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Questions >> TN XII Math

TN XII Math

Applications of Matrices and Determinants

Complex Numbers

Analytical Geometry

Differential Calculus Applications - I

Differential Calculus Applications - II

Integral Calculus and its applications

Differential Equations

Discrete Mathematics

Probability Distribution

Objective type Questions and Answers

The points $z_{1} , z_{2} , z_{3} , z_{4}$ in the complex plane are the vertices of a parallelogram taken in order if and only if

asked May 12, 2013 by poojasapani_1

1 answer

If $a=3+i$ and $z=2-3i$ then the points on the Argand diagram representing $az , 3az$ and $-az$ are

asked May 12, 2013 by poojasapani_1

1 answer

If $A+iB=(a_{1}+ib_{1})(a_{2}+ib_{2})(a_{3}+ib_{3})$ then $A^{2}+B^{2}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The modulus of the complex number $2+i\sqrt{3}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $x^{2}+y^{2}=1$ then the value of $\large\frac{1+x+iy}{1+x-iy}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $(m-5)+i(n+4)$ is the complex conjugate of $(2m+3)+i(3n-2)$ then $(n ,m )$ are

asked May 11, 2013 by poojasapani_1

1 answer

The modulus and amplitude of the complex number $[e^{3-i \pi/4}]^{3}$ is respectively

asked May 11, 2013 by poojasapani_1

1 answer

The value of $\large[\frac{-1+i\sqrt{3}}{2}]^{100}+[\frac{-1-i\sqrt{3}}{2}]^{100}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The centre and the radius of the sphere given by $x^{2}+y^{2}+z^{2}-6x+8y-10z+1=0$ is

asked May 11, 2013 by poojasapani_1

1 answer

The following two lines are $\large\frac{x-1}{2}=\frac{y-1}{-1}=\frac{z}{1}$ and $\large\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z-1}{2}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The shortest distance between the parallel lines $\large\frac{x-3}{4}=\frac{y-1}{2}=\frac{z-5}{-3}$ and $\large\frac{x-1}{4}=\frac{y-2}{2}=\frac{z-3}{3}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The shortest distance between the lines $\large\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\large\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The point of intersection of the lines $\overrightarrow{r}=(-\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k})+\overrightarrow{t}=(-\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k})$ and $\overrightarrow{r}=(\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{5k})+\overrightarrow{s}=(\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k})$ is

asked May 11, 2013 by poojasapani_1

1 answer

The point of intersection of the lines $\large\frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8}$ and $\large\frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}=\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k}$ and $\overrightarrow{b}=\overrightarrow{3i}+\overrightarrow{j}+\overrightarrow{2k}$ then a unit vector perpendicular to $\overrightarrow{a}$ and $\overrightarrow{b}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The work done by the force $\overrightarrow {f}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ acting on a particle, if the particle is displaced from $A(3 , 3 , 3 )$ to the point $B(4 , 4 , 4 )$ is

asked May 11, 2013 by poojasapani_1

1 answer

If the magnitude of moment about the point $\overrightarrow{j}+\overrightarrow{k}$ of a force $\overrightarrow{i}+\overrightarrow{aj}-\overrightarrow{k}$ acting through the point $\overrightarrow{i}+\overrightarrow{j}$ is $\sqrt{8}$ then the value of $a$ is

asked May 10, 2013 by poojasapani_1

1 answer

$\overrightarrow{r}=s\overrightarrow{i}+t\overrightarrow{j}$ is the equation of

asked May 10, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar and $[\overrightarrow{a}\times\overrightarrow{b},\overrightarrow{b}\times\overrightarrow{c},\overrightarrow{c}\times\overrightarrow{a}]=[\overrightarrow{a}+\overrightarrow{b},\overrightarrow{b}+\overrightarrow{c},\overrightarrow{c}+\overrightarrow{a}]$ then $[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}]$ is

asked May 10, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are a right handed triad of mutually perpendicular vectors of magnitude $a, b , c$ than value of $[\overrightarrow{a} \overrightarrow{b} \overrightarrow{c}]$ is

asked May 10, 2013 by poojasapani_1

1 answer

The vector $(\overrightarrow{a}\times\overrightarrow{b})\times(\overrightarrow{c}\times\overrightarrow{d})$ is

asked May 10, 2013 by poojasapani_1

1 answer

The shortest distance of the point $(2 , 10 ,1 )$ from the plane $\overrightarrow{r}.(\overrightarrow{3i}-\overrightarrow{j}+\overrightarrow{4k})=2\sqrt{26}$ is

asked May 10, 2013 by poojasapani_1

1 answer

The value of $[\overrightarrow{i}+\overrightarrow{j},\overrightarrow{j}+\overrightarrow{k},\overrightarrow{k}+\overrightarrow{i}]$ is equal to

asked May 10, 2013 by poojasapani_1

1 answer

If $[\overrightarrow{a} + \overrightarrow{b},\overrightarrow{b}+\overrightarrow{c},\overrightarrow{c} + \overrightarrow{a}]=8$ then $[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}]$ is

asked May 10, 2013 by poojasapani_1

1 answer

If $[\overrightarrow{a}\times\overrightarrow{b},\overrightarrow{b}\times\overrightarrow{c},\overrightarrow{c}\times\overrightarrow{a}]=64$ then $[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}]$ is

