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What do you mean by
significant figures?

Reduce
the following equations into normal form. Find their perpendicular
distances from the origin and angle between perpendicular and the
positive x-axis.

(i)
(ii)
y –
2 = 0 (iii) x –
y = 4

The $\underset{y\to a}{lim}[\left(\sin \frac{y-a}{2}\right)\cdot \left(\tan \frac{\pi y}{2a}\right)]$ is :

The sum of first three
terms of a G.P. is
and
their product is 1. Find the common ratio and the terms.

The domain of $f\left(x\right)=\sqrt{\frac{1-5^x}{7^{-x}-7}}$ is

A point $P$ moves such that three mutually perpendicular lines $PA,PB$ and $PC$ are drawn from it cutting $x,y$ and $z$ axis at $A,B\text{and}C$ respectively. The volume of tetrahedron $OABC$ is $\frac{4}{3}$ cubic units (where $O$ is the origin). If locus of $P$ is $(x^2+y^2+z^2{)}^{\mu }=(\lambda xyz)$ then which of the following is correct $(\lambda ,\mu \in R)$?

The letters of the word ZENITH are permuted and are arranged in an alphabetical order as in an English dictionary.

Then, the rank of the word ZENITH is ___

For some
constants a and b, find the derivative of

(i) (x
– a) (x – b) (ii) (ax²
+ b)² (iii)

Describe the sample space for the indicated experiment.
One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its upper most face is noted. Describe the sample space.

$\frac{\sqrt{sinA}-\sqrt{sinB}}{\sqrt{sinA}+\sqrt{sinB}}=\frac{a+b-2\sqrt{ab}}{a-b}$

If ${}^n{C}_r=84,{}^n{C}_{r-1}=36$ and ${}^n{C}_{r+1}=126$, then the value of $n$ is

If the sum of the roots of the equation a$x^2$ + bx + c = 0 is equal to the sum of the squares of their reciprocals, then $\frac{a}{c}$,$\frac{b}{a}$, $\frac{c}{b}$ are in :

The point $P(-2\sqrt{6},\sqrt{3})$ lies on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ having eccentricity $\frac{\sqrt{5}}{2}.$ If the tangent and normal at $P$ to the hyperbola intersect its conjugate axis at the points $Q$ and $R$ respectively, then $QR$ is equal to

Choose the correct answer.
${\int }_1^{\sqrt{3}}\frac{1}{1+x^2}dx$ is equal to
$\left(a\right)\frac{\pi }{3}\left(b\right)\frac{2\pi }{3}\left(c\right)\frac{\pi }{6}\left(d\right)\frac{\pi }{12}$

If f(x) = |x|, then f’(x), where x $\ne$ 0 is equal to

Let $A=\{x:x\ne 0,-4\le x\le 4\}$ and $f:A\to R$ be defined by $f\left(x\right)=\frac{|x|}{x}$, then the range of $f$ is

The area (in sq. units) of the region $A=\left\{\right(x,y):(x-1\left)\right[x]\le y\le 2\sqrt{x},0\le x\le 2\},$ where $\left[t\right]$ denotes the greatest integer function, is:

Match the following:

Given U is universal set.

A, B are subsets of U.

n(U), n(A), n(B) are no. of elements in U, A, B respectively.

Number of:

(1) Elements neither in A nor in B (A) $n(A\cup B)$

(2) Elements only in A (B)$n\left(B\right)-n(A\cap B)$

(3) Elements only in B (C)$n\left(A\right)-n(A\cup B)$

(4) Elements either in A (or) in B (D)$n\left(U\right)-n(A\cup B)$

(E)$n\left(A\right)-n(A\cap B)$

The line $12x\cos \theta +5y\sin \theta =60$ is tangent to which of the following curves?

Area bounded by the curve y = x³, the x-axis
and the ordinates x = –2 and x = 1 is

A. – 9

B.

C.

D.

A randomly selected year is containing 53 Mondays then probability that it is a leap year

$f\left(x\right)=cos\left\{\frac{\pi }{2}\right[x]-x^3\},1<x<2,and\left[x\right]=\text{the greatest integer}\le x,then{f}^{\prime }\left(3\sqrt{\frac{\pi }{2}}\right)isequalto:$

Let a quadratic function $f\left(x\right)=x^2+bx+c$ have two distinct roots $\alpha ,\beta$ and $\alpha <\beta .$ Then the maximum value of $g\left(x\right)=2f\left(x\right)+\frac{18}{f\left(x\right)}$ in $(\alpha ,\beta ),$ is

Show that the line x+y=1 touches the parabola y=x-x²

The point of inflection for the function $f\left(x\right)={\sin }^{-1}x$ is:

The function $x^x,x>0$ decreases in the interval

Let $A=\left[\begin{array}{ccc}1& 1& 1\\ 0& 1& 1\\ 0& 0& 1\end{array}\right]$. Then for positive integer $n,A^n$ is