Recent questions tagged class12

Show that : $\sin^{-1}\large\frac{4}{5}\normalsize+\cos^{-1}\large\frac{2}{\sqrt 5}\normalsize =\cot^{-1}\large\frac{2}{11}$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Find the equation of the ellipse whose foci are at $(-2,4)$ and $(4,4)$ and whose major and minor axes are 10 and 8 respectively.Also find the eccentricity of the ellipse.

asked Apr 22, 2013 by sreemathi.v

0 answers

If pairs of straight lines $x^2-2pxy-y^2=0$ and $x^2-2qxy-y^2=0$ be such that each pair bisects the angle between the other pair,prove that $pq=-1$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Using matrices,solve the following system of equations : $x+2y=5,y+2z=8,2x+z=5$.

asked Apr 22, 2013 by sreemathi.v

2 answers

Using properties of determinants,find the value of the following determinant : $\begin{vmatrix}x^3 & x^2 & x\\y^3 & y^2 & y\\z^3 & z^2 & z\end{vmatrix}$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Using binomial expansion,calculate the value of $(98)^{\large\frac{1}{2}}$ correct to three places of decimal.

asked Apr 22, 2013 by sreemathi.v

0 answers

Prove by the method of mathematical induction that $\large\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+....+\frac{1}{(3n+1)(3n+4)}=\frac{n}{4(3n+4)}$,for all $n\in N$.

asked Apr 22, 2013 by sreemathi.v

0 answers

If : $\begin{bmatrix}x^2 & 3 & 4\\1 & 9 & 8\end{bmatrix}+\begin{bmatrix}-3x & 1 & -5\\-3 & -2 & -6\end{bmatrix}=\begin{bmatrix}4 & 4 & -1\\-2 & 7 & 2\end{bmatrix}$,find the values of $x$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Evaluate : $\int_0^{\large\frac{\pi}{4}}\normalsize (\tan x+\cot x)^{-1}dx.$

asked Apr 22, 2013 by sreemathi.v

0 answers

Using vectors,show that the perpendiculars from the vertices to the opposite sides of the triangle ABC are concurrent.

asked Apr 22, 2013 by sreemathi.v

0 answers

Simplify : $(1-\omega)(1-{\omega}^2)(1-{\omega}^2)(1-{\omega}^3)$.

asked Apr 22, 2013 by sreemathi.v

0 answers

One number is chosen at random from the numbers 1 to 21.Find the probability that may be a prime number.

asked Apr 22, 2013 by sreemathi.v

0 answers

If $y=\tan^{-1}\bigg(\large\frac{2x}{1-x^2}\bigg)$,prove that $\large\frac{dy}{dx}=\frac{2}{1+x^2}$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Find the cosine of the angle between the planes $x+2y-2z+6=0,2x+2y+z+8=0$.

asked Apr 22, 2013 by sreemathi.v

0 answers

The equation $y^2-4y-4x+16=0$ represents a parabola.Find its vertex and focus.

asked Apr 22, 2013 by sreemathi.v

0 answers

Find the angle between the straight lines represented by the equation $3x^2-y^2-\sqrt 3x+3y-2=0.$

asked Apr 22, 2013 by sreemathi.v

0 answers

Solve the equation: $\sin^{-1}(6x) + \sin^{-1}(6\sqrt 3 x) =-\large \frac{\pi}{2}$

asked Apr 22, 2013 by smanpreet070

1 answer

The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$ out of $1000$ taxi drivers find approximately the number of driver with more than $3$ accidents in a year $[e^{-3}=0.0498].$

asked Apr 21, 2013 by poojasapani_1

1 answer

The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$. Out of $1000$ taxi drivers find approximately the number of driver with no accident in a year .$[e^{-3} = 0.0498].$

asked Apr 21, 2013 by poojasapani_1

1 answer

Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be at least $2$ emission in a particular $20$ minutes interval .$[e^{-5}=0.0067].$

asked Apr 21, 2013 by poojasapani_1

1 answer

$20\%$ of the bolts produced in a factory are found to be defective. Find the probability that in a sample of $10$ bolts chosen at random exactly $2$ will be defective using ,Poisson distribution.$ [e^{-2}=0.1353].$

asked Apr 21, 2013 by poojasapani_1

1 answer

$20\%$ of the bolts produced in a factory are found to be defective. Find the probability that in a sample of $10$ bolts chosen at random exactly $2$ will be defective using ,Binomial distribution.

asked Apr 21, 2013 by poojasapani_1

1 answer

If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that more than $3$ fuses are defective$ [e^{-4}=0.0183].$

asked Apr 21, 2013 by poojasapani_1

1 answer

If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that exactly $4$ fuses are defective

asked Apr 21, 2013 by poojasapani_1

1 answer

Let $x$ have a poisson distribution with mean $4$.Find$P(2\leq$X$<$5$)[e^{-4}=0.0183].$

asked Apr 21, 2013 by poojasapani_1

1 answer

Let $X$ have a poisson distribution with mean $4$.Find $(i) \;P(X\leq $3$)\qquad[e^{-4} = 0.0183].$

asked Apr 21, 2013 by poojasapani_1

1 answer

In a hurdle race a player has to cross $10$ hurdles. The probability that he will clear each hurdle is $\large\frac{5}{6}$. What is the probability that he will knock down less than $2$ hurdles.

asked Apr 21, 2013 by poojasapani_1

1 answer

The overall percentage of passes in a certain examination is $80$.If $6$ candidates appear in the examination what is the probability that atleast $5$ pass the examination.

