Recent questions tagged 2013

If $E,M,J$ and $G$ respectively denote energy , mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimension of $\large\frac{EJ^2}{M^5G^2}$

asked Sep 17, 2013 by meena.p

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The solution of the differential equation $\large\frac{dy}{dx}$$-2y \tan 2x =e^x\;sec 2x$ is :

asked Sep 17, 2013 by meena.p

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An integrating factor of the equation $(1+y+x^2y) dx +(x+x^3)dy=0$ is

asked Sep 17, 2013 by meena.p

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The approximate value of $ \int \limits_1^3 \large\frac{dx}{2+3x}$ using Simpson's Rule and dividing the interval $[1,3]$ into two equal parts is

asked Sep 17, 2013 by meena.p

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The area (in square units) bounded by the curves $x=-2y^2$ and $x=1-3y^2$ is

asked Sep 17, 2013 by meena.p

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If $\int \limits_0^b \large\frac{dx}{1+x^2}$$=\int \limits_b^{\infty} \large \frac{dx}{1+x^2},$ then $b=$

asked Sep 17, 2013 by meena.p

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$\int \large\frac{dx}{x (\log x -2)(\log x-3)}$$=1+c=>1=$

asked Sep 17, 2013 by meena.p

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$\int \large \frac{x -\sin x}{1+ \cos x} $$ dx=x \tan \bigg(\large\frac{x}{2}\bigg)$$+p \log \bigg |\sec \bigg(\large\frac{x}{2}\bigg)\bigg |$$+c=>p=$

asked Sep 17, 2013 by meena.p

1 answer

$\int e^x \bigg(\large\frac{2+\sin 2x}{1+\cos 2x}\bigg)$$dx=$

asked Sep 17, 2013 by meena.p

1 answer

$u=\log(x^3+y^3+z^3-3xyz)=>(x+y+z)(u_x+u_y+u_z)=$

asked Sep 17, 2013 by meena.p

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The focal length of a mirror is given by $\large\frac{2}{f}=\frac{1}{v}-\frac{1}{u}.$ In finding the values of $u$ and $v$, the error are equal and equal to 'p'. Then, the relative error in f is

asked Sep 17, 2013 by meena.p

1 answer

If the curves $x^2+py^2=1$ and $qx^2+y^2=1$ are orthogonal to each other, then

asked Sep 17, 2013 by meena.p

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The relation between pressure $p$ and volume $v$ is given by $pv^{\large\frac{1}{4}}$=Constant. If the percentage decrease in volume is $\large\frac{1}{2}$, then the percentage increase in pressure is

asked Sep 17, 2013 by meena.p

1 answer

$\cos ^{-1} \bigg(\large\frac{y}{b} \bigg)$$=2 \log \bigg(\large\frac{x}{2}\bigg),$$ x > 0=>x^2 \large\frac{d^2y}{dx^2}$$+x \large\frac{dy}{dx}=$

asked Sep 17, 2013 by meena.p

1 answer

$\large\frac{d}{dx}$$ [(x+1)(x^2+1)(x^4+1)(x^8+1)]=(15x^p-16x^q+1)(x-1)^{-2}=>(p,q)=$

asked Sep 17, 2013 by meena.p

1 answer

$\sqrt {\large\frac{y}{x}}+\sqrt {\large\frac{x}{y}}$$=2=>\large\frac{dy}{dx}=$

asked Sep 16, 2013 by meena.p

1 answer

$\lim \limits_{x \to 0} \large\frac{\tan ^3 x -\sin ^3 x}{x^5}=$

asked Sep 16, 2013 by meena.p

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$f(x)=\large\frac{1}{1+\Large\frac{1}{x}};$$g(x)=\large\frac{1}{1+\Large\frac{1}{f(x)}}$$=>g'(2)=$

asked Sep 16, 2013 by meena.p

1 answer

Let $f$ be a non-zero real valued continuous function satisfying $f(x+y)=f(x).f(y)$ for all $x,y \in R.$ If $f(2)=9,$ then $f(6)=$

