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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 $l_{1}$, $m_{1}$, $n_{1}$ and $l_{2}$, $m_{2}$, $n_{2}$ are direction cosines of lines $L_{1}$ and $L_{2}$ respectively and $\theta$ is the acute angle between them, then :

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 :

For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true ?

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 :

The order and degree of the differential equation $1+(\frac{d^{3}y}{dx^{3}})^{3}=\lambda\frac{d^{2}y}{dx^{2}}$ 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 general solution for the differential equation $\frac{dy}{dx}=e^{3x-y}$ is:

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

Product of the order and degree of differential equation $1+(\frac{dy}{dx})^{3}=\lambda(\frac{d^{3}y}{dx^{3}})^{2}$ is: