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Recent questions tagged sec-b

Find all the points of discontinuity of the function \( f(x)=[x^2]\) on [1,2), where [.] denotes the greatest integer function.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Differentiate \( \sin^{-1}(2x\sqrt{1-x^2})\) w.r.t. \( \cos^{-1} \bigg( \large\frac{1-x^2}{1+x^2} \bigg) \).

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{1}{\cos(x-a)\cos(x-b)}$$dx $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int x(\log x )^2.dx $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Evaluate : \[ \int \frac{x}{x^3-1} dx \]

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Using properties of definite integrals, evaluate \[ \int_0^x \frac{xdx}{4-cos^2x} \]

asked Feb 3, 2013 by thanvigandhi_1

0 answers

The dot products of a vector with the vectors \( \hat i - 3\hat k, \hat i - 2\hat k \) and \( \hat i + \hat j + 4\hat k\) are 0,5 and 8 respectively. Find the vector.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find the equation of plane passing through the point (1,2,1) and perpendicular to the line joining the points (1,4,2) and (2,3,5). Also, find the perpendicular distance of the plane from the origin.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find the equation of the perpendicular drawn from the point p(2,4,-1) to the line \( \frac{x+5}{1} = \frac{y+3}{4}=\frac{z-6}{-9} \).

asked Feb 3, 2013 by thanvigandhi_1

0 answers

A biased die is twice as likely to shown an even number as an odd number. The die is rolled three times. If occurance of an even number is considered a success, then write the probability distribution of number of successes. Also find the mean number of successes.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Let * be binary operation of N x N defined by (a,b)(c,d)=(a+c,b+d). Show that is commutative as well as associative. Find the identity element for the operation * on N x N, if any.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Given relation R is the set Z of all integers is given by \( R= \{(a,b) \in Z \times Z, a-b\) is an integer }. Find whether R is an equivalence relation or not.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Prove that : $ 2\tan^{-1} \frac{1}{2} + \tan^{-1}\large \frac{1}{7} $$= \tan^{-1} \large\frac{31}{17} $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Simplify : $ \cos^{-1} \bigg(\large \frac{3}{5}$$ \cos \theta +\large \frac{4}{5}$$ sin \theta \bigg) $

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Principal and staff of a school decided to award prizes to their students for three values Honesty (x), cleanliness (y) and punctuality (z) in two groups. Group A (upto class VIII) and group B (IX-XII). It is decided that Rs. 12000 for three values (x,y,z) for 3,4,5 students of group A and Rs. 11040 for 5,4,3 students of group B respectively. If all the three prizes together amount to Rs. 2880 then, (i) Represent above situation by a matrix equation and form linear equation using matrices. (ii)Is it possible to solve the system of linear equations so obtained using matrices.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Find the point (s) of discountinuity of the function 'f' given by $ f(x) = \left\{ \begin{array}{l l}|x|+3, & \quad { x \leq -3} \\ -2x, & \quad {-3 < x < 3} \\ 6x+2, & \quad { x > 3 } \end{array} \right. $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Differentiate : $ \tan^{-1} \bigg( \large\frac{\sqrt{1-x^2}}{x} \bigg)$ w.r.t. \( \cos^{-1} \bigg( 2x\sqrt{1-x^2} \bigg). \)

asked Feb 2, 2013 by thanvigandhi_1

0 answers

If $x= \bigg( \cos\theta + \log \tan\large\frac{\theta}{2} \bigg), $$y=\sin\: \theta, \large\frac{d^2y}{dx^2}$$\: at \: \theta=\large\frac{\pi}{4} $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

If \( y=log \bigg( x+\sqrt{x^2+1} \bigg)\), then prove that $(x^2+4)\large\frac{d^2y}{dx^2}$$+x\large\frac{dy}{dx}=0$.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

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

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{\sin \: 2x}{(1+x^2)(3+x^2)} $$dx $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{\sin x\cos x}{a^2\sin^2x+b^2+\cos^2x}$$dx $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Evaluate the following integral using limit of sums $\int_1^4 \: x^2-xdx $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^a \large\frac{\sqrt x}{\sqrt x+\sqrt{a-x} }$$dx $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Show that each of the given three vectors is a unit vector. \( \frac{1}{7} (2\hat i + 3\hat j + 6\hat k), \frac{1}{7} (3\hat i - 6\hat j + 2\hat k), \frac{1}{7} (6\hat i + 2\hat j - 36\hat k). \)Also, show that they are mutually perpendicular to each other.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Find the equation of a line passing through the point (-1,-1,2) and perpendicular to the planes \( 3x+2y-3z=1 \: and \: 5x-4y+z=5\)

