Recent questions tagged maths

Let $\tan^{-1}y = \tan ^{-1} x +\tan ^{-1} \bigg( \large\frac{2x}{1-x^2}\bigg)$, where $|x| < \frac{1}{\sqrt 3}$. Then a value of y is :

asked Oct 26, 2015 by meena.p

1 answer

Let A and B be two sets containing four and two elements respectively . Then the number of subset of the set $A \times B$ , each having at least three elements is :

asked Oct 26, 2015 by meena.p

1 answer

The number of integers given than $ 6,000$ that can be formed, using the digit $3,5,6,7$ and $8$ without repetition , is :

asked Oct 26, 2015 by meena.p

1 answer

The area (in sq. units) of the quadrilateral formed by the tangent at the end points of the latera recta to the ellipse $\large\frac{x^2}{9} +\frac{y^2}{5} $$=1$, is :

asked Oct 26, 2015 by meena.p

1 answer

Locus of the image of the point (2,3) in the line $(2x-3y+4) +k(x-2y+3)=0,k \in R$, is a :

asked Oct 26, 2015 by meena.p

1 answer

If m is the A.M of two distinct real numbers l and $n(l,n > 1) $ and $G_1, G_2$ and $G_3$ are three geometric means between l and n, then $G_1 ^4 +2 G_2^4+G_3^4$ equals.

asked Oct 26, 2015 by meena.p

1 answer

The area (in sq.units ) of the region described by : $[(x,y):y^2 \leq 2x$ and $y \leq 4x-1)$ is :

asked Oct 26, 2015 by meena.p

1 answer

The equation of the plane containing the line $2x-5y+z=3; x+y+4z=5$ and parallel to the plane ; $x+3y+6z=1$ , is :

asked Oct 26, 2015 by meena.p

1 answer

The distance of the point $(1,0,2) $ from the point of intersection of the line $ \large\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ and the plane $x-y+z=16$ , is:

asked Oct 26, 2015 by meena.p

1 answer

The number of points , having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0,0), (0,41)$ and $(41,0)$ is :

asked Oct 26, 2015 by meena.p

1 answer

The integral $\int \large\frac{dx}{x^2(x^4+1)^{3/4}}$ equals :

asked Oct 26, 2015 by meena.p

1 answer

A complex number z is said to be uni modular if $|z|=1$ . Suppose $z_1$ and $z_2$ are complex numbers such that $ \large\frac{z_1 -2 z_2}{2-z_1z_2}$ is unimodular. Then the point $z_1$ lies on a :

asked Oct 26, 2015 by meena.p

1 answer

If $12$ identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is:

asked Oct 26, 2015 by meena.p

1 answer

Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2 =0$. If $a_n = \alpha ^n -\beta^n$ , for $n \geq 1$, then the value of $\large\frac{a_{10}-2_{a8}}{2_{a9}}$ is equal to :

asked Oct 23, 2015 by meena.p

1 answer

Let Q be the vertex and Q be any point on the parabola $x^2=8y$ . If the piont P divides the line segment OQ internally in the ratio $1:3$ then the locus of P is :

asked Oct 23, 2015 by meena.p

1 answer

The sum of the first 9 terms of the series $\large\frac{1^3}{1} +\frac{1^3+2^3}{1+3} +\frac{1^3+2^3+3^3}{1+3+5}$+.....is :

asked Oct 23, 2015 by meena.p

1 answer

The mean of the data set comprising of 16 observations is $16$. If one of the observation valued 16 is deleted and three new observations valued 3,4,and 5 are added to the data , then the mean of the resultant data, is :

asked Oct 23, 2015 by meena.p

1 answer

Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$ If $\lim \limits_{x \to 0} \bigg[ 1+ \frac{f(x)}{x^2} \bigg] =$$3$, then $f(2) $ is equal to :

asked Oct 23, 2015 by meena.p

1 answer

The sum of coefficient of integral powers of x in the binomial expansion of $(1-2 \sqrt x)^{50}$ is :

asked Oct 23, 2015 by meena.p

1 answer

The negation of $\sim S \vee ( \sim r \wedge s)$ is equivalent to :

asked Oct 16, 2015 by meena.p

1 answer

Let $\tan^{-1}y= \tan^{-1} x +\tan^{-1} \bigg( \large\frac{2x}{1-x^2}\bigg)$, Where $|x| < \large\frac{1}{\sqrt 3}$. Then a value of y is :

asked Oct 16, 2015 by meena.p

1 answer

If the angle of elevation of the top of a tower from three collinear points A,B and C, on a line leading to the foot of the tower, are $30^{\circ}, 45^{\circ}$ and $60^{\circ}$ respectively , then the ratio, $AB: BC$, is :

asked Oct 16, 2015 by meena.p

1 answer

The mean of the data set comprising of 16 observations is $16$. If one of the observation valued $16$ is deleted and three new observation valued $3,4$ and $5$ are added to the data, then the mean of the resultant data, is :

asked Oct 16, 2015 by meena.p

1 answer

If 2 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :

asked Oct 16, 2015 by meena.p

1 answer

Let $ \overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three non- zero vectors Such that no two of them are collinear and $(\overrightarrow{a} \times \overrightarrow{b}) \times \overrightarrow{c} =\large\frac{1}{3}$$ | \overrightarrow{b}||\overrightarrow{c}| \overrightarrow{a} $. If $\theta$ is the angle between vactors $\overrightarrow{b}$ and $\overrightarrow{c}$ then a value of $\sin \theta$ is :

