Recent questions tagged q4

The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is \[ \begin{array} ((A)\: 27 \quad & (B)\: 18 \\ (C)\: 81 \quad & (D) \: 512 \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

Construct a $3\times 2$ matrix whose elements are given by $a_{ij}=e^{i.x}\sin jx$

asked Dec 22, 2012 by sreemathi.v

1 answer

Evaluate : $ \int \mathrm \: \frac{\large \cos \sqrt x}{\large \sqrt x} dx $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Evaluate : $\begin{bmatrix} a+ib & c+id \\[0.3em] -c+id & a-ib \\[0.3em] \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Let f : $R \to R$ be the function defined by $f(x)=2x-3$ $\forall x \in R$.Write $f^{-1}.$

asked Dec 18, 2012 by sreemathi.v

1 answer

Evaluate $ P(A \cup B)$, if $ 2P(A) = P(B) = \large \frac{5}{13} $ and $P(A | B) = \large \frac{2}{5} $

asked Dec 18, 2012 by thanvigandhi_1

1 answer

Sketch the graph of y=| x+3 | and evaluate$\Large \int\limits_{-6}^0\normalsize| x+3 |dx$

asked Dec 17, 2012 by sreemathi.v

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(a)\; 2x + 3y + 4z -12 = 0$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Prove the following: \[ 2 \: tan^{-1} \frac{1}{2} + tan ^{-1} \frac{1}{7} = tan^{-1} \frac{31}{17} \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Construct a 2 x 2 matrix, $A=[a_{ij}],$whose elements are given by: $\;a_{ij}=\frac{(i+2j)^2}{2}$

asked Dec 7, 2012 by sreemathi.v

1 answer

In Fig 10.6 (a square), identify the following vectors. \[(i)\; Coinitial\qquad (ii)\; Equal\qquad (iii)\; Collinear\; but\; not\; equal \]

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Find the values of $x$ and $y$ so that the vectors $2\hat i + 3\hat j$ and $x\hat i + y\hat j$ are equal.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the projection of the vector $ \hat i + 3\hat j + 7\hat k$ on the vector $7\hat i − \hat j + 8\hat k$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find an anti derivative(or integral)of the function by the method of inspection $(ax+b)^2$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function $\sin x\sin(\cos x)$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^3(2x+1)\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions $\frac{1}{\sqrt{9-25x^2}}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{x}{(x-1)(x-2)(x-3)}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Show that $ ( \overrightarrow a - \overrightarrow b) \times ( \overrightarrow a + \overrightarrow b) = 2 ( \overrightarrow a \times \overrightarrow b) $

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = \overrightarrow b + \overrightarrow c$, then is it true that $| \overrightarrow a | = | \overrightarrow b | + | \overrightarrow c |$? Justify your answer.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function $x\;\log x$

asked Dec 4, 2012 by sreemathi.v

1 answer

Using integration find the area of region bounded by the triangle whose vertices are $(-1, 0), (1, 3) $ and $(3, 2)$.

asked Dec 4, 2012 by thanvigandhi_1

2 answers

Integrate the function $\sqrt{x^2+4x+1}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums\[\int\limits_1^4(x^2-x)dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 4}\sin 2x\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 16} + \frac{\Large y^2}{\Large 9} = 1$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution $\int\limits_0^2 x\sqrt{x+2}\;(Put\;x+2=t^2)$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\pi}{2}\frac{\cos^5x\;dx}{\sin^5x+\cos^5x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{x^2(x^4+1)^\frac{3}{4}}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation\[y=\sqrt{1+x^2}\qquad:\;y'\;=\frac{xy}{1+x^2}\]

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^{2x}(a+bx)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\sec^2x\;\tan y\;dx+\sec^2y\;\tan x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $(x^2-y^2)dx+2xy\;dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}$$+(\sec x)y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of the line which passes through the point $(1, 2, 3)$ and is parallel to the vector $3\hat{i} + 2\hat{j} -2\hat{k}$. .

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the points (2, 3, 4), (-1, -2, 1), (5, 8, 7) are collinear.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[sin^{-1} \frac{8}{17} +sin^{-1} \frac{3}{5} =tan^{-1} \frac{77}{36}\]

asked Nov 29, 2012 by vaishali.a

1 answer

If a, b and c are real numbers, and $\Delta = \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c\\ a+b & b+c & c+a \end{vmatrix}=0, $ show that either $a+b+c=0$ or $a=b=c.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + y + z = 1 \] \[\quad 2x + 3y +2z = 2\] \[\quad ax + ay +2az = 4\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z = 3x + 5y$. such that $ x + 3y \geq 3, x + y \geq 2, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Prove that $x^2-y^2\;=\;c(x^2+y^2)^2$is the general solution of differential equation $(x^3-3x\;y^2)dx\;=\;(y^3-3x^2y)dy$ where $c$ is a parameter.

asked Nov 29, 2012 by sreemathi.v

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 1&-1&2 \\ 3&0&-2 \\ 1&0&3 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of third column, evaluate $ \Delta = \begin{vmatrix} 1&x&yz \\ 1&y&zx \\ 1&z&xy \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find equation of line joining (1, 2) and (3, 6) using determinants

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 1&bc&a(b+c) \\ 1&ca&b(c+a) \\ 1&ab&c(a+b) \end{vmatrix} = 0\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

\[ \text{If A = } \begin{bmatrix} 1&0&1 \\ 0&1&2 \\ 0&0&4 \end{bmatrix}, \text{then show that } |\;3A\;| = 27|\;A\;|\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the principal values of the following: <br>$ tan^{-1} (-\sqrt3)$

asked Nov 28, 2012 by vaishali.a

2 answers

Determine order and degree (if defined) of differential equation$\bigg(\large\frac{d^2y}{dx^2}\bigg)^2+\normalsize \cos\bigg(\large\frac{dy}{dx}\bigg)=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Find the equation of the normal to curve $y^2 = 4x$ which passes through the point $(1, 2).$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A discrete random variable X has the following probability distributions (see table below). (i) Find the value of a

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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