Explore topic-wise InterviewSolutions in Current Affairs.

Let ${(1-x+x^4)}^{10}=a_0+a_{1}x+a_2{x}^2+\cdots +a_{40}{x}^{40}.$ Then the correct option(s) is (are)

If $y\frac{dy}{dx}=x[\frac{y^2}{x^2}+\frac{\varphi \left(\frac{y^2}{x^2}\right)}{{\varphi }^{\prime }\left(\frac{y^2}{x^2}\right)}],$ $x>0,$ $\varphi >0$ and $y\left(1\right)=-1,$ then $\varphi \left(\frac{y^2}{4}\right)$ is equal to

If $n\left(A\right)=50,n(A\cup B)=80,n(A\cap B)=30$, then $n(B–A)=$

The equation of line passing through points $-\hat{i}+\hat{j}-2\hat{k}$ and $2\hat{j}+3\hat{k}$ is

find the equation whose roots are the squares of the roots of the equation x³+2x²-x+5=0

If A and B are independent events such that

$P\left(A\right)=p,P\left(B\right)=2p$ and

$P\left(\text{Exactly one of A and B}\right)=\frac{5}{9}$

then $p=$

The function $f\left(x\right)=\frac{x}{3}+\frac{3}{x}$ strictly decreases in

Differentiate the following functions with respect to x

sin (ax + b).

The equation of the obtuse angle bisector of lines $12x-5y+7=0$ and $3y-4x-1=0$ is

Prove the following by using the principle of mathematical induction for all n ∈ N:

The probability that $A$ speaks truth is $\frac{4}{5},$ while this probability for $B$ is $\frac{3}{5}.$ The probability of at least one of them is true when asked to speak on an event is

If A = {1, 2, 3}, B = {x, y}, then the number of functions that can be defined from A to B in

Evaluate $\int sin3xcos4xdx$

An unbiased coin is tossed. If the outcome is head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well shuffled pack of nine cards numbered $1,2,\cdots 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is :

If a chord, which is not a tangent, of the parabola $y^2=16x$ has the equation $2x+y=p$, and midpoint $(h,k)$, then which of the following is(are) possible value(s) of $p,h\text{and}k$ ?

If $p\to (\sim p\vee \sim q)$ is false, then the truth values of $p\text{and}q$ are respectively:

If $y=\frac{x}{\sqrt{a^2-1}}-\frac{2}{\sqrt{a^2-1}}{\tan }^{-1}\left(\frac{\sin x}{a+\sqrt{a^2-1}+\cos x}\right)$ where $a\in (-\infty ,-1)\cup (1,\infty ),$ then $y^{\prime }\left(\frac{\pi }{2}\right)$ is equal to

If A lies in the second quadrant and 3 tan A + 4 = 0, the value of 2 cot A - 5 cos A + sin A is equal to

Which among the following is (are) rational number(s) ?

If $y=e^{m{\sin }^{-1}x}$, then $(1-x^2)\frac{d^{2}y}{d{x}^2}-x\frac{dy}{dx}-ky=0$, where $k$ is equal to

The equation of a plane containing the lines $\overrightarrow{\gamma }=\hat{i}+2\hat{j}-\hat{k}+\lambda (\hat{i}+2\hat{j}-\hat{k})$ and $\overrightarrow{\gamma }=\hat{i}+2\hat{j}-\hat{k}+\mu (\hat{i}+\hat{j}+3\hat{k})$ is

The decomposition of dinitrogen pentoxide $\left(N_2{O}_5\right)$ follows first order rate law. Calculate the rate constant from the given data:

t = 800 s $\left[N_2{O}_5\right]=1.45\text{mol}{L}^{-1}=\left[A_1\right]$

t = 1600 s $\left[N_2{O}_5\right]=0.88\text{mol}{L}^{-1}=\left[A_2\right]$



Take:

$lo{g}_{10}\frac{\left[1.45\right]}{\left[0.88\right]}=0.217$

The critical point(s) of the function $f\left(x\right)=(x-2{)}^{2/3}(2x+1)$ is(are)