asked Oct 15, 2015 by meena.p

1 answer

The equation of the plane containing the line $2x-5y+z=3;x+y+4z=5,$ and parallel to the plane, $x+3y+6z=1,$ is:

asked Oct 15, 2015 by meena.p

1 answer

The distance of the point $(1,0,2)$ from the point of intersection of the line $ \large\frac{x-2}{3} =\frac{y+1}{4} =\frac{z-2}{12}$ and the plane $x-y+z=16$, is:

asked Oct 15, 2015 by meena.p

1 answer

Let $O$ be the vertex and Q be any point on the parabola, $x^2=8y$ . If the point P divides the line segment OQ internally in the ratio $1:3$ , then the locus of P is :

asked Oct 15, 2015 by meena.p

1 answer

The area (in sq.units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\large\frac{x^2}{9} +\frac{y^2}{5}$$=1$ , is :

asked Oct 15, 2015 by meena.p

1 answer

The number of common tangents to be circles. $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ is

asked Oct 15, 2015 by meena.p

1 answer

Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0; k \in R$ is a :

asked Oct 15, 2015 by meena.p

1 answer

The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices $(0,0),(0,41)$ and $(41,0)$ IS :

asked Oct 15, 2015 by meena.p

1 answer

Let $y(x) $ be the solution of the differential equation : $(x log x) \frac{dy}{dx}$$+y=2x \log x, (x \geq 1)$ Then $y(e) $ is equal to :

asked Oct 15, 2015 by meena.p

1 answer

The area (in sq.units) of the region described by : $[(x,y);y^2 \leq 2x\;and\;y \geq 4x-1]$ is

asked Oct 15, 2015 by meena.p

1 answer

The integral $\int\limits_2^4 \large\frac{\log x^2}{\log x^2+\log (36-12x+x^2)}$$dx$ is equal to :

asked Oct 15, 2015 by meena.p

1 answer

The integral $\int \large\frac{dx}{x^2(x^4+1)^{3/4}}$ equals :

asked Oct 15, 2015 by meena.p

1 answer

Let $f(x) $ be a polynomial of degree four having extreme values at $x=1$ and $x=2$ . If $\lim \limits_{ x \to 0} \bigg[ 1+ \frac{f(x)}{x^2} \bigg]$$=3$ , then $f(2)$ is equal to :

asked Oct 15, 2015 by meena.p

1 answer

The normal to the curve , $x^2+2xy-3y^2=0$ at $(1,1)$

asked Oct 15, 2015 by meena.p

1 answer

If the function $g(x) = \left\{ \begin{array} {1 1} k \sqrt {x+1}, & \quad 0 \leq x 3 \\ mx=2 ,& \quad 3 < x \leq 5 \end{array} \right. $ is differential, then the value of $k+m$ is :

asked Oct 15, 2015 by meena.p

1 answer

$\lim \limits_{x \to 0} \large\frac{(1- \cos 2x)(3 +\cos x )}{x \tan 4x}$ is equal to :

asked Oct 15, 2015 by meena.p

1 answer

The Sum of first 9 terms of the series $\large\frac{1^3}{1} +\frac{1^3+2^3}{1+3} +\frac{1^3+2^3+3^3}{1+3+5}+....$ is

asked Oct 15, 2015 by meena.p

1 answer

If $m$ is the A.M of two distinct real numbers $l$ and $n (l ,n > 1) $ and $G_1,G_2$ and $G_3$ are three geometric means between l and n, then $G_1^4 +2 G_2^4+G_3^4 $ equals

asked Oct 15, 2015 by meena.p

1 answer

The sum of coefficient of integral powers of x in the binomial expansion of $(1-2 \sqrt x)^{50}$ is :

asked Oct 15, 2015 by meena.p

1 answer

The number of integers greater than $6,000$ than can be formed, using the digits $3,5,6,7$ and $8$ without repetition, is :

asked Oct 15, 2015 by meena.p

1 answer

The set of all values of $\lambda$ for which the system of linear equations : $2x_1 -2x_2+x_3 =\lambda x_1 ; 2x_1 -3x_2+2x_3 =\lambda x_2 ; -x_1 +2x_2 =\lambda x_3 $ has a non- trivial solution ,

asked Oct 15, 2015 by meena.p

1 answer

If $A= \begin{bmatrix}1 & 2 & 2\\ 2 & 1 & -2\\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^T=9I$, where I is $3 \times 3 $ identify matrix , then the ordered pair $(a,b)$ is equal to :

asked Oct 15, 2015 by meena.p

1 answer

Let $ \alpha$ and $\beta$ be the roots of equation $x^2-6x-2=0$. If $a_n= \alpha^n-\beta^n $, for $n \geq 1$, then the value of $ \large\frac{a_{10}-a_{a8}}{2a_g}$ is equal to :

asked Oct 14, 2015 by meena.p

1 answer

A complex number z is said to be unimodular if $|z|=1$ .Suppose $z_1$ and $z_2$ are complex number Such that $ \large\frac{z_1 -2 z_2}{2-z_1z_2}$is unimodular and $z_2$ is not unimodular . Then the point $Z_1$ lies on a :

asked Oct 14, 2015 by meena.p

1 answer

Let A and B two set containing four and two elements respectively . Then the number of subsets of the set $A \times B$ , each having at least three elements is :

asked Oct 14, 2015 by meena.p

1 answer

Consider the following statement : P: Suman is brilliant Q: Suman is rich R: Suman is honest . The negation of the statement , "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as :

asked Oct 8, 2015 by meena.p

1 answer

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