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Questions >> JEEMAIN and NEET >> Mathematics

Mathematics

Limit, Continuity and Differentiability

Sets, Relations and Functions

If $\alpha,\beta,\gamma$ are real numbers then, $\begin{vmatrix} 1& \cos(\beta-\alpha)&\cos(\gamma-\alpha)\\\cos(\alpha-\beta)&1&\cos(\gamma-\beta)\\\cos(\alpha-\gamma)&\cos(\beta-\gamma)&1\end{vmatrix}$ is equal to

asked Apr 23, 2014 by sreemathi.v

1 answer

The roots of the equation $\begin{vmatrix}x-1&1&1\\1&x-1&1\\1&1&x-1\end{vmatrix}=0$ are

asked Apr 23, 2014 by sreemathi.v

1 answer

If a matrix A is such that $3A^3+2A^2+5A+I=0$ then its inverse is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0&1&0\\0&0&1\\1&-1&0\end{bmatrix}$ then $A^3+A$ equals

asked Apr 23, 2014 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of the same order and A is non-singular then for a positive integer n, $(A^{-1}BA)^n$ is equal to

asked Apr 23, 2014 by sreemathi.v

1 answer

If $a,b,c$ are in A.P with common difference d and $\begin{vmatrix}x+1&x+a&x+b\\x+a&x+b&x+c\\x-b+1&x-1&x-a+c\end{vmatrix}$ has absolute value 2 then d is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\Delta_r=\begin{vmatrix}2^{r-1}&\large\frac{(r+1)!}{1+\large\frac{1}{r}}&2r\\a&b&c\\2^n-1&(n+1)!-1&n(n+1)\end{vmatrix}$ then value of $\sum\limits_{r=1}^n\Delta_r$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\Delta=\begin{vmatrix} 1+x_1y_1&1+x_1y_2&1+x_1y_3\\1+x_2y_1&1+x_2y_2&1+x_2y_3\\1+x_3y_1&1+x_3y_2&1+x_3y_3\end{vmatrix}$ then $\Delta$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}1&a&a^2\\\sin(n-1) x&\sin nx&\sin(n+1)x\\\cos(n-1)x&\cos nx&\cos(n+1)x\end{vmatrix}$ then $\int_0^{\large\frac{\pi}{2}}f(x)dx$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

If the system of equations $x+ay+az=0,bx+y+bz=0$ and $cx+cy+z=0$ where $a,b,c$ are non-zero ,non unity has a non-trivial solution then the value of $\large\frac{a}{1-a}+\frac{b}{1-b}+\frac{c}{1-c}$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

In a triangle ABC $\begin{vmatrix} a^2& b\sin A & C\sin A\\b\sin A&1&\cos(B-C)\\C\sin A&\cos (B-C) & 1\end{vmatrix}$ equals

asked Apr 22, 2014 by sreemathi.v

1 answer

If $A,B,C$ are angles of a triangle and $\begin{vmatrix} 1&1&1\\1+\sin A&1+\sin B&1+\sin C\\\sin A+\sin ^2A&\sin B+\sin^2B& \sin C+\sin^2C\end{vmatrix}=0$

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma$ are such that $\alpha+\beta+\gamma=0$ then $\begin{vmatrix}1&\cos \gamma&\cos \beta\\\cos \alpha& 1&\cos\alpha\\\cos \beta&\cos \alpha&1\end{vmatrix}$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

If $f(n)=\begin{vmatrix} n& 1&5\\n^2&2r+1&2r+1\\n^3&3r^2&3r+1\end{vmatrix}$ then $\sum\limits_{n=1}^ r f(n)$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $S_r=\begin{vmatrix}2r&x&n(n+1)\\6r^2-1&y&n^2(2n+3)\\4r^32nr&z&n^3(n+1)\end{vmatrix}$ then value of $\sum\limits_{r=1}^n S_r$ is independent of

asked Apr 22, 2014 by sreemathi.v

1 answer

If $F(\alpha)=\begin{bmatrix}\cos \alpha&-\sin \alpha&0\\\sin \alpha&\cos \alpha&0\\0&0&1\end{bmatrix}$ $\alpha \in R$ then $[F(\alpha)]^{-1}$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

The repeated factor of $\begin{vmatrix}y+z&x&y\\z+x& z&x\\x+y& y&z\end{vmatrix}$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

The value of $\begin{vmatrix}1&a&a^2-bc\\1&b& b^2-ca\\1&c&c^2-ab\end{vmatrix}$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}\large\frac{1}{a}&a^2&bc\\\large\frac{1}{b}&b^2&ca\\\large\frac{1}{c}&c^2&ab\end{bmatrix}$ then $|A|$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $a,b,c$ are non zero real numbers,then $\begin{vmatrix}bc&ca&ab\\ca&ab&bc\\ab&bc&ca\end{vmatrix}$ vanishes when

asked Apr 22, 2014 by sreemathi.v

1 answer

If $f(x) = \left\{ \begin{array}{l l} \large\frac{x^3+x^2-16x+20}{(x-2)^2} & \quad when \quad x \neq 3 \\ k & \quad when \quad x = 2 \end{array} \right.$ and $f(x)$ is continuous at $x=3$ find the value of k.

asked Apr 22, 2014 by meena.p

1 answer

If $f(x) = \left\{ \begin{array}{l l} \large\frac{|x+2|}{\tan^{-1} (x+2)} & \quad x \neq -2 \\ 2 & \quad x=-2 \end{array} \right.$ then $f(x)$ is

asked Apr 22, 2014 by meena.p

1 answer

If the function $f(x) = \left\{ \begin{array}{l l} 3ax+b & \quad for \quad x > 1 \\ 11 & \quad for \quad x = 1 \\ 5ax-2b & \quad for \quad x < 1 \end{array} \right.$ is continuous at $x=1$ .find the values of a and b .

