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Which of the following is the average rate of change of f(x) with respect to x over the interval
[a, a+h]?

1. 45

${lim}_{x\to 3}\frac{x-3}{|x-3|},$ is equal to

In throwing a die, let $A$ be the event 'an odd number turns up', $B$ be the event 'a number divisible by $3$ turns up' and $C$ be the event 'a number $\le 4$ turns up', then the probability that at least one of events $A,B,C$ occur is :

If $a_1,a_2,\dots \dots a_n$ are positive real numbers whose product is a fixed number c, then the minimum value of $a_1+a_2+\dots \dots +a_{n-1}+2a_n$ is

If a vector $\overrightarrow{AB}=2\hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{OB}=3\hat{i}-4\hat{j}+4\hat{k},$ then the position vector $\overrightarrow{OA}$ is

Let $A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$

Find the value of the following:
BA

If $7^{103}$ is divided by 25 then the remainder is ___

If the area bounded by the curves $y=\left[k\right]x^2,y=\frac{\left[k\right]}{4}{x}^2$ and $2\le |x|\le 3$ is $19$, then $k$ lies in

(where [.] represent greatest integer function)

The sub-tangent at any point of the curve $x^m.y^n=a^{m+n}$ varies as

The equation of the line AB is y = x. If A and B lie on the same side of the line mirror 2x – y = 1, then the equation of the image of AB is

The determinant $\left|\begin{array}{ccc}\sin A& \cos A& \sin A+\cos B\\ \sin B& \cos A& \sin B+\cos B\\ \sin C& \cos A& \sin C+\cos B\end{array}\right|$ is equal to

A letter is chosen at random. The probability that it is the letter of the word 'RANDOM' is

The coordinates $(x_0,y_0)$ of the point on the line $y=x+2$ which is close to the parabola $y^2=4ax$ is :

The solution set of ${\log }_3(x^2-2)<{\log }_3(\frac{3}{2}|x|-1)$ contains

The slope
of a line is double of the slope of another line. If tangent of the
angle between them is,
find the slopes of he lines.

If $(1+i{)}^i$ = A+iB. Find the value of ${log}_e$(A+iB)

Evaluate $\int \frac{\mathrm{dx}}{x^2-x+1}$

Equation of the hyperbola whose vertices are $(\pm 3,0)$ and foci at $(\pm 5,0)$ is

The value of $co{s}^{-1}\left(cos\frac{5\pi }{3}\right)+si{n}^{-1}\left(cos\frac{5\pi }{3}\right)$ is

The above figure is the graph of a continuous and differentiable function y = f(x). Between point A & B the function has its derivative zero at how many points -

On which
of the following intervals is the function f given by

strictly decreasing?

(A) (B)

(C) (D) None
of these

Evaluatef(x),
where f(x) =

The value of $\left|\begin{array}{ccc}0& x{y}^2& x{z}^2\\ x^{2}y& 0& y{z}^2\\ x^{2}z& z{y}^2& 0\end{array}\right|$ is equal to

Out of 9 pins, 6 pins have fallen out. pins remain.

Let
and.
Find a vector
which
is perpendicular to both
and,
and.

A line passing through $P(2,-3)$ is making an angle ${135}^{\circ }$ in anticlockwise direction with $x-$ axis and is intersecting another line $x+2y-3=0$ at $Q$. Then the length of $PQ$ is

Let $\overrightarrow{a}=\hat{i}+\hat{j}+2\hat{k}$ and$\overrightarrow{b}=-\hat{i}+2\hat{j}+3\hat{k}$. Then the vector product $(\overrightarrow{a}+\overrightarrow{b})\times \left(\right(\overrightarrow{a}\times \left(\right(\overrightarrow{a}-\overrightarrow{b})\times \overrightarrow{b}))\times \overrightarrow{b})$ is equal to

A straight line L through the point (3, -2) is inclined at an angle ${60}^{\circ }$ to the line $\sqrt{3}x+y=1$. If L also intersects the X-axis, then the equation of L is