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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

Integrate $\int \limits_0^1 x(1-x)^n dx. n \in N$

asked Dec 12, 2013 by meena.p

1 answer

Integrate: $\int \large\frac{2}{3} \frac{e^x \sqrt {e^x-4}}{e^x+g}$ $dt$

asked Dec 12, 2013 by meena.p

1 answer

Integrate $\int \limits_0^1 x^m (1-x)^n.dx$

asked Dec 11, 2013 by meena.p

1 answer

If $\overrightarrow a=\hat i+\hat j+p\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j+\hat k$ , then $|\overrightarrow a+\overrightarrow b|=|\overrightarrow a|+|\overrightarrow b|$ holds for ?

asked Dec 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {\alpha}=(x+4y)\overrightarrow a+(2x+y+1)\overrightarrow b\:\:and\:\:\overrightarrow {\beta}=(y-2x+2)\overrightarrow a+(2x-3y-1)\overrightarrow b$ where $\overrightarrow a\:\:\overrightarrow b$ are non zero non collinear and if $3\overrightarrow {\alpha}=2\overrightarrow {\beta}$ , then $(x,y)=?$

asked Dec 10, 2013 by rvidyagovindarajan_1

1 answer

If a person standing at the point $(1,2)$ walks $5$ units towards east, then $3$ units towards north and $\sqrt 2$ units along the direction of $\hat i+\hat j$ and then walks $\sqrt 2$ unit along the direction $\perp$ to this vector towards the starting point. What is the displacement of the person from origin?

asked Dec 9, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a+2\overrightarrow b+3\overrightarrow c=\overrightarrow 0$ , then $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2p\hat i+\hat j$ is rotated about an angle of $\theta$ in anti clock wise direction and becomes $(p+1)\hat i+\hat j$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {AB}=3\hat i-2\hat j+2\hat k$ and $\overrightarrow {BC}=-\hat i-2\hat k$ are adjacent sides of a parallelogram, then the angle between the diagonals is ?

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors that are inclined at angle $2\theta$ where $0\leq \theta \leq \pi$ and $|\overrightarrow a-\overrightarrow b| < 1$ then $\theta$ lies in the interval....

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow b\:\:is\:\: \perp\:\:to \:\:\overrightarrow a+\overrightarrow b\:\:and\:\:\overrightarrow a\:\:is\:\:\perp \:\:to\:\:2\overrightarrow b+\overrightarrow a$ then $|\overrightarrow a|=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two unit vectors such that $\overrightarrow a+2\overrightarrow b\:\:and\:\:5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\:\:and\:\:\overrightarrow b$ is?

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:and\:\overrightarrow b$ are two non collinear unit vectors and $\overrightarrow u=\overrightarrow a-(\overrightarrow a.\overrightarrow b)\overrightarrow b\:\:and\:\:\overrightarrow v=\overrightarrow a\times\overrightarrow b$ , then $|\overrightarrow v|=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow v=2\hat i+\hat j-\hat k, \:\:and\:\:\overrightarrow w=\hat i+3\hat k\:\:and\:\:\overrightarrow u$ is a unit vector, then the maximum value of $[\overrightarrow u\:\overrightarrow v\:\overrightarrow w]=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are unit vectors, then the maximum value of $|\overrightarrow a-\overrightarrow b|^2+|\overrightarrow b-\overrightarrow c|^2+|\overrightarrow c-\overrightarrow a|^2$ is ?

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=|\overrightarrow c|=1, \:|\overrightarrow b|=4,\:\overrightarrow a\times\overrightarrow b=2\overrightarrow a\times\overrightarrow c\:and\:$ if the angle between $\overrightarrow b\:and\:\:\overrightarrow c$ is $cos^{-1}\large\frac{1}{4}$ then $\overrightarrow b-2\overrightarrow c=?$

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

The number of vectors $\overrightarrow b$ of unit length which are $\perp$ to $\overrightarrow a=\hat i+2\hat j\:\:and\:\:\overrightarrow c=\hat j+2\hat k$ is?

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two unit vectors, then $\overrightarrow a\times\overrightarrow b$ is also a unit vector if ?

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ are $\perp$ then $\overrightarrow a,\:\overrightarrow b\:\overrightarrow c$ are .....

