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Questions >> JEEMAIN and NEET >> Mathematics >> Class12

Class12

Relations and Functions

Inverse Trigonometric Functions

Continuity and Differentiability

Application of Derivatives

Integral Calculus

Application of Integrals

Differential Equations

If $D=\begin{vmatrix}1&1&1\\1&1+x&1\\1&1&1+y\end{vmatrix}$ for $x\neq 0,y\neq 0$ then $D$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$ and $B=\begin{bmatrix}a&0\\0&b\end{bmatrix}\;a,b\in N$ .Then

asked Nov 21, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of size $n\times n$ such that $A^2-B^2=(A-B)(A+B)$ then which of the following will be always true?

asked Nov 21, 2013 by sreemathi.v

1 answer

If $A^2-A+I=0$ then the inverse of A is

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1 &-1&1\\2&1&-3\\1&1&1\end{bmatrix}$ and $10B=\begin{bmatrix}4 &2&2\\-5&0&\alpha\\1&-2&3\end{bmatrix}$ if $B$ is the inverse of matrix A then $\alpha$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}0 &0&-1\\0&-1&0\\-1&0&0\end{bmatrix}$ .The only correct statement about the matrix A is

asked Nov 21, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}a&b\\b&a\end{bmatrix}$ and $A^2=\begin{bmatrix}\alpha&\beta\\\beta&\alpha\end{bmatrix}$ then

asked Nov 21, 2013 by sreemathi.v

1 answer

If $1,\omega,\omega^2$ are the cube roots of unity ,then $\Delta=\begin{vmatrix}1&\omega^n&\omega^{2n}\\\omega^{2n}&1&\omega^n\\\omega^{2n}&1&\omega^n\end{vmatrix}$ is equal to

asked Nov 21, 2013 by sreemathi.v

1 answer

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

asked Nov 21, 2013 by sreemathi.v

1 answer

If $a>0$ and determinant of $ax^2+2bx+c$ is -ve then $\begin{vmatrix}a&b&ax+b\\b&c&bx+c\\ax+b&bx+c&0\end{vmatrix}$ is equal to

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $\omega$ be a complex cube root of unity with $\omega\neq 1$ and $p=[P_{ij}]$ be a $n\times n$ matrix with $P_{ij}=\omega^{i+j}$ .Then $P^2\neq 0$ when $n$ =

asked Nov 21, 2013 by sreemathi.v

1 answer

If the adjoint of a $3\times 3$ matrix P is $\begin{bmatrix}1 &4&4\\2&1&7\\1&1&3\end{bmatrix}$ then the possible value(s) of the determinant of P is

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $M$ and $N$ be two $3\times 3$ non singular skew-symmetric matrices such that $MN=NM$ .If PT denotes the transpose of P,then $M^2N^2(M^TN)^{-1}(MN^{-1})^T$ is equal to

asked Nov 21, 2013 by sreemathi.v

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two non zero non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j,\:\:\overrightarrow b=2\hat j-\hat k$ and $\overrightarrow r\times \overrightarrow a=\overrightarrow b\times\overrightarrow a,\:\:\overrightarrow r\times\overrightarrow b=\overrightarrow a\times\overrightarrow b$ then a unit vector in the direction of $\overrightarrow r$ is ?

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit non collinear vectors and if $\overrightarrow u=\overrightarrow a-(\overrightarrow a.\overrightarrow b)\overrightarrow b$ and $\overrightarrow v=\overrightarrow a\times\overrightarrow b$ then $|\overrightarrow v|= ?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

If $\begin{vmatrix}6i&-3i&1\\4&3i&-1\\20&3&i\end{vmatrix}=x+iy$ then

asked Nov 20, 2013 by sreemathi.v

1 answer

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j.$ and $\overrightarrow c$ is a vector such that $\overrightarrow a.\overrightarrow c=|\overrightarrow c|,\:\:|\overrightarrow c-\overrightarrow a|=2\sqrt 2$ and angle between $\overrightarrow a\times\overrightarrow b\:\:and\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$ , then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

asked Nov 20, 2013 by rvidyagovindarajan_1

1 answer

The determinant $\begin{vmatrix}a&b&a\alpha+b\\b&c&b\alpha+c\\a\alpha+b&b\alpha+c&0\end{vmatrix}$ is equal to zero if

asked Nov 20, 2013 by sreemathi.v

1 answer

If $P$ is a $3\times 3$ matrix such that $P^T=2P+1$ where $P^T$ is the transpose of $p$ and $I$ is the $3\times 3$ identity matrix then there exists a column matrix $x=\begin{bmatrix}x\\y\\z\end{bmatrix}\neq \begin{bmatrix}0\\0\\0\end{bmatrix}$ such that

asked Nov 20, 2013 by sreemathi.v

1 answer

Let $P=[a_{ij}]$ be a $3\times 3$ matrix and let $Q=[b_{ij}]$ where $b_{ij}=2^{i+j}a_{ij}$ for $1\leq i,j\leq 3$ .If the determinant of P is 2,then the determinant of the matrix $Q$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