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting at most two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously.what is the probability of getting at least two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting exactly $2$ heads

asked Apr 21, 2013 by poojasapani_1

1 answer

If on an average $1$ ship out of $10$ do not arrive safely to ports. Find the mean and the standard deviation of ship returning safely out of a total of $500$ ships

asked Apr 20, 2013 by poojasapani_1

1 answer

A die is thrown $120$ times and getting $1$ or $5$ is considered a success.Find the mean and variance of the number of successes.

asked Apr 20, 2013 by poojasapani_1

1 answer

The mean of a binomial distribution is $6$ and its standard deviation is $3$. Is this statement true or false?comment?

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if $x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} \alpha e^{-\alpha x} ,& \quad \text{if $x$$>$$0$}\\ 0 ,& \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} \frac {1}{24} ,& \quad \text{-12$\leq$$ x$$\leq $$12$}\\ 0, & \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

The probability distribution of a random variable $x$ is given below: \[\] $\begin{array} {llllllll} \textbf{X:}& 0& 1& 2& 3 \\ \textbf{P(X=x):}& 0.1& 0.3 &0.5& 0.1& \end{array}$\[\] If $Y=X^{2}+2X$ find the mean and variance of $Y$.

asked Apr 20, 2013 by poojasapani_1

1 answer

In a gambling game a man wins Rs.$10 $ if he gets all heads or all tails and loses Rs.$5$ if he gets $1$ or $2$ heads when $3$ coins are tossed once. Find his expectation of gain.

asked Apr 20, 2013 by poojasapani_1

1 answer

Two cards are drawn with replacement from a well shuffled deck of $52$ cards. Find the mean and variance for the number of aces.

asked Apr 20, 2013 by poojasapani_1

1 answer

In an entrance examination a student has to answer all the $120$ questions. Each question has four options and only one option is correct. A student gets $1$ mark for a correct answer and loses half mark for a wrong answer. What is the expectation of the mark scored by a student if he chooses the answer to each question at random?

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the expected value of the number on a die when thrown.

asked Apr 20, 2013 by poojasapani_1

1 answer

A die is tossed twice. A success is getting as odd number on a toss. Find the mean and the variance of the probability distribution of the number of successes.

asked Apr 20, 2013 by poojasapani_1

1 answer

If $a \; =\; cos \; 2\alpha \; + \; i \; sin \; 2\alpha , \; b \; =\; cos\; 2\beta + i\; sin\; 2\beta\; $ and $\;c\; = \; cos \; 2\gamma\; + \; i sin\; 2\gamma$ prove that $\frac{a^{2}b^{2}+c^{2}}{abc}\; = \; 2\; cos \; 2\left ( \alpha \;+\;\beta \;+\;\gamma \right )$

asked Apr 19, 2013 by geethradh

0 answers

If $a \; =\; cos \; 2\alpha \; + \; i \; sin \; 2\alpha , \; b \; =\; cos\; 2\beta + i\; sin\; 2\beta\; $ and $\;c\; = \; cos \; 2\gamma\; + \; i sin\; 2\gamma$ prove that $\sqrt{abc}\; + \; \frac{1}{\sqrt{abc}}\; = \; 2\; cos\left ( \alpha \;+\;\beta \;+\;\gamma \right )$

asked Apr 19, 2013 by geethradh

0 answers

Find the middle term in the binomial expansion of $\begin{pmatrix}\large\frac{x^2}{4}-\frac{4}{x^2}\end{pmatrix}^{10}$

asked Apr 19, 2013 by sreemathi.v

0 answers

If $x\;=\cos\;\alpha +i\sin\;\alpha\;;\; y\;= \cos\;\beta + i\sin \;\beta $ prove that $x^{m}y^{n} \;+\large \frac{1}{x^{m}y^{n}}$$= \;2\cos \;\left ( m\alpha + n\beta \right )$

asked Apr 19, 2013 by geethradh

1 answer

If $x+\large\frac{1}{x}$$ =2\cos\;\theta $ and $y+\large\frac{1}{y}$$=2 \cos \;\phi$ show that $\large\frac{x^{m}}{y^{n}} - \frac{y^{n}}{x^{m}}$$ = 2i \;sin\left ( m\theta -n\phi \right )$

asked Apr 19, 2013 by geethradh

1 answer

Solve the differential equation $\large\frac{d^2y}{dx^2}\normalsize=\sin 2x$

asked Apr 19, 2013 by sreemathi.v

0 answers

Using DeMoivre's theorem find the value of $(2-2i)^{\large\frac{1}{3}}$.

asked Apr 19, 2013 by sreemathi.v

0 answers

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