## 1. The volume of parallelopiped whose adjacent sides are $\vec{a} = \hat{i} + 2 \hat{j}, \vec{b} = \hat{j} + 2 \hat{k} , \vec{c} = 2 \hat{i} - \hat{k}$ is

COMEDK 2006 Three Dimensional Geometry

## 2. If the system of linear equations x + 2ay + az = 0 ; x + 3by + bz = 0 ; x + 4cy + cz = 0 has a non-zero solution, then a, b, c.

AIEEE 2003 Determinants

## 3. $If\ f(x)=\begin{vmatrix}1 & x & x+1\\2x & x ( x - 1) & (x + 1) x\\3x(x-1) & x ( x - 1 ) ( x - 2 ) & ( x+ 1 ) x ( x - 1 )\\ \end{vmatrix},$ then f (100) is equal to

IIT JEE 1999 Determinants

## 4. Which of the following is NOT true?

KCET 2010 Mathematical Reasoning

## 5. If $\vec{a}$ and $\vec{b}$ are two vectors of magnitude 2, each inclined at an angle 60°, then angle between $\vec{a}$ and $\vec{a} +\vec{b}$ is

COMEDK 2014 Vector Algebra

## 6. $\lim_{x \to 0} \dfrac {\log_e(1+x)}{3^x-1}$ =__________

KCET 2013 Limits and Derivatives

## 8. The number $( \sqrt{5} + 2)^{1/3} - ( \sqrt{5 } - 2)^{1/3}$ is

COMEDK 2005 Probability - Part 2

## 9. If $a > 2b > 0,$ then positive value of m for which $y = mx - b \sqrt{1+m^2}$ is a common tangent to $x^2 + y^ 2 = b^2$ and $(x - a)^2 + y^ 2 = b^2$ is

IIT JEE 2002 Conic Sections

## 10. The number of common tangents to the circles $x^2+y^2=4$ and $x^2+y^2-6x-8y-24=0$ is

KCET 2007 Conic Sections

## 11. If A is any square matrix of order 3$\times$3 then |3A| is equal to

KCET 2016 Determinants

## 12. If $y = y(x) \,$ and $\, \dfrac {2+\,sinx}{y+1} \bigg ( \dfrac {dy}{dx} \bigg) = -\cos \, x, y(0)=1,$ then $y \bigg ( \dfrac {\pi}{2} \bigg )$ equals

AIEEE 2004 Differential Equations

## 13. The angle of elevation of the top of a tower from the top and bottom of a building of height $'a'$ are $30°$ and $45°$ respectively. If the tower and building stand at the same level, the height of the tower is

COMEDK 2008 Probability - Part 2

## 14. The number of common tangents to the circles $x^2+y^2=4$ and $x^2+y^2-6x-8y=24$ is

AIEEE 1998 Conic Sections

## 15. The intercepts on x-axis made by tangents to the curve, $y = \displaystyle\int_0^x |t| dt, x \in R$, which are parallel to the line $y = 2x$, are equal to

COMEDK 2013 Inverse Trigonometric Functions

## 16. If Z is a complex number with I Z I = 1 and $Z + \dfrac{1}{Z} = x + iy$, then $xy =$

COMEDK 2008 Complex Numbers and Quadratic Equations

## 17. For any vector $\vec{a}$ $\hat{i} \times (\vec{a} \times \hat{i} ) + \hat{j} \times (\vec{a} \times \hat{j} ) + \hat{k} \times (\vec{a} \times \hat{k} )$

COMEDK 2010 Vector Algebra

## 18. If the slope of one of the lines given by $ax^2 + 2hxy + by^2 = 0$ is 5 times the other, then

COMEDK 2006 Straight Lines

## 19. If $i,j, k$ are unit vectors along the positive direction of $X-, Y-$ and $Z-$axes, then a FALSE statement in the following is...............

KCET 2010 Vector Algebra

## 20. If $y = Tan^ {-1} \dfrac {{\sqrt{ 1+x^2}}-{\sqrt {1-x^2}}} {{\sqrt {1+x^2}}-{\sqrt {1-x^2}}}$ then $\dfrac {dy} {dx}$ is equal to ......

KCET 2005 Continuity and Differentiability

## 21. $\int \dfrac{x^{2}+1}{x^{4}+1}dx$

COMEDK 2009 Inverse Trigonometric Functions

## 22. The solution of the differential equation, $\dfrac{dy}{dx} = \dfrac{y}{x}+\dfrac{g\left(y /x\right)}{g'\left(y / x\right)}$, where g is a differentiable function is

COMEDK 2005 Differential Equations

## 23. The derivative of $\tan^{-1} \left(\dfrac{\sqrt{1+x^{2}} -1}{x}\right)$ with respect to $\cos^{-1}\left(\sqrt{\dfrac{1+\sqrt{1+x^{2}}}{2+\sqrt{1+x^{2}}}}\right)$ is

COMEDK 2011 Statistics

## 24. The converse of the contrapositive of the conditional $p \to \sim q$ is

KCET 2008 Mathematical Reasoning

## 25. The function $f(x) = \dfrac{\tan \{\pi [x - \dfrac{\pi}{2} ] \}}{2 + [x]^2}$ , where [x] denotes the greatest intege $\le x$, is

WBJEE 2014 Limits and Derivatives

## 26. $\int \dfrac {\sin \,2x}{\sin^2x +2 \,\cos^2x}dx$ =

KCET 2014 Integrals

## 27. The logically equivalent proposition of $p \Leftrightarrow q$ is

KCET 2001 Mathematical Reasoning

## 28. If $= \overrightarrow{a} (\widehat{i} + \widehat{j} + \widehat{k}) , \overrightarrow{a} . \overrightarrow{b} + = 1$ and $= \overrightarrow{a} \times \overrightarrow{b} = \widehat{j} - \widehat{k}$ then $\overrightarrow{b}$ is equal to

IIT JEE 2003 Vector Algebra

## 29. Consider an infinite geometric series with first term ‘a’ and common ratio ‘r. If the sum is 4 and the second term is 3/4, then

KCET 2014 Sequences and Series

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

COMEDK 2012 Mathematical Reasoning