Recent questions tagged q1

Show that the relation R in the set R of real numbers, defined as $ R = {( a, b ) : a \leq b^2}$, is neither reflexive, nor symmetric , nor transitive.

asked Jan 2, 2013 by thanvigandhi_1

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Relation R in the set of Z of all integers defined as R = {(x, y) : x-y is an integer }.

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Examine the continuity of the function $f(x)=x^3+2x^2-1$ at $x=1$

asked Dec 31, 2012 by sreemathi.v

1 answer

Write the number of all one-one functions from the set A = { a, b, c} to itself.

asked Dec 29, 2012 by thanvigandhi_1

1 answer

Give an example to show that the relation R in the set of natural numbers, defined by $ R = ( (x,y), x, y \in\: N, x \leq \: y^2) $ is not transitive.

asked Dec 26, 2012 by thanvigandhi_1

1 answer

Using the properties of determinants, evaluate $\begin{vmatrix} x^2 - x+1 & x-1 \\ x +1 & x+1 \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Let * be a binary operation on set Q of rational numbers defined as ab = $ \large\frac{3ab}{7} $. Write the identity for , if any.

asked Dec 24, 2012 by thanvigandhi_1

1 answer

Let N be the set of natural numbers and R be the relation in N defined as $R = {(a, b) : a = b – 2, b > 6}$. Then \[ \begin{array} ((A)\: (2, 4) ∈ R \quad & (B)\: (3, 8) ∈ R \\ (C) \: (6, 8) ∈ R \quad & (D)\: (8, 7) ∈ R. \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

1 answer

If a matrix has 28 elements, what are the possible orders it can have?

asked Dec 21, 2012 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 Dec 20, 2012 by thanvigandhi_1

1 answer

If $ f(x) = x + 7$ and $ g(x) = x - 7, x \in \: R $ , find ( fog ) (7)

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find the value of $\; \tan^{-1}\bigg(\tan{\frac{5\pi}{6}}\bigg)+\cos^{-1}\bigg(\cos{\frac{13\pi}{6}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

Let $A={a,b,c}$ and the relation $R$ be defined on $A$ as follows: $R= {(a,a)(b,c)(a,b)}$. Write the minimum number of ordered pairs to be ordered pairs to be added in $R$ to make $R$ reflexive and transitive.

asked Dec 18, 2012 by sreemathi.v

1 answer

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E $\cap$ F) = 0.2, find P (E|F) and P(F|E)

asked Dec 18, 2012 by thanvigandhi_1

1 answer

In each of the following cases,determine the direction cosines of the normal to the plane and the distance from the origin. $(a)\; z = 2 $

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the value of: $\cos^{-1} (\cos \large\frac{13\pi}{6} ) $

asked Dec 10, 2012 by thanvigandhi_1

1 answer

In the matrix $A=\begin{bmatrix}2 & 5 & 19 & -7\\35 & -2 & \frac{5}{2} & 12\\\sqrt 3 & 1 & -5& 17\end{bmatrix},$write:\[(i)\;The\;order\;of\;the\;matrix,\qquad(ii)\;The\;number\;of\;the\;elements,\]\[(iii)\;Write\;the\;elements\;a_{13},a_{21},a_{33},a_{24},a_{23}\]

asked Dec 7, 2012 by sreemathi.v

1 answer

Represent graphically a displacement of 40 km, 30° east of north.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$\[Find\;each\;of\;the\;following:\]\[(i)\;A+B\qquad(ii)\;(A-B)\qquad(iii)\;3A-C\]\[(iv)\;AB\qquad(v)BA\]

asked Dec 7, 2012 by sreemathi.v

1 answer

Prove the following\[3\sin^{-1}x=\sin^{-1}(3x-4x^3)\;x\in\bigg[-\frac{1}{2},\frac{1}{2}\bigg]\]

asked Dec 6, 2012 by sreemathi.v

1 answer

Compute the magnitude of the following vectors: $(i)\;\overrightarrow a = \hat i + \hat j + \hat k$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the angle between two vectors $ \overrightarrow a$ and $ \overrightarrow b$ with magnitudes $ \sqrt 3$ and $2$ , respectively having $ \overrightarrow a . \overrightarrow b = \sqrt 6.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find an anti derivative(or integral)of the function by the method of inspection $\sin 2x$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function$\frac{\large 2x}{\large 1+x^2}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function $\Large \frac{\large e^{\tan^{-1}x}}{\large 1+x^2}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^2(2x+5)\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{3x^2}{x^6+1}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

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

asked Dec 5, 2012 by sreemathi.v

1 answer

Find $| a × b |$, if $a = \hat i - 7\hat j + 7\hat k$ and $b = 3\hat i - 2\hat j + 2\hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Write down a unit vector in XY plane, making an angle of 30 degress with the positive direction of $x$ axis.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function $\;\int\;x\;sin\;x$

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the circle $4x^2 + 4y^2 = 9$ which is interior to the parabola $x^2 = 4y$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area under the given curves and given lines: $ (i) \: y = x^2, x = 1, x = 2 \: and\: x - axis$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function\[\sqrt{4-x^2}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_a^bx\;dx$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_{-1}^1(x+1)dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x$ - axis.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the integral using substitution\[\int\limits_0^1\frac{x}{x^2+1}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^\frac{\Large \pi}{\Large 2}\cos^2x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{x-x^3}\]

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 $y=e^x+1\qquad:\;y''-y'=0$

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 $\large\frac{x}{a}+\frac{y}{b}=1$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

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

asked Nov 30, 2012 by sreemathi.v

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the three lines with direction cosines $\large \frac{12}{13}, \frac{-3}{13}, \frac{-4}{13}; \;\; \frac{4}{13}, \frac{12}{13}, \frac{3}{13}; \;\; \frac{3}{13}, \frac{-4}{13}, \frac{12}{13}$ are mutually perpendicular.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If a line makes angles $90^\circ$,$135^\circ$, $45^\circ$ with the x, y and z-axes respectively, find its direction cosines.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{Prove that the determinant } \begin{vmatrix} x&sin\theta&cos\theta \\ -sin\theta&-x&1\\ cos\theta&1&x \end{vmatrix} \text{ is independent of } \theta \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 2y = 2 \] \[\quad 2x + 3y = 3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 4y$ . subject to the constraints : $x + y \leq 4, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

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