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Recent questions and answers in Class12
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JEEMAIN and NEET
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Mathematics
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Class12
Class12
Relations and Functions
Inverse Trigonometric Functions
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Continuity and Differentiability
Application of Derivatives
Integral Calculus
Application of Integrals
Differential Equations
Vector Algebra
3-D Geometry
Probability
Integrate : $ \int \large\frac{7}{3} \bigg( \frac{1}{x}-\frac{1}{x^2 }\bigg)$$ \times a (\log x + \large\frac{1}{x} ) $$dx$
jeemain
math
class12
ch7
integral-calculus
integration-by-subsitution
easy
q198
answered
Apr 4
by
shalokama
2
answers
The inverse of $f(x)=x-[x],$ where $[x]$ is greatest integer function is
jeemain
math
class12
ch1
relations-and-functions
composition
of
functions
difficult
answered
Sep 29, 2019
by
pranav.awasarmol123
2
answers
If the variance of the random variable X is 9, the standard deviation of the random variable -4x+8 is?
math
answered
Apr 6, 2019
by
yachyuth2001
1
answer
What is $\displaystyle \int \frac {(x^2 +1)(x^2+2)}{(x^2+3)(x^2+4)} dx $ ?
math
answered
Dec 13, 2018
by
nikhilgautam7000
1
answer
Two fair dice are tossed once. The probability of getting an even number on the first die or a total of 8 is
jeemain
math
cbse
class12
probability
independent events
easy
q11
answered
Mar 18, 2018
by
prakashtiwariaditya
2
answers
If $f_k(x) = \large\frac{1}{k}$$(\sin^k x + \cos^k x)$, where $x\in R$ and $k \geq 1$. The $f_4(x) - f_6(x)$ equals
jeemain
math
class12
ch1
relations-and-functions
types
of
functions
jeemain-2014
q44
medium
answered
Nov 15, 2017
by
ityagi002
1
answer
Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals
jeemain
math
cbse
class12
probability
bionomial-distribution
difficult
q8
answered
Jul 9, 2017
by
phaniajit2005
2
answers
Out of 7 consonents and 4 vowels, X number of words of 3 consonants and 2 vowels can be formed but Y number of groups of 3 consonents and 2 vowels can be formed. Find the value of X/Y .
answered
Jun 21, 2015
by
pady_1
1
answer
Find the velocity of the particle at the point(1,2,3)of a rigid body which is spinning about a fixed point (2,-1,3)with angular velocity 5 radians per second,the axis of rotation being in the direction of (-2i+j+2k)
asked
May 26, 2015
by
tintinsnowy81
0
answers
$\int \limits_0^{\pi} (x.sinx.sinx.cosx)dx$
math-arihant
answered
Apr 9, 2015
by
pady_1
1
answer
f(xy)=f(x)+f(y) . Then Prove that f(x) =Klog(x) where k is constant
answered
Dec 17, 2014
by
pady_1
1
answer
find area between the graphs log(x) , log(|x|) , |log(|x|)|
asked
Dec 12, 2014
by
vishavjeetmor
0
answers
If a square matrix A is such that $AA^T=I=A^TA$ then $|A|$ is equal to
jeemain
math
class12
ch4
medium
determinants
adjoint-and-inverse
answered
Apr 25, 2014
by
sreemathi.v
1
answer
If $A$ is square matrix of order $n\times n$ then adj(adj(A)) is equal to
jeemain
math
class12
ch4
determinants
adjoint-and-transpose
medium
answered
Apr 25, 2014
by
sreemathi.v
1
answer
The number of non trivial solutions of the system $x-y+z=0,x+2y-z=0,2x+y+3z=0$ is
jeemain
math
difficult
determinants
ch4
class12
system-of-linear-equations
answered
Apr 25, 2014
by
sreemathi.v
1
answer
If $A,B$ are two square matrices such that $AB=A$ and $BA=B$ then $A$ and $B$ are
jeemain
math
class12
ch3
matrices
types-of-matrices
medium
answered
Apr 25, 2014
by
sreemathi.v
1
answer
If $A$ is orthogonal matrix then
jeemain
math
class12
ch3
matrices
types-of-matrices
medium
answered
Apr 25, 2014
by
sreemathi.v
1
answer
The number of right inverse for the matrix $\begin{bmatrix}1&-1&2\\2&-1&1\end{bmatrix}$
jeemain
math
class12
ch3
matrices
