Recent questions tagged exemplar

Find the equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$.

asked Oct 10, 2014 by sreemathi.v

1 answer

Find the eccentricity of the hyperbola $9y^2-4x^2=36$.

asked Oct 10, 2014 by sreemathi.v

1 answer

If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$,then obtain equation of the hyperbola.

asked Oct 10, 2014 by sreemathi.v

1 answer

If the line $y=mx+1$ is tangent to the parabola $y^2=4x$ then find the value of $m$.

asked Oct 10, 2014 by sreemathi.v

1 answer

If the points $(0,4)$ and $(0,2)$ are respectively the vertex and focus of a parabola,then find the equation of the parabola.

asked Oct 10, 2014 by sreemathi.v

1 answer

Find the length of the line-segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola where the line-segment makes an angle $\theta$ to the $x$-axis.

asked Oct 10, 2014 by sreemathi.v

1 answer

Find the coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is 4.

asked Oct 10, 2014 by sreemathi.v

1 answer

Find the distance between the directrices of the ellipse $\large\frac{x^2}{36}+\frac{y^2}{20}$$=1$.

asked Oct 9, 2014 by sreemathi.v

1 answer

Find the equation of ellipse whose eccentricity is $\large\frac{2}{3}$ , latus rectum is 5 and the centre is (0, 0).

asked Oct 9, 2014 by sreemathi.v

1 answer

If the eccentricity of an ellipse is $\large\frac{5}{8}$ and the distance between its foci is 10, then find latus rectum of the ellipse.

asked Oct 9, 2014 by sreemathi.v

1 answer

Given the ellipse with equation $9x^2+25y^2=225$,find the eccentricity and foci.

asked Oct 9, 2014 by sreemathi.v

1 answer

If the latus rectum of an ellipse is equal to half of minor axis,then find its eccentricity.

asked Oct 9, 2014 by sreemathi.v

1 answer

Find the equation of a circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and has double of its area.

asked Oct 9, 2014 by sreemathi.v

1 answer

If the line $y=\sqrt 3x+k$ touches the circle $x^2+y^2=16$,then find the value of $k$.

asked Oct 8, 2014 by sreemathi.v

1 answer

Find the equation of the circle having $(1,-2)$ as its centre and passing through $3x+y=14,2x+5y=18$.

asked Oct 8, 2014 by sreemathi.v

1 answer

If one end of a diameter of the circle $x^2+y^2-4x-6y+11=0$ is $(3,4)$,then find the coordinate of the other end of the diameter.

asked Oct 8, 2014 by sreemathi.v

1 answer

Find the equation of a circle which touches both the axes and the line $3x-4y+8=0$ and lies in the third quadrant.

asked Oct 8, 2014 by sreemathi.v

1 answer

Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following : The equation of the line through the intersection of the lines 2x – 3y = 0 and4x – 5y = 2 and

asked Jul 9, 2014 by thanvigandhi_1

1 answer

Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following : The value of the $ \lambda$, if the lines $(2x + 3y + 4) +\lambda (6x – y + 12) = 0 $ are

asked Jul 9, 2014 by thanvigandhi_1

1 answer

Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following :

asked Jul 9, 2014 by thanvigandhi_1

1 answer

State whether the following is true or false and justify : Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).

asked Jul 9, 2014 by thanvigandhi_1

1 answer

State whether the following statement is true or false and justify : The lines $ ax + 2y + 1 = 0, bx + 3y + 1 = 0 $ and $cx + 4y + 1 = 0$ are concurrent if a, b, c are in G.P

asked Jul 9, 2014 by thanvigandhi_1

1 answer

Calculate the mean deviation about the mean of the set of first n natural numbers where numbers where n is an even number.

asked Jul 9, 2014 by meena.p

1 answer

Match the following :

asked Jul 9, 2014 by sreemathi.v

1 answer

Calculate the mean deviation about the mean of the set of first n natural numbers when n is odd number.

asked Jul 9, 2014 by meena.p

1 answer

Match the proposed probability under Column $C_1$ with the appropriate written description under column $C_2$ :

asked Jul 9, 2014 by sreemathi.v

1 answer

Prove that $\tan^{-1}{\frac{1}{4}}+\tan^{-1}{\frac{2}{9}}=\sin^{-1}{\frac{1}{\sqrt 5}}$

asked Jul 9, 2014 by balaji.thirumalai

1 answer

The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ________.

