Mathematics Question and Answers

1. If $x$ and $y$ are two real numbers such that $x + y = 1$ and $x^3 + y^3 = 4,$ then $x^5 + y^5$ is

COMEDK 2005 Probability - Part 2

2. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by $\frac {dP}{dx}=100-12 \sqrt x$
If the firm employees 25 more workers, then the new level of production of items is

COMEDK 2013 Differential Equations

3. The value of $\Delta=\begin{bmatrix} a^2 & 2ab&b^2 \\[0.3em] b^2 & a^2&2ab \\[0.3em]2ab&b^2&a^2 \end{bmatrix}=,$

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4. $\sqrt{2 + \sqrt{2+2\cos4\theta}}$

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5. For the curve $4x^5 = 5y^4$, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is............................

KCET 2010 Application of Derivatives

6. The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y +8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is

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7. In the group $(Q - \{-1\}, \}$ ,where is defined by $a * b = a + b + ab,$ the inverse of 3 is

COMEDK 2008 Relations and Functions - Part 2

8. If a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100, Physics 70, Chemistry 40, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18. The number of students who have opted Mathematics alone is

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9. $\int\limits_0^{2x} (\sin x + | \sin x |)dx = $

COMEDK 2007 Inverse Trigonometric Functions

10. The set of real values of x for which $ f(x) = \frac {x}{Log x}$ increasing, is____________

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11. The points $\bigg (0, \frac {8}{3} \bigg ), (1,3)$ and $(82,30)$ are vertices of

JEE Main 1986 Straight Lines

12. The value of the $\sin[\cot^{-1} . \{ \cos(\tan^{-1} x\} ]$ is

COMEDK 2009 Application of Integrals

13. The distance between the lines $\overrightarrow{r}=(4\hat{i}-7\hat{j}-\hat{k})+t(3\hat{i}-7\hat{j}+4\hat{k})\overrightarrow{r}=(7\hat{i}-14\hat{j}-5\hat{k})+s(-3\hat{i}+7\hat{j}+4\hat{k}) $is equal to

KEAM 2009 Introduction to Three Dimensional Geometry

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

KCET 2001 Mathematical Reasoning

15. The equation of the circle concentric with $x^2 + y^2 + 6x + 2y + 1 = 0$ and passing through the point (-2, -1) is

COMEDK 2007 Conic Sections

16. Coefficient of $t^{24} $ in $ (1+t^2)^{12}) (1+t^{12}(1+t^{24})$ is

IIT JEE 2003 Binomial Theorem

17. The equation $x^{\frac{3}{4}(\log_2 x)^2+\log_2x-\frac{5}{4}=\sqrt2}$ has

IIT JEE 1989 Complex Numbers and Quadratic Equations

18. I f F and F are independent events such that $O < P(E) < 1$ and $O < P (F ) < 1$, then

IIT JEE 1989 Probability

19. Number of divisors of the form $(4n + 2), n\ge 0$ of the integer 240 is

IIT JEE 1998 Permutations and Combinations

20. Let $\omega=-\frac{1}{2}+i\frac{\sqrt 3}{2},$ then value of the determinant $\begin {vmatrix} 1 & 1& 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega \\ \end {vmatrix} is $

IIT JEE 2002 Complex Numbers and Quadratic Equations

21. The equation $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,|r|<1$ represents

IIT JEE 1981 Conic Sections

22. The number of solution of the equation $\tan x = \sin (x/2)$ in the interval $(- \pi , \pi )$ is

COMEDK 2005 Application of Integrals

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

AIEEE 2002 Sets

24. The function $f\left(x\right) = \left(\frac{\log_{e}\left(1+ax\right) - \log_{e}\left(1-bx\right)}{x}\right)$ is undefined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is

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25. Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

IIT JEE 2001 Complex Numbers and Quadratic Equations

26. The orthocentre of the triangle formed by the lines $xy = 0$ and $ x+ y = 1$,is

IIT JEE 1995 Straight Lines

27. $ \, if \, I_ n = \int^{\pi}_{ -\pi} \frac { \sin \, n \, x }{ ( 1 + \pi ^x ) \sin \, x } dx , \, n = 0 , 1 , 2 , .............., then $