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a$ is any vector such that $\overrightarrow a\times \hat i+2\overrightarrow a-5\hat k=\overrightarrow 0$ , then $\overrightarrow a=?$

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow d=x(\overrightarrow a \times\overrightarrow b)+y(\overrightarrow b\times\overrightarrow c)+z(\overrightarrow c\times\overrightarrow a)$ and $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=\large\frac{1}{8}$ , then $x+y+z=?$

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=p\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow b=\sqrt q\hat i+5\hat k$ are two vectors of same magnitude, then no. of values of $(p,q)$ are?

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j-\hat k,\:\overrightarrow b=-\hat i+2\hat j+\hat k\:\:and\:\:\overrightarrow c=-\hat i+2\hat j-\hat k$ , then a unit vector $\perp$ to $\overrightarrow a+\overrightarrow b$ and $\overrightarrow b+\overrightarrow c$ is ?

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

A man walks 4 mtrs. towards west and then walks 3 mtrs in the direction of $\large\frac{\pi}{6}\:$ radians east of north. What is the displacement of the man from the starting point?

asked Dec 5, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three unit vectors such that $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c=0$ and the angle between $\overrightarrow b\:\:and\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$ , then $\overrightarrow b\times\overrightarrow c=?$

asked Dec 5, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow b\times\overrightarrow c=\overrightarrow a$ , then the magnitude of $\overrightarrow b$ is?

asked Dec 5, 2013 by rvidyagovindarajan_1

1 answer

$|\overrightarrow a\times\overrightarrow b|^2= ?$ (which one of the following )

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If vector $\overrightarrow a$ is unit vector and it makes angle $\large\frac{\pi}{4}$ with $\hat k$ and $\overrightarrow a+\hat i+\hat j$ is also a unit vector, then $\overrightarrow a=?$

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If $D\:\:and\:\:E$ are mid points of the side $\overline {AB}\:\:and\:\:\overline {AC}$ of a $\Delta \:ABC$ , then $\overrightarrow {BE}+\overrightarrow {DC}=?$

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If sum of two unit vectors is also a unit vector then the magnitude of their difference is ?

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {AB}=3\hat i+\hat j-2\hat k,\:and \:\overrightarrow {AC}=-\hat i+3\hat j+4\hat k$ are two sides af the $\Delta ABC$ , then the length of the median through $A$ is ?

asked Dec 1, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\overrightarrow b=\hat i\:\:and\:\:\overrightarrow c=x\hat i-\hat j+\hat k$ , then the value of $x$ for which $\overrightarrow a\:\overrightarrow b\:and\:\overrightarrow c$ are coplanar is ?

asked Dec 1, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are three vectors of magnitude $3,4,5$ respectively. If each vector is $\perp$ to sum of the other two vectors then $|\overrightarrow a+\overrightarrow b+\overrightarrow c|=?$

asked Nov 30, 2013 by rvidyagovindarajan_1

1 answer

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is ?

asked Nov 30, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a+\overrightarrow b|=|\overrightarrow a|$ , then the angle between $2\overrightarrow a+\overrightarrow b$ and $\overrightarrow b$ is ?

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a= x^2\hat i+2\hat j-2\hat k,\:\overrightarrow b=\hat i-\hat j+\hat k\;and\:\overrightarrow c=x^2\hat i+5\hat j-4\hat k$ are three vectors, then the values of $x$ for which the angle between $\overrightarrow a\:and\:\overrightarrow b$ is acute and that between $\overrightarrow b\:and\:\overrightarrow c$ is obtuse is ?

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b\:and\:\overrightarrow c$ are non coplanar vectors and if $\overrightarrow a'=\large\frac{\overrightarrow b\times \overrightarrow c}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\overrightarrow b'=\large\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:and \:\overrightarrow c'=\large\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},$ then $\overrightarrow a.\overrightarrow a'+\overrightarrow b.\overrightarrow b'+\overrightarrow c.\overrightarrow c'=?$

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

For any vector $\overrightarrow a\:\:and\:\:\overrightarrow b$ the angle between $|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a$ and $|\overrightarrow a|\overrightarrow b-|\overrightarrow b|\overrightarrow a$ is ?

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

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

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