Recent questions tagged mathematics

If the point (1,4) lies inside the circle $\;x^{2}+y^{2}-6x-10y+p=0\;$ and the circle does not touch or intersect the coordinate axes , then the set of all possible values of P in the interval :

asked May 7, 2014 by yamini.v

1 answer

Given three points P,Q,R with P(5,3) and R lies on the x - axis . if equation of RQ is $\;x-2y=2\;$ and PQ is parallel to the x - axis , then the centroid of $\;\bigtriangleup PQR\;$ lies on the line :

asked May 7, 2014 by yamini.v

0 answers

Let a and b be any two numbers satisfying $\;\large\frac{1}{a^{2}}+\large\frac{1}{b^{2}} =\large\frac{1}{4} \;$, then the foot of perpendicular from the origin on the variable line,$\;\large\frac{x}{a} + \large\frac{y}{b}=1\;$ , lies on

asked May 7, 2014 by yamini.v

1 answer

If the differential equation representing the family of all circles touching x - axis at the origin is $\;(x^{2}-y^{2})\large\frac{dy}{dx}=g(x) y\;$, then $\;g(x)\;$ equals :

asked May 7, 2014 by yamini.v

0 answers

Let $\;A =\{ (x,y) : y^{2} \leq 4x \;, y-2x \leq -4\}\;$. The area (in square units) of the region A is :

asked May 7, 2014 by yamini.v

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The integral $\;\int_{0}^{\large\frac{1}{2}} \large\frac{ln(1+2x)}{1+4x^{2}} dx\;$ , equals :

asked May 7, 2014 by yamini.v

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$\;\int \large\frac{sin^{8} x -cos^{8} x}{(1-2 sin^{2}x cos^{2} x)} dx\;$ is equal to :

asked May 7, 2014 by yamini.v

0 answers

If $\;f(x) = (\large\frac{3}{5})^{x}+ (\large\frac{4}{5})^{x}-1\;,x \in R \;$, then the equation $\;f(x) =0\;$ has :

asked May 7, 2014 by yamini.v

1 answer

If the Rolle's theorem holds for the function $\;f(x) = 2x^{3}+ax^{2}+bx\;$ in the interval $\; [-1 ,1]\;$ for the point $\;c=\large\frac{1}{2}\;$ then the value of 2a+b is :

asked May 7, 2014 by yamini.v

1 answer

If $\;y=e^{nx}\;$ , then $\;(\large\frac{d^{2}y}{dx^{2}}) (\large\frac{d^{2} x}{dy^{2}})\;$ is equal to :

asked May 7, 2014 by yamini.v

0 answers

If $\;f(x)\;$ is continuous and $\;f(\large\frac{9}{2}) = \large\frac{2}{9}\;$ , then $\;\lim_{x}^{0} f(\large\frac{1-cos 3x}{x^{2}})\;$ is equal to :

asked May 7, 2014 by yamini.v

1 answer

If the sum $\; \large\frac{3}{1^{2}} + \large\frac{5}{1^{2} + 2^{2}} + \large\frac{7}{1^{2} + 2^{2} +3^{2}}+----+\;$ upto 20 terms is equal to $\;\large\frac{k}{21}\;$, then k is equal to :

asked May 7, 2014 by yamini.v

1 answer

Given an A.P. whose terms are all positive integers . The sum its first nine terms is greater than 200 and less than 220 . If the second term in it is 12 , then its $\;4^{th}\;$ term is :

asked May 7, 2014 by yamini.v

1 answer

The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers 3,4,5 and 6 , without repetition is :

asked May 7, 2014 by yamini.v

0 answers

The number of terms in the expression of $\;(1+x)^{101}\;(1+x^{2}-x)^{100}\;$ in powers of x is :

asked May 7, 2014 by yamini.v

0 answers

If B is $\;3 \times 3\;$ matrix such that $\;B^{2}=0\;$ then det.$[(I+B)^{50}-50B] \;$ is equal to :

asked May 7, 2014 by yamini.v

0 answers

If a,b,c are non - zero real numbers and if the system of equations $\;(a-1)x =y+z\;,(b-1)y=(z+x)\;,(c-1)z=x-y\;$ , has a non - trivial solution , then ab+bc+ca equals :

