Recent questions in Mathematics

$f(x) =e^x \sin x,$ then $f^{(6)} (x) $ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $x^y=y^x$. then $x(x-y \log x) \large\frac{dy}{dx}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

The polar equation of the circle with center $\bigg( 2, \large\frac{\pi}{2}\bigg)$ and radius 3 units is :

asked Nov 6, 2013 by meena.p

1 answer

If the eccentricity of a hyperbola is $\sqrt 3$; then the eccentricity of its conjugate hyperbola is :

asked Nov 6, 2013 by meena.p

1 answer

The sides of the rectangle of greatest area that can be inscribed in the ellipse $x^2+4y^2=64$ are:

asked Nov 6, 2013 by meena.p

1 answer

Equations of the latus rectum of the ellipse $9x^2+4y^2-18x -8y-23=0$ are :

asked Nov 6, 2013 by meena.p

2 answers

If b and c are the lengths of the segments of any focal chord of a parabola $y^2=4ax$, then the length of the semi-latus rectum is :

asked Nov 6, 2013 by meena.p

1 answer

The length of the tangent drawn to the circle $x^2+y^2-2x+4y-11=0$ from the point $(1,3)$ is:

asked Nov 6, 2013 by meena.p

1 answer

Observe the following statements: I. The circle $x^2+y^2-6x-4y-7=0$ touches x-axis. II. The circle $x^2+y^2+6x+4y-7=0$ touches x-axis.Which of the following is a correct statement?

asked Nov 6, 2013 by meena.p

1 answer

The number of common tangent to the two circles $x^2+y^2-8x+2y=0$ and $x^2+y^2-2x-16y+25=0$ is :

asked Nov 6, 2013 by meena.p

1 answer

If the direction cosines of two lines are such that $l+m+n=0; l^2 +m^2-n^2=0$ then the angle between them is :

asked Nov 6, 2013 by meena.p

1 answer

If OA is equally inclined to OX,OY and OZ and if A is $\sqrt 3 $ units from the origin . then A is :

asked Nov 6, 2013 by meena.p

1 answer

The centroid of the triangle formed by the pair of straight lines $12x^2+20xy+7y^2=0$ and the line $2x-3y+4=0$ is

asked Nov 6, 2013 by meena.p

1 answer

The line represented by the equation $x^2-y^2-x+3y-2=0$ are :

asked Nov 6, 2013 by meena.p

1 answer

Let O be the origin and A be a point on the curve $y^2=4x$. Then the locus of the mid point of OA is :

asked Nov 6, 2013 by meena.p

1 answer

The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is :

asked Nov 6, 2013 by meena.p

1 answer

The lines $x-y-2=0,x+y-4=0$ and $x+3y=6$ meet in the common point

asked Nov 6, 2013 by meena.p

1 answer

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\large\frac{\pi}{4}$ is :

asked Nov 6, 2013 by meena.p

1 answer

In a book of 500 pages, it is found that there are 250 typing errors. Assume that Poisson law holds for the number of errors per page. Then, the probability that a random sample of 2 pages will contain no error, is :

asked Nov 6, 2013 by meena.p

1 answer

Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is :

asked Nov 6, 2013 by meena.p

1 answer

In the random experiment of tossing two unbiased dice let E be the event of getting the sum B and F be the event of getting even numbers on both the dice. Then : $I.P(E)=\large\frac{7}{36}$$ ; \quad II.P(F)=\large\frac{1}{3}$ Which of the following is a correct statement ?

asked Nov 6, 2013 by meena.p

1 answer

A number n is chosen at random from $\{1,2,3,4.......,1000\}$. The probability that n is a number that leaves remainder 1 when divided by 7, is :

asked Nov 6, 2013 by meena.p

1 answer

If A and B are two independent events such that $P(B)=\large\frac{2}{7}$$,P(A \cup B)=0.8,$ then $P(A)$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

$\overrightarrow {a}. \hat i=\overrightarrow {a}.(2 \hat i +\hat j)= \overrightarrow {a}(\hat i+\hat j+3 \hat k)=1$, then $\overrightarrow a$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If the volume of parallelopiped with conterminus edges $4 \hat i+5 \hat j+\hat k, -\hat j+\hat k$ and $3 \hat i+9 \hat j +p \hat k$ is 34 cubic units, then p is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $\hat i -3 \hat j +\hat k$ and $\lambda \hat i+ 3 \hat j$ are coplanar, then $ \lambda$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

