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2x + 3y = 5
3x - 3y = 10
Which of the following best describes the solution set to the equation shown above?

If one root is square of the other root of the equation $x^2+px+q=0$, then the relation between p and q is

If the solution set of $|2x-1|+|3x-4|=|5x-5|$ is $x\in (-\infty ,p]\cup [\frac{4}{3},\infty )$, then the value of $p$ is

Why is sinx not equal to zero in Pythagorean identities

In $\Delta ABC,$ the median AD divides $\angle BAC$ such that $\angle BAD:\angle CAD=2:1.$ then $cos\frac{A}{3}$ is equal to

A factory has $80$ workers and $3$ machines. Each worker knows to operate at least two machines. If there are $65$ persons who know to operate machine $\text{I}$, $60$ for machine $\text{II}$ and $55$ for machine $\text{III}$, what can be the minimum number of persons who know to operate all the three machines ?

The equation of the straight line which passes through the intersection of the lines $x+2y=5$ and $3x+7y=17$ and is perpendicular to the line $3x+4y=14$ is

The coefficient of $x^5$ in the expansion of $(1+x^2{)}^5(1+x{)}^4$ is

${lim}_{x\to 0^{+}}xlo{g}_{e}x$ will be equal to ___

The equation of the line passing through the point $(c,d)$ and parallel to the line $ax+by+c=0$, is

There are 15 chocolates be distributed among 3 children subject to condition that child can take any number of chocolates. Find the required number of ways to do this if chocolates are distinct.

There are two friends Ram and Sandeep. Ram has x different physics books and Sandeep has y different mathematics books. Find the number of ways in which Ram and Sandeep can exchange their books in such a way that after exchanging they still have same number of books but not the same set.

if alpha = 5/(2!×3) + (5×7)/(3!×3^2) + (5×7×9)/(4!×3^3) + ............, then alpha^2 + 4×alpha =

A) 21 B) 23 C) 25 D) 27

From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done ?

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a student qho look by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation ?

If $\cos 3x\cos 2x\cos x=\frac{1}{4}$ and $0<x<\frac{\pi }{4},$ then the value of $x$

$y=4sin3x$ is a solution of the differential equation

[AI CBSE 1986]

Consider a plane $x+y-z=1$ and point $A(1,2,-3).$ A line $L$ has the equation $x=1+3r,y=2-r$ and $z=3+4r.$

The equation of the plane containing line $L$ and point $A$ has the equation

$sin{6}^{\circ }sin{42}^{\circ }sin{66}^{\circ }sin{78}^{\circ }=\frac{1}{16}$

If $f\left(x\right)=4x-x^2,x\in R$, then $f(a+1)-f(a-1)$ is equal to

Two sides of an isosceles triangle are given by the equations $7x-y+3=0$ and $x+y-3=0$ and its third side passes through the point (1, -10). Determine the equation of the third side.

The distance of the point (2, 3) from the line 3x + 2y = 17, measured parallel to the line x – y = 4 is

Differentiate between standing and single use plans.

If $I={\int }_0^{1}x\sqrt{\frac{1-x}{1+x}}dx$, the I equals

If $\frac{(1+4p)}{4},\frac{(1-p)}{2},\text{and}\frac{(1-2p)}{2}$ are the probabilities of three mutually exclusive events , then the value of p is

The value of $cos\left(\frac{1}{2}co{s}^{-1}\left(\frac{1}{8}\right)\right)$ is

Given points A(3,9), B(4,8),C(5,7)

$\begin{array}{cc}\text{Line segment}& \text{Length of line segment(unit)}\\ \text{1.AB}& \text{P.}\sqrt{2}\\ \text{2.BC}& \text{Q.1}\\ \text{3.CA}& \text{R.2}\sqrt{2}\end{array}$

Find the total number of ways in which 20 bails can be put into 5 boxes so that first box contains just one ball.

How many lower case VOWELS are followed by a number?

If the lines 2x + y- 3 = 0, 5x + ky – 3 = 0 and 3x – y – 2 = 0 are concurrent,then the value of k is

Let $f\left(x\right)=\{\begin{array}{cc}\frac{1}{|x|}:& |x|\ge 1\\ a{x}^2+b:& |x|<1\end{array}$ be continuous and differentiable every where. Then a and b are:

How many structures of F are possible ?

If $\overrightarrow{b}$ and $\overrightarrow{c}$ are non-zero and non-collinear vectors, $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})+(\overrightarrow{a}\cdot \overrightarrow{b})\overrightarrow{b}$$=(4-2x-\sin y)\overrightarrow{b}+(x^2-1)\overrightarrow{c}$ and $(\overrightarrow{c}\cdot \overrightarrow{c})\overrightarrow{a}=\overrightarrow{c}$. Then,

Let $A=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right]\text{and}B=A^{20}.$Then the sum of the elements of the first column of $B$ is:

If the equation of the lines passing through point $(1,1)$, one making an angle $\theta$ with the positive direction of $x-$axis and the other making the same angle with the positive direction of $y-$axis, is $x^2-(a+2)xy+y^2+a(x+y-1)=0,a\ne -2,$ then the value of sin $2\theta$ is

Two different number are taken from the $0$ to $10$. The probability that their sum and positive differences are both multiple of $4$ is

Let $f:R\to R,g:R\to R$ and $h:R\to R$ be differentiable functions such that $f\left(x\right)=x^3+3x+2,g\left(f\right(x\left)\right)=x$ and $h\left(g\right(g\left(x\right)\left)\right)=x$ for all $x\in R.$ Then

If from a point $P$, $3$ normals are drawn, to parabola $y^2=4ax$. Then the locus of $P$ such that three normals intersect the $x-$ axis at points whose distances from vertex are in $A.P.$ is

Let $z_1,z_2$ be two complex numbers such that $z_1+z_2$ and
$z_1{z}_2$ both are real , then