asked May 7, 2014 by yamini.v

0 answers

If $\;\large\frac{1}{\sqrt{\alpha}}\;$ and $\;\large\frac{1}{\sqrt{\beta}}\;$ are the roots of the equation ,$\;ax^{2}+bx+c=0 \;(a \neq 0 , q ,b \in R)\;$, then the equation , $\;x(x+b^{3}) + (a^{3}-3abx)=0\;$ has roots :

asked May 7, 2014 by yamini.v

1 answer

If equations $\;ax^{2}+bx+c=0\;, (a,b,c \in R\;, a \neq 0)\;$ and $\;2x^{2}+3x+4=0\;$ have a common root then $\;a : b: c\;$ equals :

asked May 7, 2014 by yamini.v

1 answer

Let $\;w(Im\;w \neq 0)\;$ be a complex number.Then the set of all complex numbers z satisfying the equation $\;w - w \overline{w}z=k(1-z)\;$ , for some real number k , is :

asked May 7, 2014 by yamini.v

0 answers

Let P be the relation defined on the set of all real numbers such that $\;P = \{ (a,b) : sec^{2}a - tan^{2} b=1\}$ . Then P is :

asked May 7, 2014 by yamini.v

0 answers

If $\;\alpha ,\beta \neq o\;$ , and $\;f(n)=\alpha^{n} + \beta^{n}\;$ and $\;\begin{vmatrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4)\end{vmatrix} = K (1-\alpha)^{2}(1-\beta)^{2}(\alpha-\beta)^{2}\;$, then$\;K\;$is equal to :

asked May 2, 2014 by yamini.v

0 answers

The statement $\;\sim(p \leftrightarrow \sim q)\;$ is :

asked May 2, 2014 by yamini.v

0 answers

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is $\;45^{0}\;$. It flies off horizontally straight way from the point O . After one second ,the elevation of the bird from O is reduced to $\;30^{0}\;$. Then the speed in $(m/s)\;$ of the bird is :

asked May 2, 2014 by yamini.v

0 answers

Let $\;f_{k}(x)= \large\frac{1}{k}(sin^{k}x+cos^{k}x)\;$ where $\;x \in R\;$ and $\;k \geq 1\;$. Then $\;f_{4}(x) - f_{6}(x)$ equals :

asked May 2, 2014 by yamini.v

0 answers

The variance of first 50 even natural numbers is :

asked May 2, 2014 by yamini.v

1 answer

Let A and B be two events such that $\;P (\overline{A \cup B}) = \large\frac{1}{6}\;,P (\overline{A \cap B}) = \large\frac{1}{4} \;$ where $\;\overline{A}\;$ stands for the compliment of the event A .Then the events A and B are :

asked May 2, 2014 by yamini.v

0 answers

If $\;[\overrightarrow{a} \times \overrightarrow{b} \;\;\overrightarrow{b}\times \overrightarrow{c} \;\;\overrightarrow{c} \times \overrightarrow{a} ]= \lambda [\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}]^{2}\;$ then $\;\lambda\;$ is equal to :

asked May 2, 2014 by yamini.v

0 answers

The angle between the lines whose direction cosines satisfy the equations $\;l+m+n=0\;$ and $\;l^{2}=m^{2}+n^{2}\;$ is :

asked May 2, 2014 by yamini.v

0 answers

The image of the line $\;\large\frac{x-1}{3} =\large\frac{y-3}{1} =\large\frac{z-4}{-5}\;$ in the plane $\;2x-y+z+3=0\;$ is the plane :

asked May 2, 2014 by yamini.v

0 answers

The slope of the line touching both the parabolas $\;y^{2}=4x\;$ and $\;x^{2}=-32y\;$ is :

asked May 2, 2014 by yamini.v

0 answers

Let C be the circle with centre at (1,1) and radius=1 . If T is the circle centred at (0,y) ,passing through origin and touching the circle C externally ,then the radius of T is equal to :

asked May 2, 2014 by yamini.v

0 answers

The locus of the foot of perpendicular drawn from the centre of the ellipse $\;x^{2}+3y^{2}=6\;$ on any tangent to it is :