invertible-matrices
medium
answered
Apr 25, 2014
by
sreemathi.v
1
answer
If $ax^3+bx^2+cx+d=\begin{vmatrix}x^2&(x-1)^2&(x-2)\\(x-)^2&(x-2)^2&(x-3)^2\\(x-2)^2&(x-3)^2&(x-4)^2\end{vmatrix}$ then
jeemain
math
class12
ch4
determinants
evaluate-determinants
difficult
answered
Apr 25, 2014
by
sreemathi.v
1
answer
The values of $\lambda$ and $\mu$ for which the equations $x+y+z=3,x+3y+2z=6,x+\lambda y+3z=\mu$ have
jeemain
math
class12
ch4
determinants
system-of-linear-equations
difficult
answered
Apr 25, 2014
by
sreemathi.v
1
answer
If $1+\sin x+\cos x\neq 0$ the value of $x$ for which $\begin{vmatrix}1&\sin x&\cos x\\\sin x&1&\cos x\\\cos x&\sin x&1\end{vmatrix}=0$ is
jeemain
math
class12
ch4
determinants
evaluate-determinants
difficult
answered
Apr 25, 2014
by
sreemathi.v
1
answer
If $f(x)=\begin{vmatrix}\cos x&1&0\\1&2\cos x&1\\0&1&2\cos x\end{vmatrix}$ then $\int\limits_0^{\large\frac{\pi}{2}}2f(x)dx$ is equal to
jeemain
math
class12
ch4
determinants
evaluate-determinants
difficult
answered
Apr 25, 2014
by
sreemathi.v
1
answer
If $A=\begin{vmatrix}a&b&c\\x&y&z\\p&q&r\end{vmatrix}$ and $B=\begin{vmatrix}q&-b&y\\-p&a&-x\\r&-c&z\end{vmatrix}$ then
jeemain
math
class12
ch4
determinants
evaluate-determinants
difficult
answered
Apr 24, 2014
by
sreemathi.v
1
answer
If $A$ is an invertible matrix and B is a matrix then
jeemain
math
class12
ch3
matrices
invertible-matrices
medium
answered
Apr 24, 2014
by
sreemathi.v
1
answer
If $A$ is a square matrix of order $n\times n$ then adj.(adj A) is equal to
jeemain
math
class12
ch4
determinants
adjoint-and-inverse
difficult
answered
Apr 24, 2014
by
sreemathi.v
1
answer
$\begin{vmatrix}\log_3512&\log_43\\\log_38&\log_49\end{vmatrix}\times \begin{vmatrix}\log_23&\log_83\\\log_34&\log_34\end{vmatrix}=$
jeemain
math
class12
ch3
matrices
operations-on-matrices
difficult
answered
Apr 24, 2014
by
sreemathi.v
1
answer
If $D_r=\begin{vmatrix}2^{r-1}&2.3^{r-1}&4.5^{r-1}\\\alpha&\beta&\gamma\\2^n-1&3^n-1&5^n-1\end{vmatrix}$ then the value of $\sum\limits_{r=1}^n D_r$ is
jeemain
math
class12
ch4
determinants
evaluate-determinants
difficult
answered
Apr 24, 2014
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 zero solutions then $a,b,c$
jeemain
math
class12
ch4
determinants
system-of-linear-equations
difficult
answered
Apr 24, 2014
by
sreemathi.v
1
answer
Value of the determinant $\begin{vmatrix} 10!&11!&12!\\11!&12!&13!\\12!&13!&14!\end{vmatrix}$ is
jeemain
math
class12
ch4
determinants
evaluate-determinants
difficult
answered
Apr 24, 2014
by
sreemathi.v
1
answer
Let $C=\begin{bmatrix}C_{11}&C_{12}\\C_{21}&C_{22}\end{bmatrix}$ be a $2\times 2$ matrix and there exist $2\times 2$ matrices $A$ and $B$ such that $C=AB-BA$ then
jeemain
math
class12
ch3
matrices
operations-on-matrices
medium
answered
Apr 24, 2014
by
sreemathi.v
1
answer
If $a,b,c$ are all different and $\begin{vmatrix}a&a^3&a^4-1\\b&b^3&b^4-1\\c&c^3&c^4-1\end{vmatrix}=0$ then the value of $abc(ab+bc+ca)$ is
jeemain
math
class12
ch3
matrices
equality-of-matrices
difficult
answered
Apr 24, 2014
by
sreemathi.v
1
answer
The value of $\theta$ in the first quadrant satisfying the equation $\begin{vmatrix}1+\cos^2\theta&\sin^2\theta&4\sin 4\theta\\\cos^2\theta&1+\sin^2\theta&4\sin4\theta\\\cos^2\theta&\sin^2\theta&1+4\sin 4\theta\end{vmatrix}=0$ is
jeemain
math
class12
ch3
matrices-and-determinants
equality-of-matrices
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $C=2\cos \theta$ then the value of the determinant $4\Delta=\begin{vmatrix}c&1&0\\1&c&1\\0&1&c\end{vmatrix}$ is
jeemain
math
class12
ch4
determinants
evaluate-determinants
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1&2\\3&-5\end{bmatrix}$ then $A^{-1}$=
jeemain
math
class12
ch4
determinants
adjoint-and-inverse
