Explore topic-wise InterviewSolutions in Current Affairs.

Equation of circle whose parametric equations are $x=5-5\sin t$ and $y=4+5\cos t$ is

The
general solution of the differential equation
is

A. xy
= C

B. x
= Cy²

C. y
= Cx

D. y
= Cx²

If $0<a<1,b<1$, and ${\tan }^{-1}a+{\tan }^{-1}b=\frac{\pi }{4}$, then the value of $(a+b)-\left(\frac{a^2+b^2}{2}\right)+\left(\frac{a^3+b^3}{3}\right)-\left(\frac{a^4+b^4}{4}\right)+....$

$\frac{(cosx+isinx)(cosy+isiny)}{(cotu+i)(1+itanv)}$

A vector $\overrightarrow{a}=x\hat{i}+y\hat{j}+z\hat{k}$ of length $2\sqrt{3}\text{units},$ which makes equal angles with the vectors $\overrightarrow{b}=y\hat{i}-2z\hat{j}+3x\hat{k}$ and $\overrightarrow{c}=2z\hat{i}+3x\hat{j}-y\hat{k}$ and is perpendicular to $\overrightarrow{d}=\hat{i}-\hat{j}+2\hat{k}$ and makes an obtuse angle with $y-$axis is

A particle moves on a line according to the law $s=a{t}^2+bt+c.$ If the displacement after one second is $16$ cm, the velocity after $2$ seconds is $24$ cm/sec and the acceleration is $8$ cm/sec${}^2,$ then $(a,b,c)$

If set $A$ has $3$ elements and set $B$ has $4$ elements, then number of injective functions that can be defined from $A$ to $B$ is

If $x^2+y^2-2by+ac=0$ is the equation of a point circle, then $a,b,c$ are in
(where $a,b,c$ are positive real numbers)

Show that the relation R defined in the
set A of all triangles as R = {(T₁, T₂):
T₁ is similar to T₂}, is
equivalence relation. Consider three right angle triangles T₁
with sides 3, 4, 5, T₂ with sides 5, 12, 13 and T₃
with sides 6, 8, 10. Which triangles among T₁, T₂
and T₃ are related?

The value of $a$ so that the function $f\left(x\right)=\{\begin{array}{cc}\frac{1-\cos 4x}{x^2},& x<0\\ a,& x=0\\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4},& x>0\end{array}$

is continuous at $x=0$ is

If $l_1,m_1,n_1,l_2,m_2,n_{2}and{l}_3,m_3,n_3$ are the direction cosines of three mutually perpendicular lines,then prove that the line whose direction cosines are proportional to $l_1+l_2+l_3,m_1+m_2+m_{3}and{n}_1+n_2+n_3$ makes equal angles with them.

Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0

If a parallelopiped is formed by the planes drawn through the points

(2, 3, 5) and (5, 9, 7) parallel to the coordinate planes, then write the

lengths of edges of the parallelopiped and length of the diagonal.

The value of $\underset{x\to 0^{+}}{lim}{\left(\tan x\right)}^x$ is

A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle ${60}^{\circ }$ with the ground. At what height from the bottom the tree is broken by the wind? [3 MARKS]

If in a $\Delta \text{ABC},$

$b=\sqrt{3}+1,c=\sqrt{3}-1,\angle A={60}^{\circ }.$ Then the value of $\tan \left(\frac{B-C}{2}\right)$ is:

If $(2\hat{i}+6\hat{j}+27\hat{k})\times (\hat{i}+\lambda \hat{j}+\mu \hat{k})=\overrightarrow{0},$ then which of the following is/are correct ?

If $\alpha \beta \gamma$ are the zeroes of $a{x}^3+b{x}^2+cx+d$, then what is $\alpha \beta \gamma$

The number of solution pairs $(x,y)$ of the simultaneous equations
${\log }_{1/3}(x+y)+{\log }_3(x-y)=2$
$2^{y^2}={512}^{x+1}$ is

In ∆ ABC, AB = 2, AC = 4 and the median from A to BC is equal in length to BC. Then value of BC² is equal to,

The solution set of ${\log }_{1/3}(2^{x+2}-4^x)\ge -2$, is

If $A=\left[\begin{array}{cc}2\cos {60}^{\circ }& -2\sin {30}^{\circ }\\ -\tan {45}^{\circ }& \cos 0^{\circ }\end{array}\right],B=\left[\begin{array}{cc}\cot {45}^{\circ }& \text{cosec}{30}^{\circ }\\ \sec {60}^{\circ }& \sin {90}^{\circ }\end{array}\right],$ then $AB$ is equal to

The angle between the lines joining the origin to the points of intersection of the line $y=3x+2$ with the curve $x^2+2xy+3y^2+4x+8y=11,$ is

If an A.P. is such that $\frac{a_4}{a_7}=\frac{2}{3}$, find $\frac{a_6}{a_8}$