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If the value of $\underset{x\to -2}{lim}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$ is $k$, then find the value of $4k$

The mean deviation of the numbers 3, 4, 5, 6, 7 from the mean is

The equation of the plane x + 3y + 6z- 9 = 0 in the intercept form is:

The value of $\sqrt{36.6}$ is

The value of $\underset{x\to 0}{lim}\frac{\sqrt{3+x}-\sqrt{3}}{x}$ is

If $0\le x<2\pi$ , then the number of real values of x, which satisfy the equation $\cos x+\cos 2x+\cos 3x+\cos 4x=0$, is

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are vectors such that $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt{29}$ and $\overrightarrow{a}\times (2\hat{i}+3\hat{j}+4\hat{k})=(2\hat{i}+3\hat{j}+4\hat{k})\times \overrightarrow{b},$ then a possible value of $(\overrightarrow{a}+\overrightarrow{b}).(-7\hat{i}+2\hat{j}+3\hat{k})$ is

In binomial probability distribution, mean is 3 and standard deviation $\frac{3}{2}$is

The plane ax+by =0 is rotated through an angle $\alpha$ about its line of intersection with the plane z=0. Then the equation of the plane in the new position is

A bag contains some white and some black balls, all combinations of balls being equally likely. The total number of balls in the bag is 10. If three balls are drawn at random without replacement and all of them are found to be black, the probability that the bag contains 1 white and 9 black balls is

The $x$-intercept of the tangent to a curve is twice the ordinate of the point of contact. The equation of the curve through the point $(1,1)$ is

Let $S(3,4)$ and $S^{\prime }(9,12)$ be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus $S$ to a tangent of the ellipse is $(1,-4),$ then the eccentricity of the ellipse is

Let $f\left(x\right)$ be a non-negative function. If $f^{\prime }\left(x\right)\cos x\le f\left(x\right)\sin x,\forall x\ge 0,$ then value of $f\left(\frac{5\pi }{3}\right)$ is

An experiment consists of tossing a coin and then throwing it second times if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

If the line $y=11x+(b-4)$ passes through the origin, then the value of $b$ is

The solution set of $\frac{1}{x-1}+\frac{1}{x+1}\le \frac{1}{x}$ is

In a random sampling three items are selected from a lot. Each item is tested and classified as defective (D) or non-defective (N).Write the sample space of this experiment.

Let $f:[a,\infty )\to [a,\infty )$ be defined by $f\left(x\right)=x^2-2ax+a(a+1)$. If one of the solutions of the equation $f\left(x\right)=f^{-1}\left(x\right)$ is $5049$, then the other solution can be

Let $A=\{xϵR:x\ne 0,-4\le x\le 4\}$ and $f:A\to R$ be defined $f\left(x\right)=\frac{|x|}{x}$ for $xϵA$. Then A is

The sum of three distinct positive real numbers in geometric progression is $x$ times the middle term, then the value of $x$ lies in the set

Let $A(6,-5)$ and $B(-6,1)$ be the two vertices of the triangle $ABC$, if the locus of centroid of $△ABC$ is $2x+5y=1$, then the locus of vertex $C$ is

Let $A$ and $B$ be two sets defined as $A=\{x:x\in W\text{and}-1\le \frac{2x+3}{5}\le 3\}$ and $B=\{x:x\in Z\text{and}0\le \frac{3-x}{7}\le 1\}$. If $P=A-B$ and $Q=B-A$, then the value of $n(P\times Q)$ is

$\int si{n}^{-\frac{11}{3}}\left(x\right).co{s}^{-\frac{1}{3}}\left(x\right)dx$

The distance between the planes 3x - 2y + 6z + 21 = 0 and - 6x + 4y - 12z + 35 = 0 is:

Locus of the feet of the perpendicular drawn from focus of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ upon any tangent is _____

The sum of $x-$intercept and $y-$intercept of the common tangent to the parabola $y^2=16x$ and $x^2=128y$ is

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person like atleast one of the two drinks. The number of persons liking both coffee and tea is

If$\overrightarrow{u}=3\hat{i}-5\hat{j}+9\hat{k}and\overrightarrow{v}=3\hat{i}+4\hat{j}+0\hat{k}$ , then the component of u along the direction of v is

The equation of the parabola whose focus is $(-6,-6)$ and vertex is $(-2,2),$ is

The number of natural solutions of the equation $xyz=2^5\times 3^2\times 5^2$ is

If $x+1<4$ and $y-2<-1$, then which of the following can be a value of x + y?

If $a$ and $b$ are arbitary positive real numbers, then the least possible value of $\frac{6a}{5b}+\frac{10b}{3a}$ is

If sin $\theta$ + cos $\theta$ = a, cos $\theta$ - sin $\theta$ = b, then sin $\theta$ (sin $\theta$ - cos $\theta$ ) + $si{n}^2\theta (si{n}^2\theta -co{s}^2\theta )+si{n}^3\theta (si{n}^3\theta -co{s}^3\theta )$+ . . .. . is equal to

A straight line passing through the point A(–2, –3) cuts the line x + 3y = 9 and x + y + 1 = 0 at B and C respectively. If AB.AC = 20, then equation of line can be

If $x$ = $2+2^{\frac{2}{3}}+2^{\frac{1}{3}}$, then $x^3-6x^2+6x$ =

If a ray of light passing through $(2,2)$ reflects on the $x-$axis at a point $P$ and the reflected ray passes through the point $(6,5)$, then the co-ordinates $P$ is