Recent questions tagged sec-b

Evaluate the following: $\int e^{\tan^{-1}x}\bigg(\frac{1+x+x^2}{1+x^2}\bigg)dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_0^{\Large\pi} \large \frac{x}{1+\sin x}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^{\Large \frac{1}{2}}\frac{dx}{(1+x^2)\sqrt {1-x^2}}$$(Hint:let\;x=\sin\theta)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_1^2\frac{dx}{\sqrt{(x-1)(2-x)}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^{\Large \frac{\pi}{2}}\Large \frac{\tan xdx}{1+m^2\tan^2x}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^1\frac{dx}{e^x+e^{-x}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following as limits of sums: $ \int\limits_0^2e^xdx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following as limits of sums: $\int\limits_0^2(x^2+3)dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{\sqrt x}{\sqrt{a^3-x^3}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following : $\begin{align} \int \frac{\sin^6x+\cos^6x}{\sin^2x \cos^2x}dx \end{align}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{\sin^{-1}x}{(1-x^2)^{\frac{3}{2}}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{3x-1}{\sqrt{x^2+9}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{\sqrt{1+ x^2}}{x^4}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\large\int\frac{ x^{\frac{1}{2}}}{1+x^{\frac{3}{4}}}dx$ $(Hint:Put\;x=z^4)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\sqrt{\frac{a+x}{a-x}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Verify the following $ \large\int\frac{2x+3}{x^2+3x}dx=log \mid x^2+3x\mid+C$

asked Jan 14, 2013 by sreemathi.v

1 answer

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are $ \hat i +2\hat j - \hat k \: and \: -\hat i + \hat j + \hat k$ respectively in the ratio 2 : 1 (i) internally (ii) externally

asked Jan 14, 2013 by thanvigandhi_1

0 answers

Show that the plane passing through (1, 1, 1),(1, 01, 1) and (-7, -3, -5) is perpendicular to ZX-plane.

asked Jan 14, 2013 by thanvigandhi_1

0 answers

A variable plane is at a constant distance '3p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of $ \Delta $ABC is $ \frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2} $

asked Jan 14, 2013 by thanvigandhi_1

0 answers

(i) In a group of student, selection of four students for cultural activity from 3 boys and 3 girls has to be done. Find the probability that either 3 boys and 1 girl or 3 girls and one boy are selected. (ii) Write the importance of co-curricular activities in inculcating human values.

asked Jan 14, 2013 by thanvigandhi_1

0 answers

Let L be the set of all lines in XY - planes and R be the relation in L defined as R = $ { (L_1, L_2 ) : L_1 \: is \: parallel\: to\: L_2} $. Show the R is an equivalence relation. Find the set of all the lines related to the line $ y=2x+4.$

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, prove the following : $ \begin{bmatrix} b+c & a & a \\ b & c+a & b \\ c & c & a+b \end{bmatrix} = 4abc.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $ \begin{bmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{bmatrix} = 2 \begin{bmatrix} a & b & c \\ p & q & r \\ x & y & z \end{bmatrix}. $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

If $ y=e^{\large a \: cos^{-1}\: x} ; -1 \: \leq \: x \leq \: 1$, show that $ (1+x^2) \large\frac{d^2y}{dx^2}-x\frac{dy}{dx}-$$a^2y=0.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

If $ x \sqrt {1+y} + y \sqrt{1+x}=0 \: for \: -1 < x < 1$ Prove that : $\large \frac{dy}{dx}=\frac{1}{(1+x)^2} $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the equation of tangent to the curve $ x=sin \: 3t, \: y=cos\: 2t, \: at \: t=\large\frac{\pi}{4}. $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

At what point will the tangent to the curve $ y=2x^3-15x^2+36x-21$ be parallel to x - axis? Also, find the equations of tangents to the curve at these points ?

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \sin x \sqrt {1+\cos2x} dx.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{x^2+x+1}{(x+2)(x+1)^2}$$dx.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{dx}{x[6(log \: x)^2]+7( log \: x)+2}$$dx.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \tan^{-1} \sqrt{ \large\frac{1-sinx}{1+sinx}}dx. $

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation $ x(1+y^2)dx-y(1+x^2)dy=0 $ given that $ y=0, \: when \: x=1$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation $\large\frac{dy}{dx}$$+\sec x.y = \tan \: x. $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the magnitude of two vectors $ \overrightarrow a \: and \overrightarrow b $ having the same magnitude and such that the angle between them is $ 60^{\circ} $ and their scalar product is $\large\frac{1}{2}$.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

A man is known to speak the truth 3 out of 5 times. He throws a dice and reports that it is 1. Find the probability that it is actually 1.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Two bags A and B contain 2 white, 4 red and 3 white, 3 red balls respectively. One of the bags is selected at random and a ball is drawn from it. If the selected ball is of white colour, find the probability that it is drawn from bag A.

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Find the points of local maxima,local minima and the points of inflection of the function $f(x)=x^5-5x^4+5x^3-1$. Also find the corresponding local maximum and local minimum values.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that $f(x)=\sin x+\sqrt 3\cos x$ has maximum value at $x=\Large\frac{1}{6}$.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what point,the slope of the curve $y=-x^3+3x^2+9x-27$ is maximum?Also find the maximum slope.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that $f(x)=\tan^{-1}(\sin x+\cos x)$ is an increasing function in$\bigg(0,\Large \frac{1}{4}\normalsize \bigg).$

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that for a$\quad 1,f(x)=\sqrt 3\sin x-\cos x-2ax+b$ is decreasing in R.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that $f(x)=2x+\cot^{-1}x+log\bigg(\sqrt {(1+x^2)}-x\bigg)$ is increasing in R.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that the line $\Large \frac{x}{a}+\frac{y}{b}\normalsize=1$,touches the curve $y=b.e^{\Large \frac{-x}{a}}$ at the point where the curve intersects the axis of y.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what points on the curve $x^2+y^2-2x+4y+1=0$,the tangents are parallel to the y-axis?

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the equation of the normal lines to the curve $3x^2-y^2=8$ which are parallel to the line x+3y=4.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that the curves $y^2=4x$ and $x^2+y^2-6x+1=0$ touch each other at the point (1,2).

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the angle of intersection of the curves $y=4-x^2$ and $y=x^2$.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the co-ordinates of the point on the curve $\sqrt x\quad \sqrt y=4$ at which tangent is equally inclined to the axes.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that the curves $xy=4$ and $x^2+y^2=8$ touch each other.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the condition that the curves $2x=y^2$ and $2xy=k$ intersect orthogonally.

asked Jan 11, 2013 by sreemathi.v

1 answer

Ask Questions, Get Answers