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There are $4$ horizontal and $6$ vertical equi-spaced lines. If a rectangle is randomly selected, then the probability that it is a square is

If the foot of the perpendicular of a point $P(2,-3,1)$ with respect to line L is $(\frac{-22}{7},\frac{-3}{14},\frac{-13}{14})$, then the coordinates of it's image $I$ is .

The equation $x^{\frac{3}{4}(lo{g}_{2}x{)}^2+lo{g}_{2}x-\frac{5}{4}}=\sqrt{2}$ has

The expression $E=\frac{cotA-cosA}{cotA+cosA}$ is the same in value in which of the following expressions?

Angle between the curves $x^{2}y=1-y$ and $x^3=2(1-y)$ is

Which of the following is the graph of sgn (x), where sgn (x) represents the signum function?

Given that she does not achieve success, the probability she studied for 4 hours is

$\alpha ,\beta ,\gamma$ are real numbers satisfying $\alpha +\beta +\gamma =\pi$.

The value of the given expression

$sin\alpha +sin\beta +sin\gamma$ is

Let $f\left(x\right)=x^3-3x^2+3x+1$ and g be the inverse of f. Then area bounded by y = g(x) and the x-axis from x = 1 to x = 2 is

If slope of tangent at atleast one point to the curve $y=x^3+3a{x}^2+3x+7$ is negative, then

If A,B,C are square matrices of the same order, $(ABC{)}^{-1}$ is equal to

The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x=8 cm and y=6 cm, find the rate of change of the area of the rectangle.

If P, Q, R, S are the points (4, 5, 3) (6, 3, 4), (2, 4, -1), (0, 5, 1) the length of projection RS and PQ is

1. -1.25

Verify mean value theorem for function 3x^2-5x+1 defined in interval [2,5]

If A + B = ${45}^{\circ }$, find tanA + tanB

The range of $f\left(x\right)={\sin }^{2}x-2\sin x$ is

A biased ordinary die is loaded in such a way that probability of getting an even outcome is five times the probability of getting an odd outcome. This die is rolled two times. The probability that the sum of outcome will be a prime number, is equal to

Solve the following system of equations in R.

$5x-7<3(x+3),1-\frac{3x}{2}\ge x-4$

In a single throw of two dice, find the probability of obtaining 'a total of $8$'.

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form $7^m+7^n$ is divisible by 5 equals

Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.

1. -69.5

If the coefficients of $T_r,T_{r+1},T_{r+2}$ terms of $(1+x{)}^{14}$ are in A.P., then r =

Suppose $f$ is differentiable function such that $f\left(g\right(x\left)\right)=x^2$ and $f^{\prime }\left(x\right)=1+\left(f\right(x){)}^2$. Then the value of $g^{\prime }\left(2\right)$ is

If $\underset{a}{\overset{b}{\int }}|\sin x|dx=8$ and $\underset{0}{\overset{a+b}{\int }}|\cos x|dx=9$, then the value of $\underset{a}{\overset{b}{\int }}x\sin xdx$ is

If the numbers be in G.P., then their logarithms will be in

A curve is represented parametrically by the equations $x=f\left(t\right)=a^{\ln \left(b^t\right)}$ and $y=g\left(t\right)=b^{-\ln \left(a^t\right)};a,b>0$ and $a\ne 1,b\ne 1$ where $t\in R$.



The value of $\frac{d^{2}y}{d{x}^2}$ at the point where $f\left(t\right)=g\left(t\right)$ is

In a given standrard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.What is the length of transverse axis?