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Let two points be $A(1,-1)$ and $B(0,2)$. If a point $P(x^{\prime },y^{\prime })$ be such that the area of $\Delta PAB=5$ sq. units and it lies on the line, $3x+y-4\lambda =0$, then the value of $\lambda$ is:

If a unit
vector

makes an angleswith
with
and
an acute angle θ with,
then find θ and hence, the compounds of.

If A and B are 2 matrices given by general elements $a_{ij}$ and $b_{ij}$ respectively. And $b_{ij}$ = Im($a_{ij}$). Then which the following are correct if A* + B = 0. ( Im(x) means Imaginary part of the number x)

If $I_1=\underset{0}{\overset{1}{\int }}{(1-x^{50})}^{100}dx,I_2=\underset{0}{\overset{1}{\int }}{(1-x^{50})}^{101}dx$, then

If a function $f:[-2,\infty )\to R$ is such that $f\left(x\right)=x^2+4x-|x^2-4|,$ then the value(s) $f\left(x\right)$ can have is (are)

Which among the following function graph(s) are symmetrical about $y-$axis?

The lines $2x+3y=6$, $2x+3y=8$ cut the $x-$axis at $A,B$ respectively. A line $L=0$ drawn through the point $(2,2)$ meets the $x-$axis at $C$ in such a way that the abscissa of $A,B,C$ are in Arithmetic Progression. Then the equation of the line $L$ is

Let n(A) = m and n(B) = n. Then the total number of non-empty relations that can be defined from

A to B is ___________ .

Let $a_n$ be the $n^{th}$ term of a G. P. of positive terms. If $\sum _{n=1}^{100}{a}_{2n+1}=200$ and $\sum _{n=1}^{100}{a}_{2n}=100$, then $\sum _{n=1}^{200}{a}_n$ is equal to :

A 3-digit number is formed from the digits 2, 3, 5, 8 and 9, without repetition, what is the probability that it is divisible by 4?

A point source has been placed as shown in the figure. What is the length on the screen that will receive reflected light from the plane mirror?

The sum of the series $1^2+3^2+5^2+...$

$\text{The limiting value of}{\left(cosx\right)}^{1/sinx}\text{as x}\to 0is$

The angle between the line $\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}$ and the plane $10x+2y-11z=3$ is ${\cos }^{-1}\left(\frac{p}{3q}\right)-\frac{\pi }{2},$ then which of the following statement(s) is/are correct?

(where $p,q$ are relative prime, $[.]$ denotes $G.I.F.$)

If A has 4 elements and B has 6 elements, then total number of possible functions from A to B is .

The function $f\left(x\right)=\sin \frac{\pi x}{2}+2\cos \frac{\pi x}{3}-\tan \frac{\pi x}{4}$ is periodic with period

Let $C_1$ and $C_2$ be the two curves on the complex plane defined as
$C_1:z+\overline{z}=2|z-1|$
$C_2:arg(z+1+i)=\alpha$
Where $\alpha$ belongs to the interval $(0,\frac{\pi }{2})$ such that curves $C_1$ and $C_2$ have exactly one point in common and which is denoted by $P\left(z_0\right)$
The area enclosed by the curve $C_1$, $C_2$ and positive real axis is

Let $A=[a_{ij}{]}_{3\times 3}$ be a matrix such that $a_{ij}=\{\begin{array}{ccc}|i-j|,& & i>j\\ 2i+j,& & i\le j\end{array}.$ Then the value of $a_{13}+a_{31}$ is



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In a certain test there are n questions. In the test $2^{n-i}$ students gave wrong answers to at least i questions, where $i=1,2,........n$.If the total number of wrong answers given is 2047, then n is equal to

If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1, is

Let A(0,0) B(3,4) and C(6,0) be the coordinates of the triangle ABC.A point R inside the triangle is such that triangles RAB, RBC and RAC are of equal areas. Find product of coordinates of R.

If $|z_1|$ is a complex number other than -1 such that $|z_1|=1\text{and}{z}_2=\frac{z_1-1}{z_1+1}$ , then show that the real parts of $z_2$ is zero.

The eccentric angle $\theta$ of a point $(\sqrt{6}\cos \theta ,\sqrt{2}\sin \theta )$ on the ellipse $\frac{x^2}{6}+\frac{y^2}{2}=1$ whose distance from the centre of the ellipse is $2$ is