IIT JEE 2009 Integrals

28. If $A= \begin{bmatrix}1&2\\ 0&1\end{bmatrix} $, then $A"$ is

COMEDK 2009 Matrices

29. Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A \times B$ having· 3 or more elements is

COMEDK 2013 Matrices

30. If $a^2+b^2+c^2=-2$ and $f(x)=\begin{vmatrix} 1+a^2x &(1+b^2)x & (1+c^2)x \\[0.3em] (1+a^2)x^2& 1+b^2x &(1+c^2)x \\[0.3em] (1+a^2)x & (1+b^2)x & 1+c^2x \end{vmatrix}$ then f(x) is a polynomial of degree

AIEEE 2005 Determinants

Mathematics Questions

1. If $x$ and $y$ are two real numbers such that $x + y = 1$ and $x^3 + y^3 = 4,$ then $x^5 + y^5$ is

2. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by $\frac {dP}{dx}=100-12 \sqrt x$
If the firm employees 25 more workers, then the new level of production of items is

3. The value of $\Delta=\begin{bmatrix} a^2 & 2ab&b^2 \\[0.3em] b^2 & a^2&2ab \\[0.3em]2ab&b^2&a^2 \end{bmatrix}=,$

4. $\sqrt{2 + \sqrt{2+2\cos4\theta}}$

5. For the curve $4x^5 = 5y^4$, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is............................

6. The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y +8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is

7. In the group $(Q - \{-1\}, \}$ ,where is defined by $a * b = a + b + ab,$ the inverse of 3 is

9. $\int\limits_0^{2x} (\sin x + | \sin x |)dx = $

10. The set of real values of x for which $ f(x) = \frac {x}{Log x}$ increasing, is____________

11. The points $\bigg (0, \frac {8}{3} \bigg ), (1,3)$ and $(82,30)$ are vertices of

12. The value of the $\sin[\cot^{-1} . \{ \cos(\tan^{-1} x\} ]$ is

13. The distance between the lines $\overrightarrow{r}=(4\hat{i}-7\hat{j}-\hat{k})+t(3\hat{i}-7\hat{j}+4\hat{k})\overrightarrow{r}=(7\hat{i}-14\hat{j}-5\hat{k})+s(-3\hat{i}+7\hat{j}+4\hat{k}) $is equal to

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

15. The equation of the circle concentric with $x^2 + y^2 + 6x + 2y + 1 = 0$ and passing through the point (-2, -1) is

16. Coefficient of $t^{24} $ in $ (1+t^2)^{12}) (1+t^{12}(1+t^{24})$ is

17. The equation $x^{\frac{3}{4}(\log_2 x)^2+\log_2x-\frac{5}{4}=\sqrt2}$ has

18. I f F and F are independent events such that $O < P(E) < 1$ and $O < P (F ) < 1$, then

19. Number of divisors of the form $(4n + 2), n\ge 0$ of the integer 240 is

20. Let $\omega=-\frac{1}{2}+i\frac{\sqrt 3}{2},$ then value of the determinant $\begin {vmatrix} 1 & 1& 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega \\ \end {vmatrix} is $

21. The equation $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,|r|<1$ represents

22. The number of solution of the equation $\tan x = \sin (x/2)$ in the interval $(- \pi , \pi )$ is

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

24. The function $f\left(x\right) = \left(\frac{\log_{e}\left(1+ax\right) - \log_{e}\left(1-bx\right)}{x}\right)$ is undefined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is

25. Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

26. The orthocentre of the triangle formed by the lines $xy = 0$ and $ x+ y = 1$,is

27. $ \, if \, I_ n = \int^{\pi}_{ -\pi} \frac { \sin \, n \, x }{ ( 1 + \pi ^x ) \sin \, x } dx , \, n = 0 , 1 , 2 , .............., then $

28. If $A= \begin{bmatrix}1&2\\ 0&1\end{bmatrix} $, then $A"$ is

29. Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A \times B$ having· 3 or more elements is

