Explore topic-wise InterviewSolutions in Current Affairs.

$acosA+bcosB+ccosC=2bsinAsinC=2csinAsinB$

If $A=\left[\begin{array}{c}12\\ -13\end{array}\right]B=\left[\begin{array}{c}40\\ 15\end{array}\right]C=\left[\begin{array}{c}20\\ 1-2\end{array}\right]$ a = 4, and b = - 2, then show that

(vi) $(bA{)}^T$ = b $A^T$

If the lines given by ax2 +2hxy + by2 =0from an equilateral triangle with the lines Lx+my =1then show that (3a+b)(a+3b)-4h2=0

Which of the following unit vector is coplanar with vectors

$\overrightarrow{A}=2\hat{i}-3\hat{j}+\hat{k}\mathrm{and}\overrightarrow{B}=3\hat{i}-\hat{j}-3\hat{k}$

and orthogonal to the vector

$\overrightarrow{C}=8\hat{i}-5\hat{j}+2\hat{k}$

${lim}_{x\to 0^{+}}{\{1+{\tan }^2\sqrt{x}\}}^{\frac{1}{2}x}$

Check the validity of the following statements :

(i) p : 100 is a multiple of 4 and 5.

(ii) q : 125 is a multiple of 5 and 7.

(iii) r : 60 is a multiple of 3 or 5.

Let the equation of the pair of lines, $y=px$ and $y=qx$, can be written as $(y-px)(y-qx)=0$. Then the equation of the pair of the angle bisectors of the lines $x^2-4xy-5y^2=0$ is

If $\left[\begin{array}{ccc}X-Y& 2& -2\\ 4& X& 6\end{array}\right]+\left[\begin{array}{ccc}3& -2& 2\\ 1& 0& -1\end{array}\right]=\left[\begin{array}{ccc}6& 0& 0\\ 5& 2X+Y& 5\end{array}\right]$,

then

If $(1+x{)}^n=C_0+C_{1}x+C_2{x}^2+.......+C_n{x}^{n}forn\in N$ and ${\sum }_{r=0}^n(r+1{)}^2.C_r=2^{n-2}f(n)$

If the roots of the equation f(x) = 0 are $\alpha$ and $\beta$ then $(\alpha {)}^4$ + $(\beta {)}^4$ =

The value of the integral $\int \frac{\sin \theta .\sin 2\theta ({\sin }^6\theta +{\sin }^4\theta +{\sin }^2\theta )\sqrt{2{\sin }^4\theta +3{\sin }^2\theta +6}}{1-\cos 2\theta }d\theta$ is

$($where $c$ is a constant of integration$)$

A function $f:R\to R$ is defined by $f\left(x\right)=x^2$. Determine.
i) Range of f
ii) $\{x:f(x)=4\}$
iii) $\{y:f(y)=-1\}$

|3x+2|<1 then x belong to

If $\underset{0}{\overset{3}{\int }}\mathrm{sgn}(\sin x-\cos x)dx=a+\frac{b\cdot \pi }{2}$, then which of the following statement(s) is/are true $?$

Solution of $lo{g}_{x^2+6x+8}lo{g}_{2x^2+2x+3}(x^2-2x)=0$ is

Solve
the equation for x,
y, z
and t if

The arbitrary constant on which the value of the determinant

If $2^x+2^{f\left(x\right)}=2$ , then the domain of the function $f\left(x\right)$ is

A unit vector coplanar with $\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k}\text{and}\overrightarrow{i}+3\overrightarrow{j}+\overrightarrow{k}$ and perpendicular to $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is

The solution of the differential equation $(y-x\frac{dy}{dx})=a(y^2+\frac{dy}{dx})$ is (where $k$ is constant)

The area enclosed between the curves $y=a{x}^2$ and $x=a{y}^2$ (a > 0) is 1 sq. unit. Then the value of ‘a’ is

The area (in square units) of the quadrilateral formed by the two pairs of lines

$l^2{x}^2-m^2{y}^2-n(lx+my)=0$

and $l^2{x}^2-m^2{y}^2+n(lx-my)=0$ is

Differentiate the
following w.r.t. x:

If the curve $y=a{x}^{\frac{1}{2}}+bx$ passes through the point $(1,2)$ and $y\ge 0$ for $0\le x\le 9$ and the area enclosed by the curve, the $x-$ axis and the line $x=4$ is $8$ sq. units, then

The fundamental period of the function $f\left(x\right)=-2\cos (3x+\frac{\pi }{2})=$

Find the
derivative of the following functions from first principle.

(i) x³
– 27 (ii) (x – 1) (x – 2)

(ii) (iv)

Let $\theta ,\varphi \in [0,2\pi ]$ be such that $2cos\theta (1-sin\varphi )=si{n}^2\theta (tan\frac{\theta }{2}+cot\frac{\theta }{2})cos\theta -1,tan(2\pi -\theta )>0$ and -1 < $sin\theta <-\frac{\sqrt{3}}{2}$. Then $\varphi$ cannot satisfy