Mathematics Question and Answers

1. If the distance of the point $P (1, - 2,1)$ from the plane $x + 2y - 2z = a$, where $a > 0$, is 5, then the foot of the perpendicular form $ P$ to the plane is

IIT JEE 2010 Introduction to Three Dimensional Geometry

2. The general solution of the differential equation $(e^x + 1)y dy = (y + 1)e^x \,dx$ is

COMEDK 2006 Differential Equations

3. A line $I$ passing through the origin is perpendicular to the lines
$l_1 : (3+t)\hat{i} + (-1 + 2t)\hat{j} + (4 + 2t)\hat{k}, - \infty < t< \infty$
$l_2 : (3 + 2s)\hat{i} + (3 + 2s)\hat{j} + (2 + s) \hat{k} , - \infty < s < \infty$
Then, the coordinate(s) of the point(s) on $l_2$ at a distance of $\sqrt{17}$ from the point of intersection of $l$ and $l_1$ is (are)

JEE Advanced 2013 Three Dimensional Geometry

4. Negation of the statement $p$ : for every real number, either $x \geq$ or $x < 1$ is

AIEEE 2010 Mathematical Reasoning

5. The value of $\int \frac{10^{x 2}}{\sqrt{10^{-x} - 10^{x}}}dx$ is

COMEDK 2009 Inverse Trigonometric Functions

6. For $x \in R, \lim_{x \to\infty} \left(\frac{x-3}{x+2}\right)^{x} = $

IIT JEE 2000 Limits and Derivatives

7. $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} \cos^2 \frac{\pi}{15} = $

COMEDK 2009 Application of Integrals

8. A straight line meets the coordinates axes at A and B, so that the centroid of the triangle OAB is (1, 2). Then the equation of the line AB is

COMEDK 2015 Straight Lines

9. The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latusrectum recta to the ellipse $\frac{x^2}{9} +\frac{y^2}{ 5}=1 is $

JEE Advanced 2015 Conic Sections

10. If the lines $\frac{1+x}{3}=\frac{y-2}{2\alpha}=\frac{z-3}{2}$ and $\frac{x-1}{3\alpha}=y-1=\frac{6-z}{5}$ are Perpendicular then the value of $\alpha$ is

KEAM 2009 Introduction to Three Dimensional Geometry

11. If $\log_2 \: \sin x - \log_2 \cos x -\log_2(1 - \tan^2x) = - 1$, then

COMEDK 2008 Trigonometric Functions

12. A tetrahedron has vertices at $ O (0, 0, 0), A(l, 2, 1) B(2, 1, 3 )$ and $C(-1, 1, 2)$. Then the angle between the faces OAB and ABC will be

AIEEE 2003 Introduction to Three Dimensional Geometry

13. Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1} - T_n = 10$, then the · value of 11 is

COMEDK 2013 Binomial Theorem

14. If $C$ is the centre of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1 $ and S isone of the foci, then the ratio of CS to semi-minor axis of the ellipse is

COMEDK 2008 Conic Sections

15. Two lines $L_1 : x =5 , \frac{y}{3 - \alpha} = \frac{z}{-2}$ and $L_2 = x = \alpha , \frac{y}{-1} = \frac{z}{2 - \alpha}$ are coplanar. Then, $\alpha$ can take value (s)

JEE Advanced 2013 Three Dimensional Geometry

16. If the system of equations
$x + y + z = 6$
$x + 2y + 3z = 10 $
$x + 2y + lambda z = 0$
has a unique solution, then $\lambda$ is not equal to

AIEEE 2012 Determinants

17. If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} $ and $\overrightarrow{d}$ $(\overrightarrow{a}\times\overrightarrow{b}).(\overrightarrow{c}\times\overrightarrow{d})=1$ and $\overrightarrow{a}. \overrightarrow{c}=\frac{1}{2}, $ then

IIT JEE 2009 Vector Algebra

18. Let $ a > 0, b > 0 $ and $c>0$. Then, both the roots of the equation $ax^2+bx+c=0$

IIT JEE 1979 Complex Numbers and Quadratic Equations

19. The sum $\displaystyle \sum_{i-0}^{m} \binom{10}{i} \binom{20}{m-i},$ where $ \binom{p}{q}=0 \, if \, p>q,$ is maximum when m is equal to

IIT JEE 2002 Binomial Theorem

20. If $|\vec{a} \times \vec{b}| = 5$ and $|\vec{a} .\vec{b}| = 3$ , then $|\vec{a}|^2 |\vec{b}|^2 $ is equal to

COMEDK 2012 Vector Algebra

21. The value of the integral $ \int^1_0 \sqrt \frac{1 + x }{ 1 + x } \, dx \$ is

IIT JEE 2004 Integrals

22. If B is a non-singular matrix and A is a square matrix such that $B^{-1}\,AB$ exists, then $det\,(B^{-1}\,AB)$ is equal to

KEAM 2009 Matrices

23. If the line $2x + 3y + k = 0$ is at tangent to the circle $x^2 + y^2 - 6x - 8y = 0$, then the value of k is

COMEDK 2006 Conic Sections

24. The number of subsets of $\{1, 2, 3 ,............,9\}$ containing at least one odd number is

EAMCET 2009 Sets

25. 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

26. The number of integers greater than 6000 that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is

JEE Main 2015 Permutations and Combinations

27. $\frac{\sin x - \sin 3x}{\sin^{2} x -\cos^{2} x}$ is equal to

COMEDK 2015 Trigonometric Functions

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

COMEDK 2015 Matrices

29. The domain of the derivative of the function $f(x) = \begin{cases} \tan^{-1} x & \quad \text{if } | x | \le 1 \\ \frac{1}{2} (|x | - 1) & \quad \text{if } |x | > 1 \end{cases}$ is

IIT JEE 2002 Continuity and Differentiability

30. $\lim_{x \to0} \frac{\sqrt{1- \cos2x}}{\sqrt{2 } x }$

IIT JEE 2002 Limits and Derivatives

Mathematics Questions