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Recent questions in Class12

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 $A^k=0$ 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

If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are non coplanar vectors and $p,q$ are real numbers so that $[3\overrightarrow u\:p\overrightarrow v\:p\overrightarrow w]-[p\overrightarrow v\:p\overrightarrow w\:q\overrightarrow u]-[2\overrightarrow w\:q\overrightarrow v\:q\overrightarrow u]=0$ then number of values of $p,q$ is

asked Nov 22, 2013 by rvidyagovindarajan_1

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

The value of $\begin{vmatrix}x&p&q\\p&x&q\\p&q&x\end{vmatrix}$ 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 $A$ and $B$ are square matrices of the same order and $AB=3I$ then $A^{-1}$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of the same order such that $(A+B)(A-B)=A^2-B^2$ then $(ABA^{-1})^2$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If the matrix $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ is commutative with the matrix $\begin{bmatrix}1&1\\0&1\end{bmatrix}$ then

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 $A=\begin{bmatrix}1&-2\\4&5\end{bmatrix}$ and $f(1)=t^2-3t+7$ then $f(A)+\begin{bmatrix}3&6\\-12&-9\end{bmatrix}$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1&2&2\\2&1&2\\2&2&1\end{bmatrix}$ then $A^2-4A$ is equal to

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

If $\small\begin{vmatrix}a^2&b^2&c^2\\(a+1)^2&(b+1)^2&(c+1)^2\\(a-1)^2&(b-1)^2&(c-1)^2\end{vmatrix}$ = $k\small\begin{vmatrix}a^2&b^2&c^2\\a&b&c\\1&1&1&\end{vmatrix}$ then the value of $k$ is

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 the matrix $A=\begin{bmatrix}y+a&b&c\\a&y+b&c\\a&b&y+c\end{bmatrix}$ has rank 3 then

asked Nov 22, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}2&1\\3&2\end{bmatrix}A\begin{bmatrix}-3&2\\5&-3\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$ then the matrix A 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

If $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c$ and $\overrightarrow a\times\overrightarrow b=\overrightarrow a\times\overrightarrow c$ and if $\overrightarrow a\neq 0$, then

asked Nov 21, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors then $(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times (\overrightarrow c+\overrightarrow a)=?$

asked Nov 21, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors, then $[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overrightarrow a-\overrightarrow b]=?$

asked Nov 21, 2013 by rvidyagovindarajan_1

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 $A$ is a square matrix such that $A^2=I$ then $A^{-1}$ 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

Let $A=\begin{vmatrix}5 &5\alpha&\alpha\\0&\alpha&5\alpha\\0&0&5\end{vmatrix}$ if $\mid A^2\mid=25$ then $\alpha$ equals

asked Nov 21, 2013 by sreemathi.v

1 answer

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