,1)$

(iv) $y=x^{2}at(0,0)$

(v) $x=cost,y=sint=\frac{\pi }{4}$

(5-¹×7²÷5²×7-⁴)-7/2 × (5^{-²×7³÷ 5³×7to the power -5) -5/2}

Why is the sign of infinity ∞ ?

If A and B are two matrices such that AB = B and BA = A, then

The solution set of the inequality $3^{{\log }_3\sqrt{x-1}}<3^{{\log }_3(x-6)}+3$ is

If a curve $y=f\left(x\right)$ passes through the point $(1,2)$ and satisfies $x\frac{dy}{dx}+y=b{x}^4,$ then for what value of $b,$ $\underset{1}{\overset{2}{\int }}f\left(x\right)dx=\frac{62}{5}$ ?

For any two setsA and B prove that

A intersection (A' union B ) = A intersection B

The equations Kcosx - 3sin x = K + 1 is solvable only if K belongs to the interval

If the sum of the coefficients in the expansion of $(a+b{)}^n$ is 4096, then the greatest coefficient in the expansion is

The circle $x^2+y^2-8x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points A and B.
Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

Find the point of intersection of line x/a+y/b=1,x/b+y/a=1(a≠±b)

If x, y and z are the arithmetic, geometric and harmonic means of two positive numbers respectively .Then the relation between x, y and z is

Let R be a relation from N to N defined by R = {(a, b) : $a,bϵN$ and $a=b^2$}.

Are the following statements true ?

(i) $(a,a)ϵR$ for all $aϵN$

(ii) $(a,b)ϵR\Rightarrow (b,a)ϵR.$

(iii) $(a,b)ϵR$ and $(b,c)ϵR\Rightarrow (a,c)ϵR.$

Let A = {1, 2, 3} and B = {5, 6, 7, 8, 9} and let f(x) = {(1, 8), (2, 7), (3, 6)} then f is

If $15si{n}^{4}a+10co{s}^{4}a=6$, find the value of $8cose{c}^{6}a-27se{c}^{6}a$.

Which of the following statements is true?

Find the values of a,b,c and d from the equation $\left[\begin{array}{cc}a-b& 2a+c\\ 2a-b& 3c+d\end{array}\right]=\left[\begin{array}{cc}-5& 5\\ 0& 13\end{array}\right].$