Recent questions tagged class12

If the vectors $p\hat i+\hat j+\hat k,\:\hat i+q\hat j+\hat k,\: \:and\:\:\hat i+\hat j+r\hat k$ $(p\neq q\neq r\neq 1)$ are three coplanar vectors then the value of $pqr-(p+q+r)=?$

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

The value of $a$ for which the volume of the parallelopiped formed by the vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k,\:\:a\hat i+\hat k$ is minimum is ?

asked Nov 28, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow u=\hat i+\hat j,\:\overrightarrow v=\hat i-\hat j\:\:and\:\:\overrightarrow w=\hat i+2\hat j+3\hat k$. and if $\hat n$ is a unit vector such that $\overrightarrow u.\hat n=\overrightarrow v.\hat n=0$, then $|\overrightarrow w.\hat n|=?$

asked Nov 28, 2013 by rvidyagovindarajan_1

1 answer

If $\Delta=\begin{vmatrix}x^n&x^{n+2}&x^{2n}\\1&x^p&p\\x^{n+5}&x^{p+6}&x^{2n+5}\end{vmatrix}=0$ then $p$ is given by

asked Nov 26, 2013 by sreemathi.v

1 answer

If a point $(x,y)$ moves on a curve and satisfies the equation $\small\begin{vmatrix}a&b&ax+by\\b&c&bx+cy\\ax+by&bx+ay&0\end{vmatrix}=0$ then

asked Nov 26, 2013 by sreemathi.v

1 answer

Find the value of determinant $\begin{vmatrix}1&x&y+z\\1&y&z+x\\1&z&x+y\end{vmatrix}$

asked Nov 26, 2013 by sreemathi.v

1 answer

If the system of equations $x+2y-3z=1$, $(p+2)z=3$, $(2p+1)y+z=2$ is inconsistent, then the value of $p$ is

asked Nov 26, 2013 by sreemathi.v

1 answer

If the system of equations $ax+y+z=0$, $x+by+z=0$, $x+y+cz=0$, where $(a,b,c\neq 1)$ has a non-trivial solutions, then the value of $\large\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is

asked Nov 26, 2013 by sreemathi.v

1 answer

If a square matrices $A$ and $B$ are such that $AA^{\theta}=A^{\theta}A$, $BB^{\theta}=B^{\theta}B$, $AB^{\theta}=B^{\theta}A$ then $AB(AB)^{\theta}$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A,B,C$ are the angles of a $\Delta$le then the value of the determinant $\small\begin{vmatrix}-1+\cos B&\cos C+\cos B&\cos B\\\cos C+\cos A&-1+\cos A&\cos A\\-1+\cos B&-1+\cos B&-1\end{vmatrix}$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

Matrix $A$ satisfies $A^2=2A-I$ where $I$ is the identity matrix. For $n \geq 2$, $A^n$ is equal to $(n\in N)$

asked Nov 25, 2013 by sreemathi.v

1 answer

For all values of $A,B,C$ and $P,Q,R$ the value of the determinant

$(x+a)^3\small\begin{vmatrix}\cos(A-P)&\cos (A-Q)&\cos(A-R)\\\cos(B-P)&\cos(B-Q)&\cos(B-R)\\\cos(C-P)&\cos(C-Q)&\cos(C-R)\end{vmatrix}$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A^k=0$ for some value of k.$(I-A)^P=I+A+A^2+....+A^{k-1}$ thus P is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A,B$ and $C$ are the angles of a $\Delta$le then $\begin{vmatrix}\sin 2A&\sin C&\sin B\\\sin C&\sin 2B&\sin A\\\sin B&\sin A&\sin 2C\end{vmatrix}$ = $\lambda\sin A\sin B\sin C$, then $\lambda$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}3&4\\2&4\end{bmatrix},B=\begin{bmatrix}-2&-2\\0&-2\end{bmatrix}$ then $(A+B)^{-1}$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

If a square matrix A is such that $AA^T=I=A^TA$ then $\mid A\mid$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

If $\begin{vmatrix}x-1&5x&7\\x^2-1&x-1&8\\2x&3x&0\end{vmatrix}$ = $ax^3+bx^2+cx+d$ then $c$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

The characteristic root of the matrix $\begin{bmatrix}1&0&0\\2&3&0\\4&5&6\end{bmatrix}$ are

asked Nov 25, 2013 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma$ are the cube roots of unity,then the value of the determinant $\begin{vmatrix}e^{\alpha}&e^{2\alpha}&e^{3\alpha}-1\\e^{\beta}&e^{2\beta}&e^{3\beta}-1\\e^{\gamma}&e^{2\gamma}&e^{3\gamma}-1\end{vmatrix}$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

If $x,y,z$ are all distinct and $\begin{vmatrix}x&x^2&1+x^3\\y&y^2&1+y^3\\z&z^2&1+z^3\end{vmatrix}=0$ then the value of $xyz$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}6&8&5\\4&2&3\\9&7&1\end{bmatrix}$ is the sum of symmetric matrix $B$ and skew-symmetric matrix $C$ then $B$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A,B,C$ are angles of a triangle then $\begin{vmatrix}e^{2iA}&e^{-iC}&e^{-iB}\\e^{-iC}&e^{2iB}&e^{-iA}\\e^{-iB}&e^{-iA}&e^{2iC}\end{vmatrix}$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

A skew-symmetric matrix S satisfies the relation $S^2+I=0$ where $I$ is a unit matrix. Then $SS'$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}0&a\\b&0\end{bmatrix}^4=I$ then

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}$ then $A^4$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

If $E(\theta)=\begin{bmatrix}\cos^2\theta&\cos \theta\sin \theta\\\cos \theta\sin\theta&\sin^2\theta\end{bmatrix}$ and $\theta$ and $\phi$ differ by an odd multiple of $\large\frac{\pi}{2}$ then $E(\theta)E(\phi)$ is a

asked Nov 25, 2013 by sreemathi.v

1 answer

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