asked May 10, 2013 by poojasapani_1

1 answer

If a line makes $45^{\circ},60^{\circ}$ with positive direction of axes $x$ and $y$ then the angle it makes with the $z$ axis is

asked May 10, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a} \times(\overrightarrow{b}\times\overrightarrow{c})=(\overrightarrow{a}\times\overrightarrow{b})\times \overrightarrow{c}$ for non-coplanar vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ then

asked May 10, 2013 by poojasapani_1

1 answer

If the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ and the projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ are equal then the angle between $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ is

asked May 10, 2013 by poojasapani_1

1 answer

The projection of $\overrightarrow{OP}$ on a unit vector $\overrightarrow{OQ}$ equals thrice the area of parallelogram $OPRQ$ . Then $\angle{POQ}$ is

asked May 10, 2013 by poojasapani_1

1 answer

The equation of the plane passing through the point $(2 , 1 , -1 )$ and the line of intersection of the planes $\overrightarrow{r}. (\overrightarrow{i}+\overrightarrow{3j}-\overrightarrow{k})=0$ and $\overrightarrow{r}. (\overrightarrow{j}+\overrightarrow{2k})=0$ is

asked May 10, 2013 by poojasapani_1

1 answer

The point of intersection of the line $\overrightarrow{r}=(\overrightarrow{i}-\overrightarrow{k}) + t(\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{7k})$ and the plane $\overrightarrow{r}. (\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k})=8$ is

asked May 10, 2013 by poojasapani_1

1 answer

The equation of the line parallel to $\large\frac{x-3}{1}=\frac{y+3}{5}=\frac{2z-5}{3}$ and passing through the point $(1 , 2 ,5 )$ in vector form is

asked May 10, 2013 by poojasapani_1

1 answer

If $\overrightarrow{PR}=2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}, \;\overrightarrow{QS}=-\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow {2k},$ then the area of the quadrilateral $PQRS$ is

asked May 9, 2013 by poojasapani_1

0 answers

If $\overrightarrow{a}\times(\overrightarrow{b}\times \overrightarrow{c})+\overrightarrow{b} \times (\overrightarrow{c} \times \overrightarrow{a})+\overrightarrow{c} \times (\overrightarrow{a}\times \overrightarrow{b})=\overrightarrow{x}\times\overrightarrow{y}$ then

asked May 9, 2013 by poojasapani_1

1 answer

If $\overrightarrow{p} ,\overrightarrow{q}$ and $\overrightarrow{p}+\overrightarrow{q}$ are vectors of magnitude $\lambda$ than the magnitude of $|\overrightarrow{p}-\overrightarrow{q}|$ is

asked May 9, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a+b}|=|\overrightarrow{a-b}|$ then

asked May 9, 2013 by poojasapani_1

1 answer

The area of the parallelogram having a diagonal $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ and a side $\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{4k}$ is

asked May 9, 2013 by poojasapani_1

1 answer

The vectors $\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{4k}$ and $\overrightarrow{ai}+\overrightarrow{bj}+\overrightarrow{ck}$ are perpendicular when

asked May 9, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}+{b}+{c}=0,|\overrightarrow{a}|=3, |\overrightarrow{b}|=4,|\overrightarrow{c}|=5$ then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

asked May 9, 2013 by poojasapani_1

1 answer

If $A=\large\frac{1}{3}$ $\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$ .

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b}$ include an angle $120^{\circ}$ and their magnitude are $2$ and $\sqrt{3}$ then $\overrightarrow{a} .\overrightarrow{b}$ is equal to

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors and $\theta$ is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ is a non-zero vector and $m$ is a non-zero scalar then $m\overrightarrow{a}$ is a unit vector if

asked May 8, 2013 by poojasapani_1

1 answer

If the equation $-2x+y+z=i\;;x-2y+z=m\;;x+y-2z=n$ such that $i+m+n=0,$ then the system has

asked May 8, 2013 by poojasapani_1

1 answer

If $ae^{x}+be^{y}=c; pe^{x}+qe^{y}=d$ and $\bigtriangleup_{1}=\begin{vmatrix} a&b \\p&q \end{vmatrix}; \bigtriangleup_{2}=\begin{vmatrix} c&b\\d&q \end{vmatrix}; \bigtriangleup_{3}=\begin{vmatrix} a&c\\p&d \end{vmatrix}$ than the value of $(x , y )$ is

asked May 7, 2013 by poojasapani_1

0 answers

The system of equations $ax+y+z=0; x+by+z=0; x+y+cz=0$ has a non-trivial solution then $\large\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$

asked May 7, 2013 by poojasapani_1

1 answer

In a system of $3$ linear non-homogeneous equation with three unknowns,if $\bigtriangleup=0\;$ and $\;\bigtriangleup_{x}=0 ,\bigtriangleup_y\neq 0$ and $\bigtriangleup_z=0$ then the system has

asked May 7, 2013 by poojasapani_1

1 answer

Inverse of $\begin{bmatrix}2& -1 \\-5 & 3 \end{bmatrix}$ is

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ = $\begin{bmatrix} 0 & 0 \\0 & 5 \end{bmatrix}$ , then $A^{12}$ is

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ and $B$ are any two matrices such that $AB=O$ and $A$ is non-singular, then

asked May 7, 2013 by poojasapani_1

1 answer

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