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In a school $70\%$ students like oranges and $64\%$ like apples. If $x\%$ like both oranges and apples, then

Find the equation of chord of parabola
$y^2=4x$ whose midpoint is (4, 2)

An aeroplane flying with uniform speed horizontally $1$ km above the ground is observed at an elevation of ${60}^{\circ }$ from a point on the ground. After $10$ seconds, if the elevation is observed to be ${30}^{\circ },$ then the speed of the plane $($in km/hr$)$ is

The value of \theta for which $\theta =ta{n}^{-1}\left(2ta{n}^2\theta \right)-\frac{1}{2}si{n}^{-1}\left(\frac{3sin2\theta }{5+4sin2\theta }\right)$

The domain of the function f(x) defined by
$f\left(x\right)=\frac{1}{{\log }_{10}\left(2-x\right)}+\sqrt{x+2}$is

If ${\left(\frac{x^2+2x+2}{x+1}\right)}^{2018}=a_{2018}{x}^{2018}+a_{2017}{x}^{2017}+\dots \dots +a_{1}x+a_0+\frac{b_1}{x+1}+\frac{b_2}{(x+1{)}^2}+\dots \dots +\frac{b_{2018}}{(x+1{)}^{2018}}\forall xϵR-\{-1\}then(a_i,b_iϵ\text{constant})$

Minimise
and Maximise Z = 5x + 10y

subject
to.

The value of $\underset{0}{\overset{\frac{\pi }{4}}{\int }}\log (1+\tan x)dx$ is

A line $AB$ in three dimensional space makes angles ${45}^{\circ }$ and ${120}^{\circ }$ with the positive $x$ and $y-$axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $z-$axis. Then $\theta$ equals:

If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation can be:

Find an angle $\theta$, where $0<\theta \frac{\pi }{2}$, which increases twice as fast as its sine.

If $f\left(x\right)=cosx,0\le x\le \frac{\pi }{2}$, then the real number ‘c’ of the mean value theorem is

In a box containing 100 bulbs, 10 are defective. The probability
that out of a sample of 5 bulbs, none is defective is

(A) 10⁻¹

(B)

(C)

(D)

Find the centre and radius of the circle 2x² + 2y² – x = 0

Which of these would give you the atomic number of an element?

The sum of the series 7+77+777+........of n terms is .

The period of $\left|\sin \frac{x}{2}\right|+\left|\cos (\frac{x}{4}-\frac{\pi }{6})\right|$ is

If $f\left(x\right)=\{\begin{array}{cc}\frac{x-a}{|x-a|},& -\infty <x\le 0\\ 2x^2+3bx+c,& 0<x<1\\ a^{2}x+c-2,& 1\le x<\infty \end{array}$

is a differentiable function, then

The value of $\alpha$ for which $4\alpha \underset{-1}{\overset{2}{\int }}{e}^{-\alpha |x|}dx=5$, is :

A manufacturer produces two models of bikes -,model X and model Y. Model X takes a 6 man-hours to make per unit, while model Y takes 10 man hours per unit. There is a total of 450 man-hour available per week. Handling and marketing costs are Rs 2000 and Rs 1000 per units for models X and Y, respectively. The total funds available for these purposes are Rs 80000 per week. Profits per units for models X and Y are Rs 1000 and Rs 500, respectively. How many bikes of each model should the manufacturer produce, so as to yield a maximum profit ? Find the maximum profit.

The coefficient of $x^n$ in the expansion of $(1-x)(1-x{)}^n$ is :

Find the coefficient of $x^{15}$ in $(x^3+x^6+x^9+...........)(x^2+x^4+x^6+...........)(x+x^2+x^3+..........)$

Let $A(9,-6),B(1,2)$ and $C(4,4)$ be three points on the parabola $y^2=4x.$ The equation of the circumcircle formed by the point of intersections of the tangents at $A,B$ and $C$ is $x^2+y^2+kx-ky+h=0.$ Then the value of $k+h$ is

$si{n}^{-1}x+si{n}^{-1}y+si{n}^{-1}z=\frac{3\pi }{2},$ then the value of $x^{100}+y^{100}+z^{100}-\frac{9}{x^{101}+y^{101}+z^{101}}=$

Let $S=1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+\cdots \infty .$ Then the value of $S$ is

Locus of the point given by the equations $x=\frac{2at}{1+t^2},y=\frac{a(1-t^2)}{1-t^2}(-1\le t\le 1)$ is a

If $y=\sec \left({\tan }^{-1}x\right),x\in (0,\frac{\pi }{2}),$ then $\frac{dy}{dx}$ is

What should be the relation between range and codomain of a function, for a function to be an into function -