Paper Generator

Check whether $f:R-\{3\} \rightarrow R$ defined as $f(x)=\frac{x-2}{x-3}$ is onto or not.

A box contains 4 red, 5 blue and 1 green marble. A child randomly takes out a marble from the box, notes down the colour and puts it back in the box. If the activity is repeated 3 times, what is the probability that at least one marble is red?

If $3P(A)=P(B)=\frac{3}{5}$ and $P(A|B)=\frac{2}{3}$ then $P(A\cup B)$ is:

For two events A and B such that $P(A) \ne 0$ and $P(B) \ne 1$, $P(A^{\prime}/B^{\prime})=$

If E and F are two independent events such that $P(E)=\frac{3}{10}$, $P(E\cup F)=\frac{1}{2}$ then $P(E|F)-P(F|E)$ is equal to:

The corner points of the feasible region determined by the system of linear constraints are (0,0), (0, 40), (20, 40), (60, 20) and (60, 0). If the objective function of an LPP is $Z=4x+3y$, then the maximum value is :

Direction ratios of lines $l_{1}$ and $l_{2}$ are <12,-3, 9> and <4, q,-p> respectively. The values of p and q for which $l_{1}$ and $l_{2}$ are parallel are respectively:

Direction cosines of the line given by equations $\frac{2x-1}{4}=\frac{1-y}{3}=\frac{-z}{6}$ are

If points $(2, 3)$, $(0, 4)$ and $(p, 2)$ are collinear, then the value of p is:

If $(3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0}$ then the values of p and q are :

If $(\vec{a}+\vec{b}).(\vec{a}-\vec{b})=198$ and $|\vec{a}|=10|\vec{b}|$, then :

Vector of magnitude 3 making equal angles with x and y axes and perpendicular to z axis is

Three points $A(0,1,1)$, $B(2,0,-1)$ and $C(1,0,3)$ form $\Delta ABC$. The ar ($\Delta ABC$) is:

If position vector $\vec{p}$ of a point (24, n) is such that $|\vec{p}|=25$, then the value of n is:

If $|\vec{a}|=5$ and $-2 \le \lambda \le 1$ then the sum of greatest and the smallest value of $|\lambda\vec{a}|$ is

If vectors $\vec{a}=3\hat{i}+2\hat{j}+\lambda\hat{k}$ and $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$, represent the two strips of the Red Cross sign placed outside a doctor's clinic, then the value of $\lambda$ is :

$\frac{dy}{dx}=F(x,y)$ will be a homogeneous differential equation for which of the following functions? (i) $F(x,y)=3x+2y$ (ii) $F(x,y)=\sin\frac{y}{x}+\log y-\log x$ (iii) $F(x,y)=e^{y/x}+1$ (iv) $F(x,y)=\sqrt{x^{2}+y^{2}}-y$

Which of the following is not a Linear Differential Equation?

The integrating factor of the differential equation $2x\frac{dy}{dx}-y=3$ is

The general solution of the differential equation $\frac{dy}{dx}=\frac{\sqrt{y}}{\sqrt{x}}$ is