Recent questions tagged 2006

The solution of $(1+x^2) \large\frac{dy}{dx}$$+2xy-4x^2=0$ is :

asked Nov 7, 2013 by meena.p

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The solution of $(x^2+y^2)dx =2xy \;dy$ is :

asked Nov 7, 2013 by meena.p

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$\int _{-1} ^ 1 \large\frac{\cos h x }{1+e^{2x}}$$dx$ is equal to :

asked Nov 7, 2013 by meena.p

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$\int \limits_0^{\pi/2} \large\frac{dx}{1+ \tan^3 x}$ is equal to :

asked Nov 7, 2013 by meena.p

1 answer

Dividing the interval [0,6] into 6 equal parts and by using trapezoidal rule the value of $\int \limits_0^6 x^3 dx$ is approximately:

asked Nov 7, 2013 by meena.p

1 answer

Observe the following statements : $A : \int \bigg(\large\frac { x^2-1}{x^2} \bigg)e. ^{\large\frac{x^2-1}{x}}\; dx= e^{\large\frac{x^2-1}{x}}+c.$$\qquad R:\int f'(x)e^{f(x)}dx=f(x)+c.$ Then which of the following is true ?

asked Nov 7, 2013 by meena.p

1 answer

If $\int \large\frac{dx}{x^2+2x+2}$$=f(x) +c,$ then f(x) is equal

asked Nov 7, 2013 by meena.p

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If $\int \sqrt {\large\frac{x}{a^3-x^3}}dx=g(x)+c,$ then $g(x) $ is equal to :

asked Nov 7, 2013 by meena.p

1 answer

If $f(x,y )= \large\frac{\cos (x-4y)}{\cos (x+4y)}$, then $\large\frac{\partial f}{\partial x} \bigg|_{y-\large\frac{x}{2}}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $u= \sin ^{-1} \bigg( \large\frac{x^2+y^2}{x+y}\bigg)$ then $x \large\frac{\partial u}{\partial x}$$+ y \large\frac{\partial u}{\partial y}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is :

asked Nov 6, 2013 by meena.p

1 answer

In the interval $(-3,3)$ the function $f(x) =\large\frac{x}{3}+\frac{3}{x}$$x \neq 0$ is :

asked Nov 6, 2013 by meena.p

1 answer

If 0 is the angle between the curves $xy=2$ and $x^2+4y=0$ and $x^2+4y=0$, then $\tan \theta$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $f(x)= \left\{ \begin{array}{1 1} \frac{1- \sqrt 2 \sin x}{\pi-4x} & \quad if\;x \neq \frac{\pi}{4} \\ \alpha & \quad if\;x= \frac{\pi}{4} \end{array}. \right. $ is continuous at $\large\frac{\pi}{4}, $ then $\alpha$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $l_1=\lim \limits _{x \to 2^{+}} (x+[x]). l_2 \lim \limits_{x \to 2^{-}} (2x-[x])$ and $l_3=\lim \limits_{x \to x/2} \large\frac{\cos x}{(x-\pi/2)}$ then :

asked Nov 6, 2013 by meena.p

1 answer

If $\lim \limits_{x \to 0} \bigg(\large\frac{\cos 4x+a \cos 2x+b}{x^4}\bigg)$ is finite, then the values of a,b are respectively :

asked Nov 6, 2013 by meena.p

1 answer

$\lim \limits_{x \to \infty} [ \sqrt {x^2+2x-1}-x]$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

If $ 0 < p < q,$ then $\lim \limits _{n \to x}( q^n+p^n)^{1/n}$ is equal to :

asked Nov 6, 2013 by meena.p

1 answer

$f(x) =e^x \sin x,$ 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

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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

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