## 1. The equation of the tangent to the curve $x" + y" = ·2a,$, at $(a, a)$ is

COMEDK 2007 Statistics

## 2. $\int\limits_{0}^{1} \left(x^{4} +2x^{2} +1\right)d\left(x^{2} + 1\right)=$

COMEDK 2010 Inverse Trigonometric Functions

## 3. A line makes the same angle $\theta$ with each of the x-and z-axis. If the angle $\beta$, which it makes with y-axis is such that $\sin^2$ $\beta$ = 3 $\sin^2$ $\theta$, then $\cos^2 \theta$ =

AIEEE 2004 Introduction to Three Dimensional Geometry

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

Haryana PMT 2005 Principle of Mathematical Induction

## 5. The number of proper subsets of a set having $n + 1$ elements is

COMEDK 2014 Relations and Functions - Part 2

COMEDK 2015 Sets

## 7. If $A = \begin{bmatrix}1&0\\ 1&1\end{bmatrix}$ and $A^8 = aA +bI,$ then $(a , b) =$

COMEDK 2015 Matrices

## 8. The domain of the function $y = \sqrt{x-2} + \sqrt{1 -x}$ is

COMEDK 2014 Relations and Functions - Part 2

## 9. The maximum area of a rectangle that can be inscribed in a circle of radius 2 units is ______

KCET 2013 Application of Derivatives

## 10. The solution of $\frac{dy}{dx} - 1 = e^{x-y}$ is

COMEDK 2012 Differential Equations

## 11. The circle passing through the point (-1,0) and touching the Y-axis at (0, 2) also passes through the point

IIT JEE 2011 Conic Sections

## 12. The number of edges in a complete graph $K_{15}$ is

COMEDK 2006 Probability - Part 2

## 13. The general solution of the equation $\sin^2 \theta \sec\theta + \sqrt{3} \tan \theta = 0$ is

COMEDK 2007 Application of Integrals

## 14. $\left(\frac{-1 +i\sqrt{3}}{2}\right)^{50} + \left(\frac{-1 - i\sqrt{3}}{2}\right)^{50} =$

COMEDK 2010 Complex Numbers and Quadratic Equations

## 15. If y is a function of x and $\log (x + y) = 2xy$, then the value of y ' (0) is

IIT JEE 2004 Continuity and Differentiability

## 16. The contrapositive of "If $x \in A \cap B$, then $x \in A$ and $x \in B$ " is

COMEDK 2008 Mathematical Reasoning

## 17. $Lt_{x\rightarrow0} \frac{xa^{x} -x}{1 -\cos x}$ is equal to

COMEDK 2014 Statistics

## 18. $\displaystyle\int_{\pi/4}^{3\pi/4}\frac{dx}{1+\cos\,x}$ is equal to

IIT JEE 1999 Integrals

## 19. Consider three points $P=\{-\sin \, (\beta - \alpha )-\cos \, \beta \}, Q=\{\cos (\beta -\alpha ),\sin \, \beta \}$ and $R=\{\cos (\beta -\alpha + θ)sin (\beta-θ) \},$ where $0<\alpha ,\beta , θ< \frac {\pi}{4}.$ Then,

AIEEE 2008 Straight Lines

## 20. The slopes of the tangent and normal at (0, 1) for the curve $y = \sin x + e^x$ are respectively

COMEDK 2010 Statistics

## 21. If a is a parameter then a equ tion of a family of lines having the sum of the intercepts on axes equal to 7 is

COMEDK 2014 Straight Lines

## 22. Three of the six vertices of a regular hexagon are chosen at rondom. The probability that the triangle with three vertices is equilateral, equals

IIT JEE 1995 Probability

## 23. Identify the false statement

COMEDK 2012 Probability - Part 2

## 24. 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

## 25. A hyperbola, having the transverse axis of length $2 \sin\theta$ is confocal with the ellipse $3x^2+4y^2=12$. Then, its equation is

IIT JEE 2007 Conic Sections

## 26. For $0<\theta<\pi, if\,A=\begin{bmatrix} \cos\,\theta& -\sin\,\theta \\[0.3em] \sin\,\theta & \cos\,\theta \end{bmatrix}$ then

J & K CET 2009 Matrices

## 27. $\sin10^{\circ} +\sin 20^{\circ }+\sin 30^{\circ }+...+\sin360^{\circ } =$

COMEDK 2011 Application of Integrals

## 28. The value of the determinant $\begin{vmatrix} 1+\log\,a & \log\,b &\log\,c \\[0.3em] \log\,a & 1+\log\,b & \log\,c\\[0.3em] \log\,a & \log\,b & 1+\log\,c \end{vmatrix}$ is equal to

J & K CET 2010 Determinants

## 29. If $e_1$ and $e_2$ are the eccentricities of hyperbola and ii ts conjugate, then $\frac{1}{e_1^2} + \frac{1}{e^2_2} =$

COMEDK 2010 Conic Sections

## 30. The slant height of a cone is fixed at 7 cm. If the rate of increase of its height is 0.3 cm/sec, then the rate of increase of its volume when its height is 4 cm is

COMEDK 2015 Differential Equations