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

Let $\mid x\mid$ represent the greatest integer less than or equal to $x$ then the value of the determinant $\begin{vmatrix}e & \pi & \pi^{2}-6 \\ \pi & \pi^{2}-6 & e \\ \pi^{2}-6 & e & \pi \end{vmatrix}$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

$l,m,n$ are the $p^{th},q^{th}$ and $r^{th}$ terms of a GP and all positive then $\begin{vmatrix}\log l&p&1\\\log m&q&1\\\log n&r&1\end{vmatrix}$ equals

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A(\theta)=\begin{bmatrix}1&\tan\theta\\-\tan\theta&1\end{bmatrix}$ and $AB=I$ then $(\sec^2\theta)B$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $x,y,z$ are different from zero and $\Delta =\begin{vmatrix}a&b-y&c-z\\a-x&b&c-z\\a-x&b-y&c\end{vmatrix}=0$ then the value of the expression $\large\frac{a}{x}+\frac{b}{y}+\frac{c}{z}$ is

asked Nov 22, 2013 by sreemathi.v

1 answer

Inverse of the matrix $\begin{bmatrix}\cos 2\theta&-\sin 2\theta\\\sin 2\theta&\cos 2\theta\end{bmatrix}$ is

asked Nov 22, 2013 by sreemathi.v

1 answer

If $\begin{vmatrix}x^n&x^{n+2}&x^{n+3}\\y^n&y^{n+2}&y^{n+3}\\z^n&z^{n+2}&z^{n+3}\end{vmatrix}$ = $(y-z)(z-x)(x-y)(\large\frac{1}{x}+\frac{1}{y}+\frac{1}{z})$ then $n$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1&x\\x^2&4y\end{bmatrix}$ and $B=\begin{bmatrix}-3&1\\1&0\end{bmatrix}$ and adj $(A+B)=\begin{bmatrix}1 &0\\0&1\end{bmatrix}$ then values of $x$ and $y$ are

asked Nov 22, 2013 by sreemathi.v

1 answer

If $C=2\cos \theta$ then the value of the determinant $\Delta=\begin{vmatrix}c&1&0\\1&c&1\\6&1&c\end{vmatrix}$ is

asked Nov 22, 2013 by sreemathi.v

1 answer

If one root of the determinant $\begin{vmatrix}x&3&7\\2&x&2\\7&6&x\end{vmatrix}=0$ is $-9$ then the other two roots are

asked Nov 22, 2013 by sreemathi.v

1 answer

Let $a,b,c$ be any real numbers. Suppose that there are real numbers $x,y,z$ not all zero. Such that $x=cy+bz,y=az+cx,z=bx+ay$ . Then $a^2+b^2+2abc$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $a_1,a_2,a_3.....a_n$ are in G.P then the determinant $\Delta=\begin{vmatrix}\log a_n&\log a_{n+1}& \log a_{n+2}\\\log a_{n+3}&\log a_{n+4}&\log a_{n+5}\\\log a_{n+6}&\log a_{n+7}&\log a_{n+8}\end{vmatrix}$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

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

asked Nov 22, 2013 by sreemathi.v

1 answer

The system of equations $\alpha x+y+z=\alpha-1$ , $x+\alpha y+z=\alpha-1$ , $x+y+\alpha z=\alpha-1$ has infinite solutions if $\alpha$ is

asked Nov 22, 2013 by sreemathi.v

1 answer

$A=\begin{bmatrix}1&0&0\\0&1&1\\0&-2&4\end{bmatrix}$ and $I=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$ and $A^{-1}=[\large\frac{1}{6}$ $(A^2+cA+dI)]$ then the value of $c$ and $d$ are

asked Nov 22, 2013 by sreemathi.v

1 answer

The parameter on which the value of the determinant $\begin{vmatrix}1&x&x+1\\\cos(p-d)x&\cos px&\cos(p+d)x\\\sin(p-d)x&\sin px&\sin(P+d)x\end{vmatrix}$ does not defined upon is

asked Nov 22, 2013 by sreemathi.v

1 answer

For positive numbers $x,y$ and $z$ the numerical value of the determinant $\begin{vmatrix}1 &\log_xy&\log_xz\\\log_yx&1&\log_yz\\\log_zx&\log_zy&1\end{vmatrix}$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $a,b,c$ be the real numbers. Then the following system of equations in $x,y$ and $z$ : $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$ , $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ , $\large\frac{-x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ has

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $p\lambda^4+q\lambda^3+r\lambda^2+s\lambda+t$ = $\begin{vmatrix}\lambda^3+3\lambda&\lambda-1&\lambda+3\\\lambda+1&-2\lambda&\lambda-4\\\lambda-3&\lambda+4&3\lambda\end{vmatrix}$ be an identity in $\lambda$ where $p,q,r,s$ and $t$ are constant. Then the value of $t$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

Inverse of $\begin{bmatrix}1&2&3\\2&3&4\\3&4&6\end{bmatrix}$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

If $B$ is a non-singular matrix and A is a square matrix then $det(B^{-1}AB)$ is equal to

asked Nov 21, 2013 by sreemathi.v

1 answer

If $a_1,a_2,a_3.......a_n$ are in G.P then the value of the determinant $\begin{vmatrix}\log a_n&\log a_{n+1}&\log a_{n+2}\\\log a_{n+3}&\log a_{n+4}&\log a_{n+5}\\\log a_{n+6}&\log a_{n+7}&\log a_{n+8}\end{vmatrix}$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

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

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 $1,\omega,\omega^2$ 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

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

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

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

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

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

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 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

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

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

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

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

Evaluate : $\begin{vmatrix}0 &a-b&b-c\\b-a&0&b-c\\c-a&c-b&0\end{vmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate : $\begin{vmatrix}1&\omega&\omega^2\\\omega&\omega^2&1\\\omega^2&1&\omega\end{vmatrix}$

( $\omega$ : Cube root of unity)

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate : $\begin{vmatrix}3 &2& 12\\0 &1&8\\2&9&7\end{vmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

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