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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

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

An ant is observed crawling on a sheet of paper along a straight line given by equation $y=2x-4$. Area of the surface covered by the ant bounded by y-axis, x-axis and $x=1$ is :

The area of the shaded region of the circle given below is equal to :

Which of the following expressions will give the area of region bounded by the curve $y=x^{2}$ and line $y=16$?

If $\int_{0}^{2a}\frac{1}{1+4x^{2}}dx=\frac{\pi}{6}$, then the value of a is

$\int_{-1}^{1}(1-|x|)dx$ is equal to:

If $\int_{0}^{1}\frac{dx}{e^{x}+e^{-x}}=\tan^{-1}e+k$, then the value of k is:

$\int\frac{dx}{2^{x}+2^{-x}}$ is equal to:

For $f(x)=x+\frac{1}{x} (x \ne 0)$

The rate of change of volume of a sphere with respect to its diameter, when its radius is 5 cm, is:

The surface area of a sphere when its volume changes at the same rate as its radius is :