Recent questions tagged q3

For what value of x, is the following matrix singular? $ \begin{bmatrix} 3-2x & x+1 \\ 2 & 4 \end{bmatrix}.$

asked Jan 9, 2013 by thanvigandhi_1

0 answers

The probability that at least one of the two events A and B occurs is 0.6.If A and B occur simultaneously with probability 0.3,evaluate $P(\bar{A})+P(\bar{B})$.

asked Jan 8, 2013 by sreemathi.v

1 answer

Find the value of x if $ \begin{bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} $

asked Jan 8, 2013 by thanvigandhi_1

1 answer

Maximise the function $Z=11x+7y$,subject to the constraints : $x\leq 3,y\leq 2,x\geq 0,y\geq 0.$

asked Jan 7, 2013 by sreemathi.v

1 answer

Compute the following : $\begin{bmatrix} a^2+b^2 & b^2+c^2 \\ a^2+c^2 & a^2+b^2 \end{bmatrix} + \begin{bmatrix} 2ab & 2bc \\ -2ac & -2ab \end{bmatrix} $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \begin{bmatrix} sin30^{\circ} & cos30^{\circ} \\ -sin60^{\circ} & cos60^{\circ} \end{bmatrix} $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

A matrix A, of order 3 x 3, has determinant 4 find the value of |3A|.

asked Jan 3, 2013 by thanvigandhi_1

1 answer

Find the value of y if $\begin{bmatrix} x-y & 2 \\ x & 5 \end{bmatrix} = \begin{bmatrix} 2 & 2 \\ 3 & 5 \end{bmatrix} $

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Find the value of x and y if : $2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{1-\cos 2x}{x^2} & \normalsize if\;x\neq 0\\5 & if\;x=0\end{array}\right.$at x=0.

asked Dec 31, 2012 by sreemathi.v

1 answer

What is the value of $ | 3\: I_3 | $ where $ I_3 $ is the identity matrix of order 3?

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find x, if $ \begin{bmatrix} 5 & 3x \\ 2y & z \end{bmatrix} $ = $ \begin{bmatrix} 5 & 4 \\ 12 & 6 \end{bmatrix}^T $

asked Dec 26, 2012 by thanvigandhi_1

1 answer

Solve for $x$ and $y$ $\begin{bmatrix} 3 & \quad -4 \\ 1 & \quad 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 11 \end{bmatrix} $

asked Dec 25, 2012 by thanvigandhi_1

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} 0 & xy^2 & xz^2 \\ x^2y & 0 & yz^2 \\ x^2z & zy^2 & 0 \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

$ sin \bigg (\frac{\pi}{3} - sin^{-1} (\frac{1}{2}) \bigg) $ is equal to \[ \begin{array} ((A) \: \frac{1}{2} \quad & (B)\: \frac{1}{3} \\ (C)\: \frac{1}{4} \quad & (D) \: 1 \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

1 answer

Construct $a_{2\times 2}$ matrix where $a_{ij} =\frac{(i + 2j)^2}{2}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Evaluate : $ \int_0^{\Large\frac{1}{\sqrt 2}} \mathrm \: \frac{\large 1}{\large \sqrt{1-x^2}} dx $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Find the value of $x$ and $y$ if : $ 2\begin{bmatrix} 1 & 3 \\[0.3em] 0 & x \\[0.3em] \end{bmatrix} + \begin{bmatrix} y & 0 \\[0.3em] 1 & 2 \\[0.3em] \end{bmatrix} = \begin{bmatrix} 5 & 6 \\[0.3em] 1 & 8 \\[0.3em] \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Let $f,g:R \rightarrow $R be defined by $f(x)=2x+1$ and $g(x)=x^2-2,\forall x \in R,$respectively. Then, find $g\;of(x)$.

asked Dec 18, 2012 by sreemathi.v

1 answer

If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find \[ \begin{array} ((i) P(A \cap B) \quad & (ii) P(A|B) \quad & (iii) P(A ∪ B) \end{array} \]

asked Dec 18, 2012 by thanvigandhi_1

1 answer

Find the Cartesian equation of the plane $\;(a)\; \overrightarrow r. (\hat i + \hat j - \hat k) = 2$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

What does $ 2\sin^{-1} \frac{3}{5}$ reduce to

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Compute the indicated products\begin{array}{1 1 1}(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}\begin{bmatrix}a &-b\\b & a\end{bmatrix}\;(ii)\;\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2 & 3 & 4\end{bmatrix} & (iii)\;\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix}\\(iv)\;\begin{bmatrix}2 & 3 &4\\3 & 4 &4\\4 & 5 & 6\end{bmatrix}\begin{bmatrix}1 & -3 & 5\\0 & 2 &4\\3 & 0 & 5\end{bmatrix} & (v)\;\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix}\\(vi)\;\begin{bmatrix}3 & -1 &3\\-1 & 0 &2\end{bmatrix}\begin{bmatrix}2 & -3\\1 & 0\\3 & 1\end{bmatrix}\end{array}

asked Dec 7, 2012 by sreemathi.v

1 answer

If a matrix has 18 elements,what are the possible orders it can have?What, if it has 5 elements?

asked Dec 7, 2012 by sreemathi.v

1 answer

Classify the following as scalar and vector quantities. $ (i)\; $time period.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Prove the following\[\tan^{-1}\frac{2}{11}+\tan^{-1}\frac{7}{24}=\tan^{-1}\frac{1}{2}\]

asked Dec 6, 2012 by sreemathi.v

1 answer

Write two different vectors having same direction.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the projection of the vector $ \hat i − \hat j$ on the vector $ \hat i + \hat j $.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find an anti derivative(or integral)of the function by the method of inspection $e^{2x}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function $\frac{\large 1}{\large x+x\;log x}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\cos2x\;\cos4x\;\cos6x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{(2-x)^2+1}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

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

asked Dec 5, 2012 by sreemathi.v

1 answer

If a unit vector $\overrightarrow a$ makes angles $ \frac{\large \pi}{\large 3} $ with $ \hat i, \frac{\large \pi}{\large 3} $ with $ \hat j$ and an acute angle $θ$ with $ \hat k$ , then find $ θ $ and hence, the components of $ \overrightarrow a $ .

asked Dec 5, 2012 by thanvigandhi_1

1 answer

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function\[x^2e^x\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by the curves $y = x^2 + 2, y = x, \: x = 0$ and $x = 3.$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region lying in the first quadrant and bounded by $y = 4x^2, x = 0, y = 1$ and $y = 4$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function $\sqrt{x^2+4x+6}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums $\begin{align}\int\limits_2^3x^2dx \end{align}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_1^2(4x^3-5x^2+6x+9)\;dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by $x^2 = 4y, y = 2, y = 4$ and the $y$ - axis in the first quadrant.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution $\begin{align}\int\limits_0^1\sin^{-1}\bigg(\frac{2x}{1+x^2}\bigg)dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\pi}{2}\frac{\sin^\frac{3}{2}\;x\;dx}{\sin^\frac{3}{2}\;x+\cos^\frac{3}{2}\;x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{x\sqrt{ax-x^2}}[Hint:Put\;x=\frac{a}{t}]\]

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 $y=\cos x+C\qquad:y'+\sin x=0$

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. $y=a\: e^{3x}+b\: e^{-2x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$+y=1(y\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve\[(x-y)\;dy-(x+y)\;dx=0\]

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}+\frac{y}{x}$$=x^2$

asked Nov 29, 2012 by sreemathi.v

1 answer

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