asked Sep 16, 2013 by meena.p

1 answer

A variable plane passes through a fixed point $(1,2,3)$. Then the foot of the perpendicular from the origin to the plane lies on

asked Sep 16, 2013 by meena.p

1 answer

A plane passing through $(-1,2,3)$ and whose normal makes equal angles with the coordinate axes is

asked Sep 16, 2013 by meena.p

1 answer

The direction ratio's of two lines $AB,AC$ are $1,-1,-1$ and $2,-1,1.$ The direction ratios of the normal to the plane $ABC$ are

asked Sep 16, 2013 by meena.p

1 answer

$D(2,1,0),E(2,0,0),F(0,1,0)$ are mid-points of the sides $BC,CA,AB$ of $\Delta ABC$ respectively. Then, the centroid of $\Delta ABC$ is

asked Sep 16, 2013 by meena.p

0 answers

The perpendicular distance from the point $(1,\pi)$ to the line joining $(1,0^{\circ})$ and $(1, \large\frac{\pi}{2}),$ (in polar coordinates) is

asked Sep 16, 2013 by meena.p

1 answer

If $x=9$ is a chord of contact of the hyperbola $x^2-y^2=9,$ then the equation of the tangent at one of the points of contact is

asked Sep 16, 2013 by meena.p

1 answer

If the foci of the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ and the hyperbola $\large\frac{x^2}{4}-\frac{y^2}{b^2}=1$ coincide, then $b^2=$

asked Sep 16, 2013 by meena.p

1 answer

The midpoint of a chord of the ellipse $x^2+4y^2-2x+20 y=0$ is $(2,-4)$. The equation of the chord is?

asked Sep 16, 2013 by meena.p

1 answer

A circle of radius 4, drawn on a chord of the parabola $y^2=8x$ as diameter, touches the axis of the parabola. Then the slope of the chord is

asked Sep 16, 2013 by meena.p

1 answer

If the circle $x^2+y^2+4x-6y+c=0$ bisects the circumference of the circle $x^2+y^2-6x+4y-12=0,$ then $c=$

asked Sep 16, 2013 by meena.p

1 answer

$(a,0)$ and $(b,0)$ are center of two circles belonging to a co-axial system of which y-axis is the radical axis. If radius of one of the circles is 'r', then the radius of the other circle is

asked Sep 16, 2013 by meena.p

1 answer

If the length of the tangent from $(h,k)$ to the circle $x^2+y^2=16$ is twice the length of the tangent from the same point to the circle $x^2+y^2+2x+2y=0,$ then

asked Sep 16, 2013 by meena.p

1 answer

For the given circle $C$ with the equation $x^2+y^2-16x -12y +64=0$ match the list -I with the list II given below:

asked Sep 16, 2013 by meena.p

1 answer

The circle $4x^2+4y^2-12 x-12y+9=0$

asked Sep 16, 2013 by meena.p

1 answer

If the equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is

asked Sep 16, 2013 by meena.p

1 answer

The equation $x^2-5xy+py^2+3x-8y+2=0$ represents a pair of straight lines. If $\theta$ is the angle between them, then $\sin \theta=$

asked Sep 16, 2013 by meena.p

1 answer

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean geometric mean of 4 and 9 is

asked Sep 16, 2013 by meena.p

2 answers

If the points $(1,2)$ and $(3,4) $ lie on the same side of the straight line $ 3x-5y+a=0$ then a lies in the set

asked Sep 16, 2013 by meena.p

1 answer

If $2x+3y=5$ is the perpendicular bisector of the segment joining the points $A\bigg[1,\large\frac{1}{3}\bigg]$ and $B$ then $B=$

asked Sep 16, 2013 by meena.p

1 answer

If $p$ and $q$ are the perpendicular distance from the origin to the straight lines $x\; \sec \theta-y \;cosec \theta=a$ and $x \cos \theta+ y \sin \theta= a \cos 2 \theta,$ then

