Recent questions in Mathematics

$\bigg \{ x \in R :\large\frac{2x-1}{x^3+4x^2+3x} \in$ $R \bigg \} =$

asked Oct 8, 2013 by meena.p

1 answer

If $f:[2,3] \to R$ is defined by $f(x) =x^3+3x-2,$ then the range $f(x)$ is contained in the interval:

asked Oct 8, 2013 by meena.p

1 answer

A family of curves has the differential equation $xy \large\frac{dy}{dx}$ $=2y^2-x^2$ . Then the family of curves is :

asked Sep 29, 2013 by meena.p

1 answer

The solution of $\tan y \large\frac{dy}{dx}$ $=\sin (x+y)+\sin (x-y)$ is :

asked Sep 29, 2013 by meena.p

1 answer

The values of a function $f(x)$ at different values of x are as follows: $x : \; 0\; 1\; 2\; 3\; 4\; 5\; \qquad f(x):\; 2\; 3 \; 6\; 11\; 18\; 27$ Then the approximate area (in square units) bounded by the curve $y=f(x)$ and X-axis between $x=0$ and 5, using Trapezoidal rule, is :

asked Sep 29, 2013 by meena.p

1 answer

The area ( in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is :

asked Sep 29, 2013 by meena.p

1 answer

IF $I_n=\int \limits_0^{\frac{\pi}{4}} \tan ^n x dx,$ then $I_2+I_4, I_3+I_5,I_4+I_6,$ ......... are in :

asked Sep 29, 2013 by meena.p

1 answer

$\int (1- \cos x) cosec^2 x dx =f(x)+c=>f(x)=$

asked Sep 29, 2013 by meena.p

0 answers

If $f_n(x)=\log \;\log\; \log\;......... \log\;x$ ( $\log$ is repeated n-times ), then $\int ( x f_1(x)f_2(x).......f_n(x))^{-1}dx=$

asked Sep 29, 2013 by meena.p

1 answer

$\int \large\frac{7x^8+8x^7}{(1+x+x^8)^2}dx$ $=f(x)+c => f(x)=$

asked Sep 27, 2013 by meena.p

1 answer

$u= \sin ^{-1} \bigg(\large\frac{x^4+y^4}{x+y}\bigg)$ $=> x \large\frac{du}{dx}$ $+y \frac{du}{dy}=$

asked Sep 27, 2013 by meena.p

1 answer

A variable triangle ABC is inscribed in a circle of diameter in a circle of diameter x units. At a particular instant, the rate of change in side a is $\large\frac{x}{2}$ times the rate of change in its opposite angle A. Then A=

asked Sep 27, 2013 by meena.p

1 answer

The longest distance of the point $(a,0)$ from the curve $2x^2+y^2=2x$ is :

asked Sep 27, 2013 by meena.p

1 answer

The height of the cone of maximum volume inscribed in a sphere of radius R is :

asked Sep 27, 2013 by meena.p

1 answer

$y= \sin (m \sin ^{-1} x) =>(1-x^2)y_2-xy_1=$ (Here $y_n$ denotes $\large\frac{d^ny}{dx^n}$ )

asked Sep 27, 2013 by meena.p

1 answer

$f(x) = \sin x + \cos x=>f(x)=> f \bigg(\large\frac{\pi}{4}\bigg)$ $f^{(iv)} \bigg (\large\frac{\pi}{4}\bigg)=$

asked Sep 27, 2013 by meena.p

1 answer

$y= \cos ^{-1}\bigg[\large\frac{a^2-x^2}{a^2+x^2}\bigg]+ \sin ^{-1} \bigg[\large\frac{2ax}{a^2+x^2}\bigg]=>\frac{dy}{dx}=$

asked Sep 27, 2013 by meena.p

1 answer

$f(x)=(\cos x) (\cos 2x).........( \cos nx) => f'(x)+ \sum \limits _{r=1} ^ n (r \tan rx) f(x)=$

asked Sep 27, 2013 by meena.p

1 answer

If $f :R \to R$ defined by $f(x)= \left\{ \begin{array}{1 1} \frac{1+3x^2-\cos 2x}{x^2}, & \quad for\; x \neq 0 \\ k & \quad for \; x=0 \end{array}. \right.$ is continuous at x=0, then k=

asked Sep 27, 2013 by meena.p

1 answer

$\lim \limits_{x \to x} \large\frac{\tan x -\sin x}{x^2}=$

asked Sep 27, 2013 by meena.p

1 answer

If $(2,3,-3)$ is one end of a diameter of the sphere $x^2+y^2+z^2-6x-12y-2z+20=0$ then the other end of the diameter is :

asked Sep 27, 2013 by meena.p

1 answer

A plane meets the coordinate axes at A,B,C so that the centroid of the triangle ABC is (1,2,4). Then the equation of the plane is :

asked Sep 27, 2013 by meena.p

1 answer

If $\alpha, \beta,\gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a= \alpha ^2+\beta^2+\gamma^2, \;b= \alpha \beta + \beta \gamma+ \gamma \alpha$ and $c= (\alpha+\beta)(\beta+\gamma)(\gamma+\alpha),$ then the correct inequality among the following is :

asked Sep 27, 2013 by meena.p

1 answer

The point dividing the join of $(3,-2,1)$ and $(-2,3,11)$ in the ratio $2:3$ is:

asked Sep 27, 2013 by meena.p

1 answer

The length of the latus rectum of the conic $\large\frac{5}{r}$ $=2+3 \;\cos \theta +4 \sin \theta$ is :

