Recent questions tagged 2014

The integral $\; \int x cos^{-1}(\large\frac{1-x^{2}}{1+x^{2}}) dx\;(x > 0)\;$ is equal to :

asked May 10, 2014 by yamini.v

0 answers

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = $\;\sqrt{3}\;$ is :

asked May 10, 2014 by yamini.v

1 answer

Two ships A and B are sailing straight away from a fixed point O along routes such that $\;\angle{AOB}\;$ is always $\;120^{0}\;$ . At a certain distance , OA=8 km ,OB=6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr . Then the distance between A and B is changing at the rate ( in km/hr ) :

asked May 10, 2014 by yamini.v

1 answer

For the curve $\;y=3 sin \theta cos \theta \;,x=e^{\theta} sin \theta\;, 0 \leq \theta \leq \pi ,\;$ the tangent is parallel to x - axis when $\;\theta\;$ is :

asked May 10, 2014 by yamini.v

0 answers

Let $\;f(x)=x|x|\;,g(x)=sinx\;$ and $\;h(x) =(gof)(x)\;$.Then

asked May 10, 2014 by yamini.v

0 answers

If $\;\lim_{x\to2} \large\frac{tan(x-2) \{ x^{2}+(k-2)x-2k\}}{x^{2}-4x+4}=5\;$ ,then k is equal to :

asked May 8, 2014 by yamini.v

0 answers

The sum of the first 20 terms common between the series $\;3+7+11+15+----\;$ and $\;1+6+11+16+---\;$, is :

asked May 8, 2014 by yamini.v

0 answers

In a geometric progression , if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49 , and the sum of the first and the third term is 35 .Then the first term of this geometric progression is :

asked May 8, 2014 by yamini.v

0 answers

The coefficient of $\;x^{50}\;$ in the binomial expansion of $\;(1+x)^{1000} +x (1+x)^{999}+x^{2}(1+x)^{998}+----+x^{1000}\;$ is :

asked May 8, 2014 by yamini.v

0 answers

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits . The number of ways in which this can be done is :

asked May 8, 2014 by yamini.v

0 answers

Let for $\;i=1,2,3,p_{i}x\;$ be a polynomial of degree 2 in $\;x,p_{i}^{'}x,p_{i}^{''}x\;$ be the first and second order derivatives of $\;p_{i}x\;$ respectively . Let , $\;A(x) = \begin{bmatrix} p_{1}(x)&p_{1}^{'}(x)&p_{1}^{''}(x) \\[0.3em] p_{2}(x)&p_{2}^{'}(x)&p_{2}^{''}(x) \\[0.3em] p_{3}(x)&p_{}^{'}(x)&p_{3}^{''}(x) \end{bmatrix}\;$ and $\;B(x) =[A(x)]^{T}A(x) \;$.Then determinant of $\;B(x)\;$ :

asked May 8, 2014 by yamini.v

0 answers

Let A be a $\;3 \times 3\;$ matrix such that $\;A \begin{bmatrix} 1&2&3\\[0.3em] 0&2&3 \\[0.3em] 0&1&1 \end{bmatrix}= \begin{bmatrix} 0&0&1\\[0.3em] 1&0&0 \\[0.3em] 0&1&0 \end{bmatrix}\;$ then $\;A^{-1}\;$ is

asked May 8, 2014 by yamini.v

0 answers

If $\;\alpha\;$ and $\;\beta\;$ are roots of the equation , $\;x^{2} - 4 \sqrt{2}k x +2e^{4 ln k}-1=0\;$ for some k , and $\;\alpha^{2} + \beta^{2} =66\;$ , then $\;\alpha^{3} + \beta^{3}\;$ is equal to :

asked May 8, 2014 by yamini.v

0 answers

If $\;z_{1} ,z_{2}\;$ and $\;z_{3} ,z_{4}\;$ are 2 pairs of conjugate numbers , then $\;arg(\large\frac{z_{1}}{z_{4}}) + arg(\large\frac{z_{2}}{z_{3}})\;$ equals :

asked May 8, 2014 by yamini.v

0 answers

Let f be an odd function defined on the set of real numbers such that for $\;x \geq 0\;$ ,$\;f(x)=3 sinx + 4 cos x$ .Then $\;f(x)\;$ at $\;x=-\large\frac{11 \pi}{6}\;$ is equal to :

asked May 8, 2014 by yamini.v

0 answers

The contrapositive of the statement " I go to school if it does not rain " is :

asked May 8, 2014 by yamini.v

0 answers

If $\;cosec\theta = \large\frac{p+q}{p-q}\;(p \neq q \neq 0)\;$, then $\;|cot(\large\frac{\pi}{4} + \large\frac{\theta}{2})|\;$ is equal to :

asked May 8, 2014 by yamini.v

1 answer

The number of values of $\;\alpha\;$ in $\;[0,2\pi]\;$ for which $\;2 sin^{3} \alpha -7 sin^{2} \alpha + 7 sin \alpha =2\;$is :

asked May 8, 2014 by yamini.v

0 answers

If A and B are two events such that $\;P(A) \cup P(B) = P(A) \cap P(B)\;$ , then the incorrect statement amongst the following statements is :

asked May 8, 2014 by yamini.v

0 answers

In a set of 2n distinct observations , each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3.Then the mean of the new set of observations :

asked May 8, 2014 by yamini.v

0 answers

If $\;\overrightarrow{|a|}=3\;,\overrightarrow{|b|}=3 \;$ and $\;|2\overrightarrow{a} - \overrightarrow{b}|=5\;$ , then $\;|2\overrightarrow{a} + \overrightarrow{b}|\;$ equals :

asked May 8, 2014 by yamini.v

0 answers

A line in the 3 - dimensional space makes an angle $\;\theta (0 < \theta < \large\frac{\pi}{2})\;$ with both the x and y axes . Then the set of values of $\;\theta \;$ is the interval :

asked May 8, 2014 by yamini.v

0 answers

Equation of the plane which passes through the point of intersection of lines $\;\large\frac{x-1}{3} = \large\frac{y-2}{1}=\large\frac{z-3}{2}\;$ and $\;\large\frac{x-3}{1}=\large\frac{y-1}{2}=\large\frac{z-2}{3}\;$ and has the largest distance from the origin is :

asked May 7, 2014 by yamini.v

0 answers

If OB is the semi - minor axis of an ellipse ,$\;F_{1}\;$ and $\;F_{2}\;$ are its foci and the angle between $\;F_{1}B\;$ and $\;F_{2}B\;$ is a right angle , then the square of the eccentricity of the ellipse is :

asked May 7, 2014 by yamini.v

0 answers

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

0 answers

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

0 answers

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

For the compounds $\;CH_{3}Cl \;,CH_{3}Br\; ,CH_{3}I\;$ and $\;CH_{3}F\;$ , the correct order of increasing C - halogen bond length is :

asked May 6, 2014 by yamini.v

0 answers

Which one of the following class of compounds is obtained by polymerization of acetylene ?

asked May 6, 2014 by yamini.v

0 answers

Which is the major product formed when acetone is heated with iodine and potassium hydroxide ?

asked May 6, 2014 by yamini.v

0 answers

In the hydroboration - oxidation reaction of propene with diborane , $\;H_{2}O_{2}\;$ and $\;NaOH\;$ the organic compound formed is :

asked May 6, 2014 by yamini.v

0 answers

Which one of the following reactions will not result in the formation of carbon - carbon bond :

asked May 6, 2014 by yamini.v

1 answer

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