asked Sep 16, 2013 by meena.p

1 answer

The origin is translated to (1,2). The point $(7,5)$ in the old system undergoes the following transformations successively. (i) Moves to the new point under the given translation of origin. (ii) Translated through 2 units along the negative direction of the new X-axis. (iii) Rotated through an angle $\large\frac{\pi}{4}$ about the origin of new system in the clockwise direction. The final position of the point (7,5) is

asked Sep 16, 2013 by meena.p

1 answer

If $X$ is a Poisson variate and $P(X=1)=2P(X=2)$ then $P(X=3)=$

asked Sep 16, 2013 by meena.p

1 answer

The random variable takes the value $1,2,3,..........,m$. If $P(X=n)=\large\frac{1}{m}$ to each n, then the variance of $X$ is

asked Sep 16, 2013 by meena.p

1 answer

A bag contains $2n+1$ coins. It is known that $n$ of these coins have a head on both sides. Whereas the remaining $n+1$ coins are fair. A coins is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\large\frac{31}{42}.$ then $n$=

asked Sep 16, 2013 by meena.p

1 answer

Two fair dice are rolled. The probability of the sum of digits on their faces to be greater that or equal to 10 is

asked Sep 16, 2013 by meena.p

1 answer

Two numbers are chosen at random from $\{1,2,3,4,5,6,7,8\}$ at a time. The probability that smaller of the two numbers is less than 4 is:

asked Sep 16, 2013 by meena.p

1 answer

If $\overrightarrow {a}$ and $\overrightarrow {b}$ are two non-zero perpendicular vectors, then a vector $\overrightarrow {y}$ satisfying equations $\overrightarrow {a}.\overrightarrow {y}=c$ (c scalar) and $\overrightarrow {a} \times \overrightarrow {y} = \overrightarrow {b}$ is

asked Sep 16, 2013 by meena.p

1 answer

A unit vector co planar with $ \overrightarrow {i}+\overrightarrow {j}+ 3\overrightarrow {k}$ and $ \overrightarrow {i} +3 \overrightarrow {j}+ \overrightarrow {k}$ and perpendicular to $\overrightarrow {i}+ \overrightarrow {j}+ \overrightarrow {k}$ is

asked Sep 16, 2013 by meena.p

1 answer

The shortest distance between the lines $ \overrightarrow {r}=3\overrightarrow {i}+5 \overrightarrow {j}+ 7 \overrightarrow {k}+ \lambda (\overrightarrow {i}+2 \overrightarrow {j}+\overrightarrow {k})$ and $\overrightarrow {r}=- \overrightarrow {i} -\overrightarrow {j} -\overrightarrow {k}+ \mu (7\overrightarrow {i}-6 \overrightarrow {j}+\overrightarrow {k}) $ is

asked Sep 16, 2013 by meena.p

1 answer

$\overrightarrow {a} \neq \overrightarrow {0},\;\overrightarrow {b} \neq \overrightarrow {0},\;\overrightarrow {c} \neq \overrightarrow {0},\;\overrightarrow {a} \times \overrightarrow {b} = \overrightarrow {0},\;\overrightarrow {b} \times \overrightarrow {c}=0\;=>\; \overrightarrow {a} \times \overrightarrow {c}=$

asked Sep 16, 2013 by meena.p

1 answer

$P,Q,R$ and $S$ are four points with the position vectors $3 \overrightarrow {i}- 4 \overrightarrow {j}+5 \overrightarrow {k}, 4 \overrightarrow {k},-4 \overrightarrow {i}+ 5\overrightarrow {j}+\overrightarrow {k}$ and $-3\overrightarrow {i}+ 4\overrightarrow {j}+3 \overrightarrow {k}$ respectively. Then the line $PQ$ meets the line RS at the point.

asked Sep 16, 2013 by meena.p

1 answer

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