## 1. If $p \to (\sim q \vee r)$ is false then the truth values of $p,q,r$ are

COMEDK 2012 Mathematical Reasoning

## 2. An, ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ and a parabola $y^{2} =4cx \left(c >0\right)$ are such that line joining the points of intersection coincides with the latus rectum of the parabola as well as with one of the Latus rectum of the ellipse. The eccentricity of the ellipse is

COMEDK 2005 Conic Sections

## 3. If the $2^{nd}, 5^{th}$ and $9^{th}$ terms of a non-constant $A.P.$ are in $G.P.$, then the common ratio of this $G.P.$ is :

JEE Main 2016 Sequences and Series

## 4. The value of $x$ for which $f(x) = x^3 - 6x^2 - 36x + 7$ is increasing, belong to

COMEDK 2008 Application of Derivatives

## 5. If the system of equations $x - k y - z = 0, kx - y - z = 0, x + y - z = 0$ has a non-zero solution, then possible values of k are

IIT JEE 2000 Determinants

## 6. The distance of the point $(1, -2, 4)$ from the plane passing through the point $(1, 2, 2)$ and perpendicular to the planes $x - y + 2z = 3$ and $2x - 2y + z + 12 = 0$, is :

JEE Main 2016 Three Dimensional Geometry

## 7. $\int^{1/2}_0 \frac{dx}{(1+x^2) \sqrt{1-x^2}}$ is equal to

KCET 2018 Integrals

## 8. The coefficient of $x^n$ in the expansion of $\frac{e^{7x} + e^{x}}{e^{3x}}$ is

WBJEE 2011 Binomial Theorem

## 9. Ten different letters of an alphabet are given, Words with five letters are formed from these given letters. The number of words which have at least one of their letter repeated is

IIT JEE 1980 Permutations and Combinations

## 10. The general solution of $| \sin \: x | = \cos \: x$ is (when $n \in Z$ ) given by

KCET 2008 Trigonometric Functions

## 11. A particular solution of $\frac{dy}{dx} = (x+9y)^2$ when $x = 0, y = \frac{1}{27}$ is

COMEDK 2007 Differential Equations

## 12. If the sum of distances from a point $P$ on two mutually perpendicular straight lines is $1$ unit, then the locus of $P$ is

WBJEE 2010 Straight Lines

## 13. If $x$ and $y$ are the roots of the equation $x^2 + bx + 1 = 0,$ then the value of $\frac{1}{x+b} + \frac{1}{y+b}$ is

KEAM 2017 Complex Numbers and Quadratic Equations

## 14. The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$

JEE Main 2015 Conic Sections

KEAM 2014 Sets

## 16. Mean of $n$ observations $x_{1}, x_{2}, ........ , x_{n}$ is $\bar{x}.$ If an observation $x_q$ is replaced by $x'_q$ then the new mean is

WBJEE 2017 Statistics

## 17. If the equations $x^2+2x+3=0$ and $ax^2+bx+c=0, a, b, c \in R$ have a common root, then $a : b : c$ is

JEE Main 2013 Complex Numbers and Quadratic Equations

## 18. If $|\vec{a} | = 4,|\vec{b}| = 2, |\vec{c}| = 6$ and each of the angles between the vectors is $60^\circ$, then $|\vec{a} | + |\vec{b}|+|\vec{c}| =$

COMEDK 2011 Vector Algebra

## 20. $\displaystyle\sum_{k=0}^n \frac{^nC_k}{k+1} =$

COMEDK 2008 Binomial Theorem

## 21. If ST and SN are the lengths of the subtangent and the subnormal at the point $\theta =\frac {\pi}{2}$ on the curve x = a $(\theta + Sin \theta).y=a(1-Cos\theta) a \neq 1$ ,then

KCET 2005 Application of Derivatives

## 22. Let $S$ be a set containing $n$ elements. Then, number of binary operations on $S$ is

VITEEE 2010 Relations and Functions - Part 2

## 23. Let $f(x) = 2^{100} x + 1$, $g(x) = 3^{100} x + 1$. Then the set of real numbers $x$ such that $f(g(x)) = x$ is

WBJEE 2013 Relations and Functions - Part 2

## 24. Let $F \left(x\right)=f \left(x\right)+f\left(\frac{1}{x}\right),$ where $f(x)=\int\limits^{x}_{{1}}$$\frac{log\,t}{1+t}dt$. Then $F(e)$ equals

AIEEE 2007 Integrals

## 25. A solution of $y" - xy' + y + 4 = 0$ is

COMEDK 2011 Differential Equations

## 26. The two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 = 2$

KCET 2016 Application of Derivatives

## 27. The derivative of $\sin x^{\circ} \, \, \cos x$ with respect to $x$ is

COMEDK 2008 Statistics

## 28. The functions $f , g$ and $h$ satisfy the relations $f ^{'}\left(x\right)=g\left(x+1\right)$. Then $f ^{"}\left(2x\right)$ is equal to

KEAM 2015 Continuity and Differentiability

## 29. The domain of definition of the function $y = \frac{1}{\log{10} ( 1 -x)} + \sqrt{x + 2}$ is

JEE Advanced 1983 Relations and Functions

## 30. The statement $P(n) : 1\times1!+2\times2!+3\times3! + ... + n \times n ! = (n + 1)! - 1$ is.

Haryana PMT 2005 Principle of Mathematical Induction