asked Jul 9, 2014 by sreemathi.v

1 answer

If A and B are two events associated with a random experiment such that $P(A)=0.3,P(B)=0.2$ and $P(A \cap B)=0.1$ then the value of $P(A \cap \bar{B})$ is _________

asked Jul 9, 2014 by sreemathi.v

1 answer

Find the standard deviation of the first n natural numbers.

asked Jul 9, 2014 by meena.p

1 answer

The mean and standard deviation of a set of $n_1$ observations are $\bar{x_1}$ and $s_1$ respectively , while the mean and standard deviation of another set of $n_2$ observations are $x_2$ and $s_2$ respectively. Show that the standard deviation of the combined set of $(n_1+n_2)$ observations is given by $ S.D= \sqrt {\large\frac{n_1 (s_1)^2 +n_2 (s_2)^2}{n_1+n_2} +\frac{n_1n_2(\bar {x_1} -\bar {x_2} )^2}{(n_1+n_2)^2}}$

asked Jul 9, 2014 by meena.p

1 answer

Let S={1,2,3,4,5,6} and E={1,3,5},then $\bar{E}$ is_________.

asked Jul 9, 2014 by sreemathi.v

1 answer

If $e_1,e_2,e_3,e_4$ are the four elementary outcomes in a sample space and $P(e_1) = .1, P(e_2) = .5, P (e_3) = .1$, then the probability of $e_4$ is ______.

asked Jul 9, 2014 by sreemathi.v

1 answer

The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is _____________

asked Jul 9, 2014 by sreemathi.v

1 answer

True-or-False : The sum of probabilities of two students getting distinction in their final examinations is 1.2

asked Jul 9, 2014 by sreemathi.v

1 answer

True-or-False : The probability of an occurrence of event A is 0.7 and that of the occurrence of event B is 0.3 and the probability of occurrence of both is 0.4.

asked Jul 9, 2014 by sreemathi.v

1 answer

True-or-False : The probability of intersections of two events A and B is always less than or equal to those favorable to the event A.

asked Jul 9, 2014 by sreemathi.v

1 answer

True-or-False : If A and B are two candidates seeking admission in an engineering college.The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3.Is it possible that the probability of B getting selected is 0.7?

asked Jul 9, 2014 by sreemathi.v

1 answer

True-or-False : The probabilities that a typist will make 0,1,2,3,4,5 or more mistakes in typing a report are,respectively,0.12,0.25,0.36,0.14,0.08,0.11

asked Jul 9, 2014 by sreemathi.v

1 answer

True-or-False : The probability that a student will pass his examination is 0.73,the probability of the student getting a compartment is 0.13,and the probability that the student will either pass or get compartment is 0.96.

asked Jul 9, 2014 by sreemathi.v

1 answer

State whether the following statement is true or false and justify : The equation of the line joining the point (3, 5) to the point of intersection of the lines $4x + y – 1 = 0 $ and $7x – 3y – 35 = 0$ is equidistant from the points (0, 0) and (8, 34)

asked Jul 9, 2014 by thanvigandhi_1

1 answer

The standard deviation is __________ the mean deviation taken from the arithematic mean

asked Jul 9, 2014 by meena.p

1 answer

The mean deviation of the data is ________ when measured from the median .

asked Jul 9, 2014 by meena.p

1 answer

True-or-False : The probability that a person visiting a zoo will see the giraffee is 0.72,the probability that he will see the bears is 0.84 and the probability that he will see both is 0.52.

asked Jul 9, 2014 by sreemathi.v

1 answer

The sum of the squares of the deviations of the values of the variable is _______ when taken about their arithmetic mean.

asked Jul 9, 2014 by meena.p

1 answer

The standard deviation of data is _ of any change in origin, but is ______ on the change of scale.

asked Jul 9, 2014 by meena.p

1 answer

If M and N are any two events,the probability that at least one of them occurs is

asked Jul 9, 2014 by sreemathi.v

1 answer

If the variance of a data is 121, then the standard deviation of the data is _______

asked Jul 9, 2014 by meena.p

1 answer

If $\bar {x}$ is the mean of n values of x, then $\sum \limits_{i=1}^{n} (x_i -\bar{x} )$ is always equal to _______. If a has any value other than $\bar {x}$ , then $\sum \limits_{i-1}^{n} (x_i -\bar {x} )^2$ is _________ than $\sum (x_i -a)^2$

asked Jul 9, 2014 by meena.p

1 answer

The probability that at least one of the events A and B occurs is 0.6.If A and B occur simultaneously with probability 0.2.Then $P(\bar{A})+P(\bar{B})$ is

asked Jul 9, 2014 by sreemathi.v

1 answer

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