30. If $a^2+b^2+c^2=-2$ and $f(x)=\begin{vmatrix} 1+a^2x &(1+b^2)x & (1+c^2)x \\[0.3em] (1+a^2)x^2& 1+b^2x &(1+c^2)x \\[0.3em] (1+a^2)x & (1+b^2)x & 1+c^2x \end{vmatrix}$ then f(x) is a polynomial of degree

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Mathematics Questions

1. If $x$ and $y$ are two real numbers such that $x + y = 1$ and $x^3 + y^3 = 4,$ then $x^5 + y^5$ is

2. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by $\frac {dP}{dx}=100-12 \sqrt x$ If the firm employees 25 more workers, then the new level of production of items is

3. The value of $\Delta=\begin{bmatrix} a^2 & 2ab&b^2 \\[0.3em] b^2 & a^2&2ab \\[0.3em]2ab&b^2&a^2 \end{bmatrix}=,$

4. $\sqrt{2 + \sqrt{2+2\cos4\theta}}$

5. For the curve $4x^5 = 5y^4$, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is............................

6. The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y +8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is

7. In the group $(Q - \{-1\}, *\}$ ,where * is defined by $a * b = a + b + ab,$ the inverse of 3 is

9. $\int\limits_0^{2x} (\sin x + | \sin x |)dx = $

10. The set of real values of x for which $ f(x) = \frac {x}{Log x}$ increasing, is____________

11. The points $\bigg (0, \frac {8}{3} \bigg ), (1,3)$ and $(82,30)$ are vertices of

12. The value of the $\sin[\cot^{-1} . \{ \cos(\tan^{-1} x\} ]$ is

13. The distance between the lines $\overrightarrow{r}=(4\hat{i}-7\hat{j}-\hat{k})+t(3\hat{i}-7\hat{j}+4\hat{k})\overrightarrow{r}=(7\hat{i}-14\hat{j}-5\hat{k})+s(-3\hat{i}+7\hat{j}+4\hat{k}) $is equal to

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

15. The equation of the circle concentric with $x^2 + y^2 + 6x + 2y + 1 = 0$ and passing through the point (-2, -1) is

16. Coefficient of $t^{24} $ in $ (1+t^2)^{12}) (1+t^{12}(1+t^{24})$ is

17. The equation $x^{\frac{3}{4}(\log_2 x)^2+\log_2x-\frac{5}{4}=\sqrt2}$ has

18. I f F and F are independent events such that $O < P(E) < 1$ and $O < P (F ) < 1$, then

19. Number of divisors of the form $(4n + 2), n\ge 0$ of the integer 240 is

20. Let $\omega=-\frac{1}{2}+i\frac{\sqrt 3}{2},$ then value of the determinant $\begin {vmatrix} 1 & 1& 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega \\ \end {vmatrix} is $

21. The equation $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,|r|<1$ represents

22. The number of solution of the equation $\tan x = \sin (x/2)$ in the interval $(- \pi , \pi )$ is

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

24. The function $f\left(x\right) = \left(\frac{\log_{e}\left(1+ax\right) - \log_{e}\left(1-bx\right)}{x}\right)$ is undefined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is

25. Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

26. The orthocentre of the triangle formed by the lines $xy = 0$ and $ x+ y = 1$,is

27. $ \, if \, I_ n = \int^{\pi}_{ -\pi} \frac { \sin \, n \, x }{ ( 1 + \pi ^x ) \sin \, x } dx , \, n = 0 , 1 , 2 , .............., then $

28. If $A= \begin{bmatrix}1&2\\ 0&1\end{bmatrix} $, then $A"$ is

29. Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A \times B$ having· 3 or more elements is

30. If $a^2+b^2+c^2=-2$ and $f(x)=\begin{vmatrix} 1+a^2x &(1+b^2)x & (1+c^2)x \\[0.3em] (1+a^2)x^2& 1+b^2x &(1+c^2)x \\[0.3em] (1+a^2)x & (1+b^2)x & 1+c^2x \end{vmatrix}$ then f(x) is a polynomial of degree

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2. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by $\frac {dP}{dx}=100-12 \sqrt x$
If the firm employees 25 more workers, then the new level of production of items is

7. In the group $(Q - \{-1\}, \}$ ,where is defined by $a * b = a + b + ab,$ the inverse of 3 is