Explore topic-wise InterviewSolutions in Current Affairs.

If $y=\frac{4\sin x}{2x+\cos x},$ then $\frac{dy}{dx}=$

Evaluate the integrals using substitution.
${\int }_0^{\frac{\pi }{2}}\sqrt{sin\varphi }co{s}^5\varphi d\varphi .$

If the length of the subnormal of a curve is constant and if it passes through the origin, then the equation of curve is

If a, b $\epsilon$ R, a $\ne$ 0 and the quadratic equation $a{x}^2-bx+2$ =0 has imaginary roots, then a + b + 2 is

Let $a$ and $b$ be positive real numbers such that $a>1$ and $b<a.$ Let $P$ be a point in the first quadrant that lies on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ Suppose the tangent to the hyperbola at $P$ passes through the point $(1,0),$ and suppose the normal to the hyperbola at $P$ cuts off equal intercepts on the coordinate axes. Let $\Delta$ denote the area of the triangle formed by the tangent at $P,$ the normal at $P$ and the $x-$axis. If $e$ denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?

Let $f\left(x\right)=x+\ln x-x\ln xx\in (0,\infty )$

If $y=e^{\sqrt{\cot x}},$ then $\frac{dy}{dx}=$

The area of the circle x²
+ y² = 16 exterior to the parabola y²
= 6x is

A.

B.

C.

D.

Let $S=\left\{xϵ\right(-\pi ,\pi ):x\ne 0,\pm \frac{\pi }{2}\}$. The sum of all distinct solutions of the equation $\sqrt{3}secx+cosecx+2(tanx-cotx)=0$ in the set S is equal to

Question 4 (ii)

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(ii) $2,\frac{5}{2},3,\frac{7}{2},\dots$

In $R^3$, consider the planes $P_1:y=0$ and $P_2:x+z=1$. Let $P_3$ be a plane , different from $P_1$ and $P_2$, which passes through the intersection of $P_1$ and $P_2$. If the distance of the point (0, 1, 0) from

$P_3$ is 2, then which of the following relation(s) is/are true?

In a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides.

OR

How many times must a fair coin be tossed so that the probability of getting at least one head is more than $80\%$?

Let $ABC$ be a triangle with $A(-3,1)$ and $\angle ACB=\theta ,0<\theta <\frac{\pi }{2}.$ If the equation of the median through $B$ is $2x+y-3=0$ and the equation of angle bisector of $C$ is $7x-4y-1=0,$ then $\tan \theta$ is equal to

Find the
derivative offor
some constant a.

Which of the following expressions have value equal to four times the area of the triangle $ABC$?
(All symbols used have their usual meaning in a triangle)

Which of the following functions are identical to f(x) =

$f\left(x\right)=\{\begin{array}{cc}x,& 1\le x<2\\ x^2,& 2\le x<3\end{array}$

(1 $\le$ x < 3)

Find
the inverse of each of the matrices, if it exists.

Let $l$ be the length of median from vertex $A$ to side $BC$ of a $\Delta ABC,$ then which of the following is/are true:

What will be the next number in the following sequence?

12, 1212, 121212, ...

1+1/2+1/3+...+1/1023

The extremities of the latus rectum of an ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is

If $a,b,c$ are positive real numbers such that $a^{{\log }_{3}7}=27,b^{{\log }_{11}7}=49\text{and}{c}^{{\log }_{11}25}=\sqrt{11}$, then the middle digit in the value of $(a^{({\log }_{3}7{)}^2}+b^{({\log }_{7}11{)}^2}+c^{({\log }_{11}25{)}^2})$ equals to

If $L=\underset{x\to 0}{lim}\frac{3px+(p-2)\sin x}{{\left({\sin }^{-1}x\right)}^3}$ is finite for real value of $p,$ then

Let $f\left(x\right)=\{\begin{array}{cc}\alpha \left(x\right)\sin \frac{\pi x}{2}& \text{for}x\ne 0\\ 1& \text{for}x=0\end{array}$

where $\alpha \left(x\right)$ is such that $\underset{x\to 0}{lim}|\alpha \left(x\right)|=\infty$.
Then the function $f\left(x\right)$ is continuous at $x=0$ if $\alpha \left(x\right)$ is chosen as :

Find the
coordinates of a point on y-axis which are at a distance
offrom
the point P (3, –2, 5).

The values of $x$ for which the logarithmic function $f\left(x\right)={\log }_{|-x^2+2x-4|}\left(x\right(3-x\left)\right)$ is defined, is

In a $\Delta ABC,$ the value of $2ac\sin \frac{A-B+C}{2}$ is