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $x^ay^b=e^m,x^cy^d=e^n$ $\Delta_1=\begin{vmatrix}m&b\\n&d\end{vmatrix}$,$\Delta_2=\begin{vmatrix}a&m\\c&n\end{vmatrix}$,$\Delta_3=\begin{vmatrix}a&b\\c&d\end{vmatrix}$ then the values of $x$ and $y$ are respectively
jeemain
math
class12
ch4
determinants
system-of-linear-equations
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $a=1+2+4+.........$upto n terms,$b=1+3+9+.....$upto n terms,$c=1+5+25+.....$upto n terms then $\begin{vmatrix}a&2b&4c\\2&2&2\\2^n&3^n&5^n\end{vmatrix}=$
jeemain
math
class12
ch3
matrices
operations-on-matrices
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
The value of $\begin{vmatrix}a&a+b&a+2b\\a+2b&a&a+b\\a+b&a+2b&a\end{vmatrix}$ is equal to
jeemain
math
class12
ch3
matrices
elementary-operation-(transformation)-of-a-matrix
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If 5 is one root of the equation $\begin{vmatrix}x&3&7\\2&x&-2\\7&8&x\end{vmatrix}=0$ then the other two roots of the equation are
jeemain
math
class12
ch4
determinants
evaluate-determinants
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $f(x)=\begin{vmatrix}\sin x&\cos x&\tan x\\x^3&x^2&x\\2x&1&1\end{vmatrix}$ then $\lim\limits_{x\to 0}\large\frac{f(x)}{x^2}$ is
jeemain
math
class12
ch3
matrices
evaluate-determinants
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
The number of solutions of the system of equations $2x+y-z=7,x-3y+2z=1,x+4y-3z=5$ is
jeemain
math
class12
ch4
determinants
system-of-linear-equations
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $p\neq a,q\neq b,r\neq c$ and $\begin{vmatrix}p&b&c\\p+a&q+b&2c\\a&b&r\end{vmatrix}=0$ then $\large\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}$=
jeemain
math
class12
ch3
matrices
elementary-operation-(transformation)-of-a-matrix
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}0&2\\3&-4\end{bmatrix}$ and $kA=\begin{bmatrix}0&3a\\2b&24\end{bmatrix}$ then the values of $k,a,b$ are respectively
jeemain
math
class12
ch3
matrices
operations-on-matrices
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $\omega$ is cube root of unity then $\Delta=\begin{vmatrix}x+1&\omega&\omega^2\\\omega&x+\omega^2&1\\\omega^2&1&x+\omega^2\end{vmatrix}=$
jeemain
math
class12
ch4
determinants
properties-of-determinants
evaluate-determinants
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$ then $A^5=$
jeemain
math
class12
ch3
matrices
invertible-matrices
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $\begin{vmatrix}x+\alpha&\beta&\gamma\\\alpha&x+\beta&\gamma\\\alpha&\beta&x+\gamma\end{vmatrix}=0$ then $4x$ is equal to
jeemain
math
class12
ch3
matrices
elementary-operation-(transformation)-of-a-matrix
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1&\tan\large\frac{\theta}{2}\\-\tan\large\frac{\theta}{2}&1\end{bmatrix}$ and $AB=I$ then $B$=
jeemain
math
class12
ch4
determinants
adjoint-and-inverse
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
The value of a for which the system of equations $a^3x+(a+1)^3y+(a+2)^3z=0,ax+(a+1)y+(a+2)z=0,x+y+z=0$ has a non-zero solution is
jeemain
math
class12
ch4
determinants
system-of-linear-equations
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If $A$ and $B$ are two matrices such that $AB=B$ and $BA=A$ then $A^2+B^2=$
jeemain
math
class12
ch3
matrices
invertible-matrices
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
For each real numbers $x$ such that $-1 < x < 1$ let $A(x)$ be the matrix.$(1-x)^{-\large\frac{1}{2}}\begin{bmatrix}1&-x\\-x&1\end{bmatrix}$ and $z=\large\frac{x+y}{1+xy}$.Then
jeemain
math
class12
ch3
matrices
operations-on-matrices
difficult
answered
Apr 23, 2014
by
sreemathi.v
1
answer
If A is singular matrix then adj.A is
jeemain
math
class12
ch4
determinants
adjoint-and-inverse
medium
answered
Apr 23, 2014
by
sreemathi.v
1
answer
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