Recent questions in Class12

Four dice are rolled. The number of possible outcomes in which at least one dice shown 2 is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

An integer is chosen at random from first two hundred numbers. Then the probability that the integer chosen is divisible by 6 or 8 is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

The probability that the same number appear on throwing three dice simultaneously is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

From a pack of 52 cards, two cards are drawn at random. Then the probability that one is a king and the other is a queen is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

A pair of dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is 6. The probability that it is actually a 6 is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required. The probability that $ x = 3$ equals

asked Jan 15, 2014 by thanvigandhi_1

1 answer

Let $w$ be a complex cube root of unity with $ W \neq 1$. A fair die is thrown three times. If $r_1, r_2\:and \: r_3$ are the numbers obtained on the die, then the probability that $ W^{r_1}+W^{r_2}+W^{r_3}=0$ is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

The value of K for which function $ f(x) =\left\{ \begin{array}{l l} k\: e^{-3x} & \quad \text{ $x$ >0}\\ 0 & \quad \text{ elsewhere} \end{array} \right.$ is a Probability Distribution Function.

asked Jan 15, 2014 by thanvigandhi_1

1 answer

The mean deviation for normal curve measured from mean value is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

If X is a Poisson variate such that $ P(2)=9\: P(4)+90\: P(6)$. then mean of X is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

The probability for a razor blade to be defective is 0.002. The blades are in packet of 10. The number of packets containing no defective blades in a stock of 10,000 packet is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

For normal distribution the third moment about the mean is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

Under a normal curve mean $ \pm 3\: \sigma $ covers an area equal to

asked Jan 15, 2014 by thanvigandhi_1

1 answer

The mean of Poisson's distribution with parameter m is

asked Jan 15, 2014 by thanvigandhi_1

1 answer

In a probability distribution of a random variable X, the sum of probability is always

asked Jan 15, 2014 by thanvigandhi_1

1 answer

The volume of a parallelopiped formed by $\hat i+a\hat j+\hat k,\:\hat j+a\hat k\:and\:\:a\hat i+\hat k$ is minimum if $a=?$

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow u=\hat i+\hat j,\:\overrightarrow v=\hat i-\hat j\:and\:\overrightarrow w=\hat i+2\hat j+3\hat k$ and $\overrightarrow n$ is a unit vector such that $\overrightarrow n.\overrightarrow u=\overrightarrow n.\overrightarrow v=0$, then $|\overrightarrow n.\overrightarrow w|=?$

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow v=2\hat i+\hat j-\hat k\:\:and\:\;\overrightarrow w=\hat i+3\hat k$ and $\overrightarrow u$ is a unit vector,then the maximum value of $ [\overrightarrow u\:\overrightarrow v\:\overrightarrow w]$ is ?

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

A and B throw a dice each. The probability that A's throw is not greater than B's throw is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

A is targetting to B, b and C are targetting to A. probability of hitting the target by A,B and C are $ \large\frac{2}{3}, \large\frac{1}{2} \: and \: \large\frac{1}{3}$ respectively. If A is hit then the probability that B hits the target and C does not is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

Ordinary dice are rolled. The probability that at least half of them will show at least 3 is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

A fair coin is tossed 100 times. The probability of getting tails on odd number of times is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

A coin is tossed 7 times. The probability that he wins the toss on more occasions is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

In a binomial distribution $B \bigg( n, P = \large\frac{1}{4} \bigg)$ If the probability of at least one success is greater than or equal to $ \large\frac{9}{10}$ then $n$ is greater than

asked Jan 9, 2014 by thanvigandhi_1

1 answer

It is given that the events A and B are such that $P(A) = \large\frac{1}{4}\: \: P \bigg( \large\frac{A}{B} \bigg) \large\frac{1}{2}\: and \: P \bigg( \large\frac{B}{A} \bigg) = \large\frac{2}{3}$ Then $P(B)$ is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

If X is binomial variate with parameters $n$ and $p$ where $ 0 < P < 1$ such that $ \large\frac{P(x=r)}{P(x=n-r)}$ is independent of n and r then p equals.

asked Jan 9, 2014 by thanvigandhi_1

1 answer

The probability that $ \sin^{-1} ( \sin \: x)+ \cos^{-1} ( \cos\: y)$ is an integer $ x,y \in \{ 1,2,3,4 \} $ is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

