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Recent questions tagged q12

Bag contains 2 white,1 black and 3 red balls,Bag B contains 3 white ,2 black and 4 red balls and Bag C contains 4 white ,3 black and 2 red balls.One Bag is chosen at random and 2 balls are drawn at random from that Bag.If the randomly drawn balls happen to be red and black,what is the probability that both balls come from Bag B?

asked Apr 11, 2013 by sreemathi.v

1 answer

A box contains 4 red and 5 black marbles.Find the probability distribution of the red marbles in a random draw of three marbles.Also find the mean and standard deviation of the distribution.

asked Apr 11, 2013 by sreemathi.v

1 answer

The probability that a bulb produced by a factory will fuse in 100 days of use is 0.05.Find the probability that out of 5 such bulbs,after 100 days of use :

asked Apr 10, 2013 by sreemathi.v

0 answers

In a class of 75 students,15 are above average,45 are average and the rest below average achievers.The probability that an above average achieving student fails is 0.005,then an average achieving student fails is 0.05 and the probability of a below average achieving student failing is 0.15.If a student is known to have passed,what is the probability that he is a below average achiever?

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the vector cartesian equation of the plane containing the line $\large\frac{x-2}{2}=\frac{y-2}{3}=\frac{z-1}{-2}$ and passing through the point $(-1 , 1 , -1 )$

asked Apr 8, 2013 by poojasapani_1

1 answer

Verify $(\overrightarrow{a}\times\overrightarrow{b}) \times (\overrightarrow{c}\times\overrightarrow{d})=[\overrightarrow{a} \overrightarrow{b} \overrightarrow{d} ] \overrightarrow{c} - [\overrightarrow{a} \overrightarrow{b} \overrightarrow{c} ] \overrightarrow{d}$, For $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},\overrightarrow{ b}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{c}=\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}, \overrightarrow{d}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{2k}.$

asked Apr 6, 2013 by poojasapani_1

1 answer

Show that the vectors $\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{k},\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{5k}$ and $\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{4k}$ form a right angled tringle.

asked Apr 3, 2013 by poojasapani_1

1 answer

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

asked Mar 20, 2013 by sreemathi.v

1 answer

Evaluate: $\int\large \frac{cos 2x-cos 2\alpha}{cos x-cos\alpha}$$dx$

asked Mar 20, 2013 by sreemathi.v

1 answer

If x=$acos^3\theta$ and y=$asin^3\theta,$then find the value of $\Large \frac{d^2y}{dx^2}$ at $ \theta=\Large \frac{\pi}{6}$.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the value of k, for which $f(x) =\left\{\begin{array}{1 1}\frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, & if\;-1\leq x<0\\\frac{2x+1}{x-1}, & if\;0\leq x<1\end{array}\right.$ is continuous at x=0.

asked Mar 20, 2013 by sreemathi.v

1 answer

Solve the following equation :$\cos\big(tan^{-1}x\big)=sin\bigg(cot^{-1}\frac{3}{4}\bigg)$

asked Mar 20, 2013 by sreemathi.v

1 answer

Show that: $tan\bigg(\frac{1}{2}sin^{-1}\frac{3}{4}\bigg)=\frac{4-\sqrt 7}{3}$

asked Mar 20, 2013 by sreemathi.v

1 answer

State whether the following statement is true or false. Justify. ii) If $\ast$ is a commutative binary operation on N, then $a \ast (b \ast c) = (c \ast b) \ast a$.

asked Mar 20, 2013 by balaji.thirumalai

1 answer

State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation $\ast$ on a set N, $a \ast a=a \forall a \in N$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iv)\quad k=\{(1,4),(2,5)\} $

asked Mar 13, 2013 by sreemathi.v

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iii)\quad h=\{(1,4),(2,5),(3,5)\} $

asked Mar 13, 2013 by sreemathi.v

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(ii)\quad g=\{(1,4),(2,4),(3,4)\} $

asked Mar 13, 2013 by sreemathi.v

1 answer

Prove that $tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac{1}{2}cos^{-1}x^2$

asked Feb 19, 2013 by sreemathi.v

1 answer

Prove that : $ \sin^{-1} \bigg(\large \frac{4}{5} \bigg)$$+\sin^{-1} \bigg(\large \frac{5}{13} \bigg) $$+ \sin^{-1} \bigg( \large\frac{16}{65} \bigg) = \large\frac{\pi}{2} $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Solve for x : \( \tan^{-1}3x+\tan^{-1}2x=\large\frac{\pi}{4} \)

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Solve : \[ tan^{-1}(x+1)+tan^{-1}(x-1)=tan^{-1}\frac{8}{31}\]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Prove the following : \[ tan^{-1} \bigg( \frac{x}{y} \bigg)- tan^{-1} \bigg( \frac{x-y}{x+y} \bigg)= \frac{\pi}{4},y \neq 0. \]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

(i) Is the binary operation defined on set N, given by \( a*b = \large\frac{a+b}{2}\) for all a,b \( \in\) N. commutative? (ii) Is the above binary operation associative?