asked Apr 22, 2014 by meena.p

1 answer

If $f(x+y)=f(x).f(y)$ for all x and y and if $f(5)=2$ and $f'(0) =3$ find $f'(5)$

asked Apr 22, 2014 by meena.p

1 answer

Find the values of K. So that the function $f(x) = \left\{ \begin{array}{l l} \large\frac{k \cos x}{\pi -2x} & \quad if \quad x \neq \large\frac{\pi}{2} \\ 3 & \quad if \quad x =\large\frac{\pi}{2} \end{array} \right.$ is continuous at $x =\large\frac{\pi}{2}$ .

asked Apr 22, 2014 by meena.p

1 answer

Determine the value of K so that the function. $f(x) = \left\{ \begin{array}{l l} Kx^2 & \quad if \quad x \leq 2 \\ 3 & \quad if \quad x > 2 \end{array} \right.$ is continuous .

asked Apr 22, 2014 by meena.p

1 answer

Evaluate $\lim \limits _{x \to \pi/6} \large\frac{(\sqrt 3 \sin x - \cos x)}{(x-\pi/6)}$

asked Apr 22, 2014 by meena.p

1 answer

Evaluate $\lim \limits_{x \to 0} \bigg(\large\frac{x^3 \cot x}{1- \cos x} \bigg)$

asked Apr 22, 2014 by meena.p

1 answer

Evaluate $\lim \limits_{x \to 0} \bigg( \large\frac{\sin 2x+ \sin 6x}{\sin 5x -\sin 3x} \bigg)$

asked Apr 22, 2014 by meena.p

1 answer

Evaluate $\lim \limits_{x \to 2} \bigg( \large\frac{e^x-e^2}{x-2} \bigg)$

asked Apr 22, 2014 by meena.p

1 answer

Define $f(0)$ so that $f(x)=(x+1)^{\cot x}$ becomes continuous at $x=0$

asked Apr 22, 2014 by meena.p

1 answer

If vertex and focus of hyperbola are $(2,3)$ and $(6,3)$ respectively and eccentricity e of the hyperbola is 2 then equation of the hyperbola is

asked Apr 21, 2014 by meena.p

1 answer

Equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm2,0)$ is

asked Apr 21, 2014 by meena.p

1 answer

The eccentricity of the hyperbola $9y^2 -4x^2=36$ is

asked Apr 21, 2014 by meena.p

1 answer

The distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$ . Its equation is

asked Apr 21, 2014 by meena.p

1 answer

Equation of the chord of the hyperbola $25x^2-16y^2=400$ which is bisected at the point $(6,2)$ is

asked Apr 21, 2014 by meena.p

1 answer

Find the equation of hyperbola if the distance between the foic is $16, e=\sqrt 2$ and axis along x-axis with centre oxgin.

asked Apr 21, 2014 by meena.p

1 answer

Find the equation of the tangents drawn from the point $(-1,-2)$ to the hyperbola $2x^2-3y^2=6$

asked Apr 21, 2014 by meena.p

1 answer

A rectangular hyperbola whose cetre is C is cut by any circle of radius r in four points $P,Q,R$ and S. Then $CP^2+CQ^2+CR2+CS^2$ is equal to.

asked Apr 21, 2014 by meena.p

1 answer

If angle between the asymptotcs of the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$ $=1$ is $45^{\circ}$ then value of eccentricity $e$ is :

asked Apr 21, 2014 by meena.p

1 answer

Equation of chord of the hyperbola $25x^2-16y^2=400$ which is bisected at the point $(6,2)$ is

asked Apr 21, 2014 by meena.p

1 answer

If $e$ and $e'$ be the eccentricities of a hyperbola and its conjugate then $\large\frac {1}{e^2}+\frac{1}{e^{12}}$ is equal to

asked Apr 21, 2014 by meena.p

1 answer

The locus of a point $p(\alpha, \beta)$ moving under the condition that the line $y=\alpha x + \beta$ is a tangent to the hyperbola $\large\frac{x^2}{a^2} -\frac{y^2}{b^2}$ $=1$ is

asked Apr 21, 2014 by meena.p

1 answer

A circle touches the x-axis and also touches the circle with centre at $(0,3)$ and radius the circle with centre at $(0,3)$ and radius 2. The locus of the center of circle is

asked Apr 21, 2014 by meena.p

1 answer

If the foci of the ellipse $\large\frac{x^2}{16}+\frac{y^6}{b^2}$ $=1$ and the hyperbola. $\large\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide, then the value of $b^2$ is

asked Apr 21, 2014 by meena.p

1 answer

Angle between the asymptotes of the hyperbola $3x^2+7xy+2y^2-11x-7y+10=0$ is

asked Apr 21, 2014 by meena.p

1 answer

If $e_1$ and $e_2$ are the eccentricities of the hyperbolas $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$ $=1$ and $\large\frac{y^2}{b^2}-\frac{x^2}{a^2}$ $=1$ Then value of $\large\frac{1}{e_1^2}+\frac{1}{e_2^2}$ is

asked Apr 21, 2014 by meena.p

1 answer

The value of P for which the sum of squares of roots of equation $x^2-(p-2)x-(p+1)=0$ attains the least value is :

asked Apr 15, 2014 by sreemathi.v

1 answer

The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are

asked Apr 11, 2014 by meena.p

1 answer

The diameter of $16x^2-9y^2=144$ which is conjugate to $x=2y$ is

asked Apr 11, 2014 by meena.p

1 answer

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