Explore topic-wise InterviewSolutions in Current Affairs.

The negation of $(p\vee q)\wedge (q\vee \sim r)$ is

For Balmer series, the initial state n₁ is:

Numerically greatest term in the expansion of $(x-\frac{1}{x}{)}^{11}$ when x=2 is given by

If 3sin$\theta$ + 5 cos$\theta$ = 5 then value of sin$\theta$ - 3 cos$\theta$ is equal to

If 2(y - a) is the H.M. of y - x and y - z, then x - a, y - a, z - a are in

An equilateral triangle inscribed in the circle $x^2+y^2+2gx+2fy+c$ = 0 then its side is

Prove cot π/24=√2+√3+√4+√6

Coordinates of parametric point on the parabola, whose focus is $(\frac{-3}{2},-3)$ and the directrix is $2x+5=0$ is given by

If $sin\theta$ = x + $\frac{a}{x}\forall x\in R$ - {0} then

If $co{s}^{3}x.sin2x={\sum }_{x=0}^n{a}_{r}sin\left(\pi x\right),\forall x\in R$, then

The value of tan(sin^-1x + cos^-1x) is

Find the value of cos18⁰+sin36⁰

The value of $2^{sinx}+2^{cosx}$ is

A curve passes through the point $(2,0)$ and the slope of the tangent at any point $(x,y)$ is $x^2-2x$ for all value of $x$. The point of maxima of the curve is

If $|z_1|$ = $|z_2|$ and arg$\left(\frac{z_1}{z_2}\right)$ = $\pi$, then $z_1+z_2$ is equal to

If $f\left(x\right)=\{\begin{array}{cc}\frac{1}{x}sin{x}^2,& x\ne 0\\ 0,& x=0\end{array}$ , then

In $△ABC,R,r,r_1,r_2,r_3$ denote the circumradius, inradius, the exradii opposite to the vertices $A,B,C$ respectively. Given that $r_1:r_2:r_3=1:2:3$.
The sides of the triangle are in the ratio

If A is a symmetric matrix, then matrix M'AM is

[MP PET 1990]

If x = acost, y = asint, then $\frac{d^{2}y}{d{x}^2}$ at $t=\frac{\pi }{4}$ is

The points on the parabola $y^2=12x$ whose focal distance is 4 , are

The value of $si{n}^2$ B+ 4 cos (A + B) sin B + cos 2(A + B) is

Let $a,b(b>a)$ are the roots of the quadratic equation $(k+1)x^2-(20k+14)x+91k+40=0;$ where $k>0$, then which among the following option(s) is/are correct for the roots

On the occasion of Dipawali festival each student of a class sends greeting cards to others. If there are $20$ students in the class, the number of cards send by students is

The curve $y-e^{xy}+x=0$ has a vertical tangent at the point

$Iftan\beta =\frac{nsin\alpha cos\alpha }{1-nsi{n}^2\alpha },thentan(\alpha -\beta )isequalto$

In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is

The straight lines joining the origin to the points of intersection of the line 2x + y = 1 and curve $3x^2+4xy-4x+1=0$ include an angle

Find the equations of the straight lines passing through (2, -1) and making an angle of ${45}^{\circ }$ with the line $6x+5y-8=0$.

The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0 is
[MP PET 1991]

The focus of the parabola $x^2-2x=2y$ is

Let $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ and $B=A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ are two matrices such that AB = BA and $c\ne 0$, then value of $\frac{a-d}{3b-c}$ is :

If the equation $x^2+\lambda x+\mu =0$ has equal roots and one root of the equation $x^2+\lambda x-12=0$ is 2,then $(\lambda ,\mu )=$

A curve is represented by c $\equiv$ $3(x–3y+2{)}^2+2(3x+y–1{)}^2=180$. Eccentricity of the curve is

Determine the product $\left[\begin{array}{ccc}-4& 4& 4\\ -7& 1& 3\\ 5& -3& -1\end{array}\right]\left[\begin{array}{ccc}1& -1& 1\\ 1& -2& 2\\ 2& 1& 3\end{array}\right]$ and use it to solve system of equations $x-y+z=4,x-2y-2z=9,2x+y+3z=1$

Dividing $f\left(z\right)byz-i$, we obtain the remainder i and dividing it by $z+i$, we get the remainder $1+i$. The remainder upon the division of
$f\left(z\right)by{z}^2+1$ is

If the line (6x-7y+8)+$\lambda$(3x-y+5)=0 is parallel to y-axis, then $\lambda$=

Given slope m, find the equation of normal having slope m to the parabola $y^2=4ax$

Let $f:R^{+}\to R^{+}$ be a differentiable function satisfying $f\left(xy\right)=\frac{f\left(x\right)}{y}+\frac{f\left(y\right)}{x}$ for all $x,yϵR^{+}$. Also $f\left(1\right)=0,f^{\prime }\left(1\right)=1$. If M is the greatest value of $f\left(x\right)$ then $[m+e]$ is ___ (where [.] represents Greatest Integer Function).

The range of $f\left(x\right)=\frac{x}{x^2+4}$ is

The solution of differential equation $\frac{x+y\frac{dy}{dx}}{y-x\frac{dy}{dx}}=\frac{x{\cos }^2(x^2+y^2)}{y^3}$ is

The tangent to the curve $y=x^2-5x+5$, parallel to the line $2y=4x+1$, also passes through the point :

Two dice are thrown. The events A, B, C, D, E and F are described as follows :

A = Getting an even number on the first die.

B = Getting an odd number on the first die.

C = Getting at most 5 as sum of the numbers on the two dice.

D = Getting the sum of the numbers on the dice greater than 5 but less than 10.

E = Getting at least 10 as the sum of the numbers on the dice.

F = Getting an odd number on one of the dice.

(i) Describe the following events : A and B, B or C, B and C, A and E, A or F, A and F

(ii) State true or false :

(a) A and B are mutually exclusive.

(b) A and B are mutually exclusive and exhaustive events.

(c) A and C are mutually exclusive events.

(d) C and D are mutually exclusive and exhaustive events.

(e) C, D and E are mutually exclusive and exhaustive events.

(f) A' and B' are mutually exclusive events.

(g) A, B, F arc mutually exclusive and exhaustive events.

Evaluate ${lim}_{x\to 3}\frac{x^2-9}{x-3}$

Consider two points whose ordinates differ by 3, on the ellipse. The tangents at these variable points, intersect at P. find the locus of P.

A circle of radius ‘r’ is concentric with the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ .Then inclination of common tangent with major axis is _______(b<r<a)

Which of the following is incorrect?