# Q. Domain of definition of the function $f(x)=\frac{3}{4-x^2}+ \log_{10}(x^3-x)$

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## 1. For $r = 0, 1, ... , 10,$ if $A_r,B_r$ and $C_r$ denote respectively the coefficient of $x^r$ in the expansions of $(1 + x)^{10}, (1 + x)^{20}$ and $(1 + x)^{30}$. Then, $\displaystyle \sum A_r(B_{10}B_r-C_{10}A_r)$ is equal to

IIT JEE 2010 Binomial Theorem

## 2. Let $\omega \ne 1$ be a cube root of unity and S be the set of all non-singular matrices of the form $\begin {bmatrix} 1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1 \end {bmatrix}$ where each of a , b and c is either $\omega \ or \ omega^2$ Then, the number of distinct matrices in the set S is

IIT JEE 2011 Determinants

## 3. Perpendicular are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}= \frac{z}{3}$ to the plane $x+ y + z = 3$. The feet of perpendiculars lie on the line

JEE Advanced 2013 Introduction to Three Dimensional Geometry

## 4. A ray of light along $x+\sqrt 3 \, y=\sqrt 3$ gets reflected upon reaching X-axis, the equation of the reflected ray is

JEE Main 2013 Straight Lines

## 5. A ray of light along $x+\sqrt 3 \, y=\sqrt 3$ gets reflected upon reaching X-axis, the equation of the reflected ray is

JEE Main 2013 Straight Lines

## 6. A ray of light along $x+\sqrt 3 \, y=\sqrt 3$ gets reflected upon reaching X-axis, the equation of the reflected ray is

JEE Main 2013 Straight Lines

## 7. The centre of the circle passing through the point (0, 1)and touching the curve $y = x^2 at (2,4)$ is

IIT JEE 1983 Conic Sections

## 8. Let AB be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then, the locus of the centroid of the $\Delta PAB$ as P moves on the circle, is

IIT JEE 2001 Conic Sections

## 9. The integral $\int^{\pi/2}_{\pi/4} ( 2 \, cosec \, x )^{17} \, dx$ is equal to

JEE Advanced 2014 Integrals

## 10. The coefficient of $x^n$ in expansion of $(1+ x)(1- x)^n$ is

AIEEE 2004 Binomial Theorem