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Find the equation of a line passing through the point (2,1,3) and perpendicular to the lines $ \large\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}$ and $\large\frac{x}{-3}=\frac{y}{2}=\frac{z}{5} $.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

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.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Solve : $ \tan^{-1}2x+tan^{-1}3x = \large\frac{\pi}{4}. $

asked Feb 2, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 4 & 3 \\ 2 & 5 \end{bmatrix}$, find $x$ and $y$ such that $ A^2-xA+yI=0. $

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, prove that : $ \begin{vmatrix} a+b+nc & (n-1)a & (n-1)b \\ (n-1)c & b+c+na & (n-1)b \\ (n-1)c & (n-1)a & c+a+nb \end{vmatrix} = n(a+b+c)^3$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Assuming that petrol burnt per hour in driving a motor boat varies as the cube of its velocity. Show that the most economical speed when going against a current of k km/hour is \( \large\frac{3k}{2} \) km/hour.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

If $ x=a(\cos t+t\sin t), \: y=a(\sin t - t\cos t), \: find \; \large\frac{d^2y}{dx^2}$$ \: at \: t=\large\frac{\pi}{4}. $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Show that the function $ f(x) = \left\{ \begin{array}{l l}-x^2, & \quad { x \leq 0} \\ x^2, & \quad { x \geq 0} \end{array} \right. $ is continuous at x = 0, also show that f is differentiable at x = 0.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{1}{1+x^4}$$ dx$

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int\large \frac{dx}{2e^{2x}+3e^x+1} $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\Large\frac{1}{\sqrt 2}} \large\frac{\sin^{-1}x}{(1-x^2)^{\frac{3}{2}}} $$dx.$

asked Jan 31, 2013 by thanvigandhi_1

0 answers

If \( \hat i+\hat j + \hat k, \: 2\hat i + 5\hat j,\: 3\hat i + 2\hat j - 3\hat k\) and \( \hat i - 6\hat j - \hat k\) respectively are the position vectors of the point A, B, C and D, then find the angle between AB and CD are parallel.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Using vectors, prove cosine formula $ \cos \: A = \large\frac{b^2+c^2-a^2}{2bc} $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^3 f(x) \: dx $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Solve the differential equation : $ (x^2+xy)dy=(x^2+y^2)dx$

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Solve the differential equation : $ (x^2-1)\large\frac{dy}{dx}$$+2xy=\large\frac{1}{x^2-1} $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

In a meeting, 70% of the members favour a certain proposal, 30% being opposite. A member is selected at random and we take X = 0, if he opposed, and x = 1, if he is in favour. Find E(X) and variance (X).

asked Jan 31, 2013 by thanvigandhi_1

0 answers

In a family the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other.

asked Jan 31, 2013 by thanvigandhi_1

1 answer

Given relation R in the set Z of all integers is given by \( R = {(a,b) \in Z * Z\: a-b \: is\: an\: integer }\). Find whether R is an equivalence relation or not.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Let * be binary operation of N x N defined by (a,b)(c,d)=(a+c, b+d). Show that is commutative as well as associative. Find the identity element for the operation * on N x N, if any.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Solve for x : \( 2\: tan^{-1}(\cos x)=tan^{-1}(2 cosec x) \)

asked Jan 31, 2013 by thanvigandhi_1

1 answer

There are two families P and Q. There are 3 men, 3 women and 12 children in family P and 2 men, 2 women and 4 children in family Q. The recommended daily allowance for calories is : Man : 2400, woman : 2000, child: 1400 and man : 60 g for proteins is : woman: 40 g and child: 35 g. (i) Represent the above information by matrices. Using matrix multiplication, calculate the total requirement of calories and proteins of each of the two families.

asked Jan 31, 2013 by thanvigandhi_1

1 answer

If the function \( f(x) = \left\{ \begin{array}{l l}3ax+b, & \quad if\: { x > 1} \\ 11, & \quad if \: { x = 1} \\ 5ax-2b, & \quad if \: { x < 1} \end{array} \right. \) is continuous at x = 1, find the values of a and b.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Find $ \large\frac{dy}{dx}, \: if \: x^y+y^x=a^b.$

asked Jan 31, 2013 by thanvigandhi_1

0 answers

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