Let A and B be two independent events such that $P(A) = \large\frac{1}{5} \: P( A \cup B ) = \large\frac{7}{10}$. Ten $ P(\overline B)$ is equal to

asked Jan 8, 2014 by thanvigandhi_1

1 answer

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form $ 7^m+7^n$ is divisible by 5 equals.

asked Jan 8, 2014 by thanvigandhi_1

1 answer

A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

The mean and variance of a binomial variate X are 2 and 1 respectively. The probability that X takes a value greater than 1 is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

A and B are two independent events. The probability that both A and B occur is $ \large\frac{1}{6}$ and the probability that neither of them occurs is $ \large\frac{1}{3}$. Then the probability of the two events are respectively

asked Jan 8, 2014 by thanvigandhi_1

1 answer

A pair of dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

asked Jan 8, 2014 by thanvigandhi_1

2 answers

A box contains 24 identical bals of which 12 are white and remaining black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

A fair die is tossed until a number greater than 4 appears. The probability that an even number of tosses shall be required is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

If the probability for A to fail in an examination is 0.2 and that for B is 0.3 then the probability that either A or B fails is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

An unbiased die with faces marked 1,2,3,4,5 and 6 is rolled four times out of four values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is :

asked Jan 8, 2014 by thanvigandhi_1

1 answer

If $ \overrightarrow r\times\overrightarrow b=\overrightarrow c\times\overrightarrow b$ and $\overrightarrow r.\overrightarrow a=0$, where $\overrightarrow a=2\hat i+3\hat j-\hat k,\:\overrightarrow b=3\hat i-\hat i+\hat k\:and\:\:\overrightarrow c=\hat i+\hat j+3\hat k$, then $\overrightarrow r=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=(-1,1,1)\:\:\overrightarrow b=(2,0,1)\:and\:\overrightarrow x$ is vector such that $\overrightarrow x.\overrightarrow a=7,\:\overrightarrow x.\overrightarrow b=0$ and $\overrightarrow a,\overrightarrow b,\overrightarrow x$ are coplanar, then $\overrightarrow x=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

In a rt. angled triangle $ABC$ if hypotenuse, $AB=p$, then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}$= ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

A vector $a\hat i+b\hat j+c\hat k$ is such that its magnitude is $ |a|+|b|+|c|$. This is possible only if

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $P$ is point whose position vector is $\overrightarrow r=x\hat i+y\hat j+z\hat k$ where $x,y,z \in N$ and $\overrightarrow a=\hat i+\hat j+\hat k$, then the number of possible points $P$ for which $\overrightarrow r.\overrightarrow a=10$ is ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow c=\hat j-\hat k$ and $\overrightarrow b$ is such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow a.\overrightarrow b=3$ then $\overrightarrow b=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\;and\:\:\overrightarrow b=\hat i+\hat j$ and $\overrightarrow c$ is such that $\overrightarrow c.\overrightarrow a=|\overrightarrow c|$, $|\overrightarrow c-\overrightarrow a|=2\sqrt 2$ and the angle between $\overrightarrow a\times\overrightarrow b$ and $\overrightarrow c$ is $30^{\circ}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b$ are mutually $\perp$ unit vectors and the vectors $x\overrightarrow a+x\overrightarrow b+z(\overrightarrow a\times\overrightarrow b ),\:\:\overrightarrow a+(\overrightarrow a\times\overrightarrow b),\:\:and\:\:z\overrightarrow a+z\overrightarrow b+y(\overrightarrow a\times\overrightarrow b)$ lie in a plane then $Z$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The probability that a number selected at random from the set of numbers { 1,2,3,.....100} is a cube is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are unit vectors and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ is also a unit vector and $\alpha,\beta,\gamma $ are angles between $\overrightarrow a\:and\:\overrightarrow b,\:\:\overrightarrow b\:and\:\overrightarrow c\:\:\overrightarrow c\:and\:\overrightarrow a$ respectively, then among the three angles,

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are any three vectors such that $\overrightarrow a=\overrightarrow b+\overrightarrow c$ and $\overrightarrow b$ is $\perp$ to $\overrightarrow c$, then ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

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