asked Sep 27, 2013 by meena.p

1 answer

If the lines $2x+3y+12=0,x-y+k=0$ are conjugate with respect to the parabola $y^2=8x,$ then $k=$

asked Sep 27, 2013 by meena.p

1 answer

The product of the perpendicular distances from any point on the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$ $=1$ to its asymptotes is :

asked Sep 27, 2013 by meena.p

1 answer

The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is :

asked Sep 27, 2013 by meena.p

1 answer

Let M be the foot of the perpendicular from a point P on the parabola $y^2=8(x-3)$ onto its directrix and let S be the focus of the parabola. If $\Delta SPM$ is an equilateral triangle, then $P=$

asked Sep 27, 2013 by meena.p

1 answer

The length of the common chord of the circles of radii 15 and 20 whose centers are 25 units of distance apart, is :

asked Sep 27, 2013 by meena.p

1 answer

If the circle $x^2+y^2+2x+3y+1=0$ cuts another circle $x^2+y^2+4x+3y+2=0$ in A and B, then the equation of the circle with AB as a diameter is :

asked Sep 27, 2013 by meena.p

1 answer

The equation of the circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and of double its area is :

asked Sep 27, 2013 by meena.p

1 answer

If the lengths of tangents drawn to the circles : $x^2+y^2-8x+40=0; 5x^2+5y^2-25x+80=0;x^2+y^2-8x+16y+160=0$ from the point P are equal, then P=

asked Sep 27, 2013 by meena.p

1 answer

The equation of the radical axis of the pair of circles $7x^2+7y^2-7x+14y+18=0$ and $4x^2+4y^2-7x+8y+20=0$ is :

asked Sep 27, 2013 by meena.p

1 answer

If $3x^2-11xy+10y^2-7x+13y +k=0$ denotes a pair of straight lines, then the point of intersection of the lines is :

asked Sep 27, 2013 by meena.p

1 answer

A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve $x^2+y^2 =4$ with $x+y=a,$ where $a > 0$ . Then $a=$

asked Sep 27, 2013 by meena.p

1 answer

The distance between the two lines represents by $8x^2-24 xy +18 y^2-6x+9y-5=0$

asked Sep 27, 2013 by meena.p

1 answer

A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the straight line $y=2x+3+\sqrt 2$ at $(x_0,y_0).$ Then $2x_0+y_0=$

asked Sep 27, 2013 by meena.p

1 answer

The image of the line $x+y-2=0$ in the $Y-axis$ is :

asked Sep 27, 2013 by meena.p

1 answer

The image of point $(4,-13)$ with respect to the line $5x+y+6=0$ is :

asked Sep 27, 2013 by meena.p

1 answer

If a straight line L is perpendicular to the line $4x-2y=1$ and forms a triangle of area 4 square units with the coordinate axes, then an equation of the line L is :

asked Sep 27, 2013 by meena.p

1 answer

If the mean and variance of a binomial variable X are 2 and 1 respectively, the $P(X \geq 1)=$

asked Sep 27, 2013 by meena.p

1 answer

Suppose that a random variable X follows Poisson distribution. If $P(X=1)=P(X=2)$ then $P(X=5)=$

asked Sep 27, 2013 by meena.p

1 answer

Suppose A and B are two events such that $P(A \cap B)=\large\frac{3}{25}$ and $P(B-A)=\large\frac{8}{25}$ . Then $P(B)=$

asked Sep 27, 2013 by meena.p

1 answer

If $A_i (i =1,2,3..........,n)$ are $n$ independent events with $P(A_i)=\large\frac{1}{1+i}$ for each i, then the probability that none of $A_i$ occurs is :

asked Sep 27, 2013 by meena.p

1 answer

An urn A contains 3 white and 5 black balls. Another urn B contains 6 white and 8 black balls. A ball is picked from A at random and then transferred to B. Then a ball is picked at random from B. The probability that it is a white ball is :

asked Sep 26, 2013 by meena.p

1 answer

Let $OA,OB,OC$ be the co-terminal edges of a rectangular parallelopiped of volume V and let P be the vertex opposite to O. Then $[\overrightarrow{AP} \overrightarrow {BP} \overrightarrow {CP} ]=$

asked Sep 26, 2013 by meena.p

1 answer

If the angle $\theta$ between the vectors $\overrightarrow {a}=2x^2 \overrightarrow {i}+ 4x \overrightarrow {j}+ \overrightarrow {k}$ and $\overrightarrow {b}=7 \overrightarrow{i}-2 \overrightarrow {j}+x \overrightarrow {k}$ is such that $90^{\circ} < \theta <180^{\circ}$ then $x$ lies in the interval ::

asked Sep 26, 2013 by meena.p

1 answer

$\overrightarrow {u}=\overrightarrow {a}-\overrightarrow {b},\overrightarrow {v}=\overrightarrow {a}+\overrightarrow {b},| \overrightarrow {a} | =| \overrightarrow {b} |=2 => | \overrightarrow {u} \times \overrightarrow {v} |=$

asked Sep 26, 2013 by meena.p

1 answer

$\bigg[ \overrightarrow {a}+ 2 \overrightarrow {b}- \overrightarrow {c}\bigg].\bigg[\overrightarrow {a}- \overrightarrow {b}\bigg] \times \bigg[\overrightarrow {a}-\overrightarrow {b}-\overrightarrow {c}\bigg]=$

asked Sep 26, 2013 by meena.p

1 answer

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