asked May 2, 2014 by yamini.v

1 answer

Let a,b,c and d be non-zero numbers .If the point of intersection of the lines $\;4ax+2ay+c=0\;$ and $\;5bx+2by+d=0\;$ lies in the fourth quadrant and is equidistant from the two axis then :

asked May 2, 2014 by yamini.v

0 answers

Let PS be the median of the triangle with vertices P(2,2) , Q(6,-1) and R(7,3) . The equation of the line passing through (1,-1) and parallel to PS is :

asked May 2, 2014 by yamini.v

0 answers

Let the population of rabbits surviving at a time t be governed by the differential equation $\; \large\frac{d p(t)}{dt} = \large\frac{1}{2} p(t) -200 \;$ . If$\;p(0) = 100\;$ , then $\;p(t)\;$ equals :

asked May 2, 2014 by yamini.v

1 answer

The area of the region described by $\;A=\{(x,y) : x^{2}+y^{2} \leq 1 \;and\; y^{2} \leq 1-x\}\;$ is :

asked May 2, 2014 by yamini.v

0 answers

The integral $\; \int_{0}^{\pi} \sqrt{1+4sin^{2} \large\frac{x}{2}-4 sin \large\frac{x}{2}} dx\;$ equals :

asked May 2, 2014 by yamini.v

0 answers

The integral $\;\int (1+x-\large\frac{1}{x})\;e^{x+\large\frac{1}{x}} dx\;$ is equal to :

asked May 2, 2014 by yamini.v

0 answers

If x=-1 and x=2 are extreme points of $\;f(x) =\alpha log|x|+ \beta x^{2}+x\;$ then :

asked May 2, 2014 by yamini.v

0 answers

If f and g are differentiable functions in [0 , 1] satisfying $\;f(0)=2=g(1)\;,g(0)=0\;$ and $\;f(1)=6\;$, then for some $\;c \in ]0 ,1[\;$ :

asked May 1, 2014 by yamini.v

0 answers

If g is the inverse of a function f and $\;f^{'}(x) =\large\frac{1}{1 + x^{5}}\;$ , then $\;g^{'}(x)\;$ is equal to :

asked May 1, 2014 by yamini.v

0 answers

$\; \lim_{x \to 0} \large\frac{sin (\pi cos^{2} x)}{x^{2}}\;$ is equal to :

asked May 1, 2014 by yamini.v

0 answers

Three positive numbers from an increasing G.P. if the middle term in this G.P. is doubled , the new numbers are in A.P. Then the common ratio of the G.P. is :

asked May 1, 2014 by yamini.v

0 answers

If $\;(10)^{9} + 2 (11)^{1} (10)^{8} + 3(11)^{2} (10)^{7}+....+10 (11)^{9} = k (11)^{9}\;$, then k is equal to :

asked May 1, 2014 by yamini.v

0 answers

If the coefficients of $\;x^{2}\;$ and $\;x^{3}\;$ in the expansion of $\;(1+ax+bx^{2}) (1-2x)^{18}\;$ in powers of x are both zero , then (a,b) is equal to :

asked May 1, 2014 by yamini.v

0 answers

If A is an $\;3 \times 3\;$ non - singular matrix such that $\;A^{'}A=AA^{'}\;$ and $\;B=A^{-1}A^{'}\;$ , then $\;BB^{'} =\;$ :

asked May 1, 2014 by yamini.v

0 answers

Let $\;\alpha\;$ and $\;\beta\;$ be the roots of equation $\;px^{2} +qx + r=0\;,p \neq 0\;$ .if p ,q ,r are in A.P. and $\;\large\frac{1}{\alpha} + \large\frac{1}{\beta}=4\;$ then the value of $\;|\alpha - \beta|\;$ is :

asked May 1, 2014 by yamini.v

0 answers

If $\; a \in R\;$ and the equation $\;-3(x-[x])^{2} + 2(x-[x]) + a^{2} =0\;$ (where [x] denotes the greatest integer $\; \leq x )\;$ has no integral solution , then all possible values of a lie in the interval :

asked May 1, 2014 by yamini.v

0 answers

If z is a complex number such that $\;|z| \geq 2\;$ , then the minimum value of $\;|z + \large\frac{1}{2}|\;$ :

asked May 1, 2014 by yamini.v

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