Let $\omega\neq 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form $\begin{vmatrix}1&a&b\\\omega&1&c\\\omega^2&\omega&1\end{vmatrix}$ where each of a,b and c is either $\omega$ or $\omega^2$ .Then the number of distinct matrices in the set S is

asked Nov 20, 2013 by sreemathi.v

1 answer

The number of $3\times 3$ matrices A whose entries are either 0 or 1 and for which the system $A=\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$ has exactly two distinct solution is

asked Nov 20, 2013 by sreemathi.v

1 answer

Given : $2x-y+2z=2,x-2y+z=-4,x+y+\lambda z=4$ then the value of $\lambda$ such that the given system of equation has No solution is

asked Nov 20, 2013 by sreemathi.v

1 answer

If $A=\begin{vmatrix}\alpha &0\\1 &1\end{vmatrix}$ and $B=\begin{vmatrix}1 &0\\5 &1\end{vmatrix}$ then the value of $\alpha$ for which $A^2=B$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

Let $\omega=-\large\frac{1}{2}$ $+i\large\frac{\sqrt 3}{2}$ .Then the value of the determinant $\begin{vmatrix}1&1&1\\1&-1-\omega^2&\omega^2\\1&\omega^2&\omega^4\end{vmatrix}$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

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

asked Nov 20, 2013 by sreemathi.v

1 answer

If the system of equations $x+ay=0,az+y=0$ and $ax+z=0$ has infinite solution then the value of a is

asked Nov 20, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}\alpha&2\\2&\alpha\end{bmatrix}$ and $\mid A^3\mid=125$ then the value of $\alpha$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

The number of values of k for which the system of equations $(k+1)x+8y=4k,kx+(k+3)y=3k-1$ has infinitely many solutions is

asked Nov 20, 2013 by sreemathi.v

1 answer

If the system of equations : $x-ky-z=0,kx-y-z=0,x+y-z=0$ has a non zero solutions then the possible value of k are

asked Nov 20, 2013 by sreemathi.v

1 answer

The determinant $\begin{vmatrix}xp+y&x&y\\yp+z&y&z\\0 &xp+y&yp+z\end{vmatrix}=0$ if

asked Nov 20, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of equal degree,then which one is correct among the following

asked Nov 20, 2013 by sreemathi.v

1 answer

If $\omega(\neq 1)$ is a cube root of unity,then $\begin{vmatrix}1 &1+i+\omega^2&\omega^2\\1-i&-1&\omega^2-1\\-i&-i+\omega-1&-1\end{vmatrix}$ =

asked Nov 20, 2013 by sreemathi.v

1 answer

Consider the set A of all determinants of order 3 with entries 0 or 1 only.Let B be the subset of A consisting of all determinants with value 1.Let C be the subset of A consisting of all determinants with value -1.Then

asked Nov 20, 2013 by sreemathi.v

1 answer

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

asked Nov 20, 2013 by sreemathi.v

1 answer

Given that $x=-9$ is a root of $\begin{vmatrix}x&3&7\\2 &x&2\\7&6&x\end{vmatrix}$ = 0, the other two roots are

asked Nov 20, 2013 by sreemathi.v

1 answer

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of determinant chosen is +ve is

asked Nov 20, 2013 by sreemathi.v

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are non zero, non collinear vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow b\times\overrightarrow c=\overrightarrow c\times\overrightarrow a$ , then $\overrightarrow a+\overrightarrow b+\overrightarrow c=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

If the magnitude of the vector $a\hat i+b\hat j+c\hat k$ is $|a|+|b|+|c|$ , then $a,b,c$ should be ?

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:and\:\overrightarrow c$ are unit and collinear vectors and $|\overrightarrow b|=6$ , then $\overrightarrow b-3\overrightarrow c=\lambda \overrightarrow a,$ if $\lambda=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=|\overrightarrow b|=1$ and $|\overrightarrow a+\overrightarrow b|=\sqrt 3$ and $\overrightarrow c$ is such that $\overrightarrow c-\overrightarrow a-2\overrightarrow b=3(\overrightarrow a\times\overrightarrow b)$ , then $\overrightarrow c.\overrightarrow b=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

The solution set of the equation $\begin{vmatrix}1 &4&20\\1 &-2&5\\1 &2x&5x^2\end{vmatrix}=0$ is

asked Nov 19, 2013 by sreemathi.v

1 answer

The system of equations $\lambda x+y+z=0$ , $-x+\lambda y+z=0$ , $-x-y+\lambda z=0$ will have a non-zero solutions if real values of $\lambda$ are given by

asked Nov 19, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}1 &-\tan\theta\\\tan\theta&1\end{bmatrix}\begin{bmatrix}1 &\tan\theta\\-\tan\theta&1\end{bmatrix}^{-1}$ = $\begin{bmatrix}a &-b\\b&a\end{bmatrix}$ then find $a,b$

asked Nov 19, 2013 by sreemathi.v

1 answer

Find the product of the matrices $\begin{bmatrix}2 &3&4\\-1&2&-5\end{bmatrix}$ and $\begin{bmatrix}1&2\\3&-4\\-5&6\end{bmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

Given matrices $A=\begin{bmatrix}5 &-2&0\\3&0&5\\-1&0&8\end{bmatrix}$ , $B=\begin{bmatrix}0 &-2\\1 &0\\0&5\end{bmatrix}$ , find $(A+B)$ .

asked Nov 19, 2013 by sreemathi.v

1 answer

Find the value of $\lambda$ for which the set of equations $x+y-2z=0$ , $2x-3y+z=0$ , $x-5y+4z=\lambda$ are consistent.

asked Nov 19, 2013 by sreemathi.v

1 answer

For what value of $k$ do the following homogeneous system of equations posses a non-trivial. $x+ky+3z=0,3x+ky-2z=0,2x+3y-4z=0$

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate : $\begin{vmatrix}y+z&z&y\\z&z+x&x\\y&x&x+y\end{vmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

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