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Prove that the relation R on the set A = {1,2,3,4,5} given by R = { (a,b) : | a - b | is even } is an equivalence relation.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Prove that : \[ 2tan^{-1} \bigg( \frac{1}{2} \bigg) + tan^{-1} \bigg( \frac{1}{7} \bigg) = tan^{-1} \bigg( \frac{31}{17} \bigg) \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Solve the following for x : \[ tan^{-1} \bigg( \frac{x-1}{x-2} \bigg) + tan^{-1} \bigg( \frac{x+1}{x+2} \bigg) = \frac{\pi}{4} \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If $ f(x)=\sqrt x (x \geq 0)\: and \: g(x) = x^2-1$ are two real functions, find \( fog\: and \: gof.\: Is\: fog = gof. \)

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find \( \frac{dy}{dx} \), if \( y=tan^{-1} \bigg( \frac{3x-x^3}{1-3x^2} \bigg), \frac{1}{\sqrt 3} < x < \frac{1}{3} \)

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Show that the relation R in the set \( A = \{ x/x \in W, 0 \leq x \leq 12 \} \) given by \( R = \{ (a,b):(a-b)\) is a multiple of 4 } is an equivalence relation. Also find the set of all element related to 2.

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Examine which of the following is a binary operation.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

For what value of \( \lambda \) is the function $ f(x) = \left\{ \begin{array}{l l}\lambda (x^2-2x), & \quad if { x \leq 0 } \\ 4x+1, & \quad if { x > 0 } \end{array} \right. $ is continuous at \( x=0.\)

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Prove the following : $\large\frac{9\pi}{8}-\frac{9}{4}sin^{-1}\bigg(\large\frac{1}{3} \bigg) = \frac{9}{4}sin^{-1}\bigg(\large \frac{2\sqrt 2}{3} \bigg) $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Solve the following equation for x : $ \tan^{-1} \bigg( \large\frac{1-x}{1+x} \bigg) = \large\frac{1}{2}\tan^{-1}(x), x > 0 $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

$P(A)=\frac{1}{2},P(B)=\frac{7}{12}P(not A \;or\; nor B)=\frac{1}{4}$ state whether A and B are independent.

asked Feb 5, 2013 by meena.p

0 answers

Using properties of determinants, solve the following for x : $\begin{vmatrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{vmatrix} = 0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the length and co-ordinates of the foot of perpendicular from point (1,1,2) to the plane 2x-2y+4z+5 = 0

asked Feb 5, 2013 by meena.p

0 answers

L and M are the mid-points of sides BC & DC of a paralellogram ABCD. Prove that $ \overline{AL}+\overline{AM}=\frac{3}{2}\overline{AC}$

asked Feb 4, 2013 by meena.p

1 answer

Solve:\[(x^3y^3+xy)\frac{dy}{dx}=1\]

asked Feb 4, 2013 by meena.p

0 answers

Find the value of a and b such that the following function f(x) is a continuous functions : $ f(x) = \left\{ \begin{array}{l l}5, & \quad { x \leq 2} \\ ax+b, & \quad { 2 < x < 10} \\ 21, & \quad { x \geq 10 } \end{array} \right. $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Using integration find the area of the triangle ABC whose vertices are A(3,0), B(4,6) and C(6,2)

asked Feb 4, 2013 by meena.p

0 answers

Prove the following : $ \cot^{-1} \bigg[ \large\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}} \bigg] = \frac{x}{2}, x \in \bigg( 0, \frac{\pi}{4} \bigg). $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the value of \( \tan{-1} \bigg(\large \frac{x}{y} \bigg)-\tan^{-1} \bigg(\large \frac{x-y}{x+y} \bigg). \)

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Let * be binary operation on Q defined by $ ab=\large\frac{3ab}{5} $ show that is commutative as well as associative. Also find its identity element if it exists.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Solve for x : $ 2\tan^{-1}(\sin x)=\tan^{-1} (2\sec x),0 < x < \large\frac{\pi}{2} $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Show that : $ \tan\large\frac{1}{2} \bigg[ \sin^{-1}\frac{2x}{1+x^2} + \cos^{-1}\large\frac{1-y^2}{1+y^2} \bigg] =\large \frac{x+y}{1-xy}$$, |x| < 1, y > 0 \: xy < 1 $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

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

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

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