The position vector of a point lying on the line joining the points whose positions vectors are $ \hat i+\hat j-\hat k$ and $\hat i- \hat j +\hat k$ is :

asked Nov 6, 2013 by meena.p

1 answer

If $\overrightarrow {a} + \overrightarrow {b}+ \overrightarrow c=\overrightarrow {0}$ and $| \overrightarrow {a} |=3, | \overrightarrow {b}|=4$ and $|\overrightarrow {c}|=\sqrt {37},$ then the angle between $\overrightarrow{a}$ and $\overrightarrow {b}$ is :

asked Nov 6, 2013 by meena.p

1 answer

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be $30^{\circ}$. After walking 120 metres towards it on level ground the elevation is found to be $60^{\circ}$. Then the height of the object (in meters) is :

asked Nov 6, 2013 by meena.p

1 answer

If $b+c=3a,$ then $cot \large\frac{B}{2}$$ \cot \large\frac{C}{2}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

The angles of a triangle are in the ratio $3:5:10$.Then the ratio of the smallest side to the greatest side is :

asked Nov 6, 2013 by meena.p

1 answer

If, in a $\Delta \; ABC, \tan \large\frac{A}{2}=\frac{5}{6}$ and $\tan \large\frac{C}{2}=\frac{2}{5},$ then $a,b,c$ are such that:

asked Nov 6, 2013 by meena.p

1 answer

$e^{\log (\cos h^{-1}2)}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $x=\tan 15^{\circ},y=cosec 75^{\circ}$ and $z=4 \sin 18^{\circ}$ then :

asked Nov 6, 2013 by meena.p

1 answer

For all values of $\theta$, the values of $3- \cos \theta+ \cos \bigg(\theta+\large\frac{\pi}{3}\bigg)$ lie in the interval :

asked Nov 6, 2013 by meena.p

1 answer

The quadratic equation whose roots are $\sin ^2 18^{\circ}$ and $\cos ^2 36^{\circ}$ is :

asked Nov 6, 2013 by meena.p

1 answer

If $5 \cos x +12 \cos y=13$, then the maximum value of $5 \sin x +12 \sin y$ is :

asked Nov 6, 2013 by meena.p

1 answer

$cosec 15^{\circ}+ \sec 15^{\circ}$ is equal to :

asked Nov 5, 2013 by meena.p

1 answer

$\sin 120^{\circ} \cos 150^{\circ}- cos 240^{\circ} \sin 330^{\circ}$ is equal to :

asked Nov 5, 2013 by meena.p

1 answer

The product of the distinct (2n)th roots of $1+i \sqrt 3$ is equal to :

asked Nov 5, 2013 by meena.p

1 answer

The equation of the locus of z such that $\bigg|\large\frac{z-i}{z+i} \bigg|$$=2$ Where $z=x+iy$ is a complex number, is

asked Nov 5, 2013 by meena.p

1 answer

The locus of the point $z=x+iy$ satisfying the equation $\bigg|\large\frac{z-i}{z+i} \bigg|$$=1$is given by :

asked Nov 5, 2013 by meena.p

1 answer

$\begin {bmatrix} \log\;e & \log\;e^2 & \log\;e^3 \\ \log\;e^2 & \log\;e^3 & \log\;e^4 \\ \log \;e^3 & \log\;e^4 & \log \;e^5 \end {bmatrix}$ is equal to:

asked Nov 5, 2013 by meena.p

1 answer

If A is an invertible matrix of order n , then the determinant of adj A is equal to :

asked Nov 5, 2013 by meena.p

1 answer

$A= \begin {bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end {bmatrix}$ then $A^3-4A^2-6A$ is equal to :

asked Nov 5, 2013 by meena.p

1 answer

If $\alpha,\beta, \gamma$ are the roots of the equation $x^3-6x^2+11x+6=0,$ then $ \sum \alpha^2 \beta+ \sum \alpha \beta^2$ is equal to :

asked Nov 5, 2013 by meena.p

1 answer

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is 2. Then the roots of the equation are :

asked Nov 5, 2013 by meena.p

1 answer

If $\sqrt {9x^2+6x+1} < (2-x) ,$ then :

asked Nov 5, 2013 by meena.p

1 answer

If $ |x| < 1 $ and $y=x-\large\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+......$ then x is equal to :

asked Nov 5, 2013 by meena.p

1 answer

The coefficient of $x^n$ in $\large\frac{1-2x}{e^x}$ is :

asked Nov 5, 2013 by meena.p

1 answer

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