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Recent questions tagged mathematics

If $\;f(x) = x^{2}-x+5\;,x > \large\frac{1}{2}\;$ , and $\;g(x)\;$ is its inverse function , then $\;g^{'}(7)\;$ equals :

asked May 21, 2014 by yamini.v

0 answers

Let $\;f , g :R \to R\;$be two functions defined by $\;f(x)=\{ \begin{matrix}x sin(\large\frac{1}{x}) \;, x \neq 0 \\ 0\;,x=0 \end{matrix}\;$ , and $\;g(x)=x f(x)\;$\[\] Statement I : f is a continuous function at x=0 .\[\] Statement II : g is differential function at x=0 .

asked May 21, 2014 by yamini.v

0 answers

The least positive integer n such that $\;1-\large\frac{2}{3} -\large\frac{2}{3^{2}}- ..... -\large\frac{2}{3^{n-1}} < \large\frac{1}{100}\;$, is :

asked May 21, 2014 by yamini.v

1 answer

Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of $\;\large\frac{1}{a} \;$ and $\;\large\frac{1}{b}\;$ . If $\;\large\frac{1}{M} : G \;$ is 4 : 5 , then a : b can be :

asked May 21, 2014 by yamini.v

0 answers

If $\;(2 + \large\frac{x}{3})^{55}\;$ is expanded in the ascending powers of x in two consecutive terms of the expansion are equal , then these terms are :

asked May 21, 2014 by yamini.v

0 answers

If $\; A=\begin{bmatrix} 1 & 2 & x \\[0.3em] 3 & -1 & 2\end{bmatrix}\;$ and $\; B=\begin{bmatrix} y & x & 1\end{bmatrix}\;$ be such that $\;AB= \begin{bmatrix} 6 \\[0.3em] 8 \end{bmatrix}\;$ , then :

asked May 21, 2014 by yamini.v

0 answers

If $\; \begin{vmatrix} a^{2} & b^{2} & c^{2} \\[0.3em] (a+\lambda)^{2} &(b+\lambda)^{2} & (c+\lambda)^{2} \\[0.3em] (a-\lambda)^{2} & (b-\lambda)^{2} & (c-\lambda)^{2} \\[0.3em] \end{vmatrix}=k \lambda \begin{vmatrix} a^{2} & b^{2} & c^{2} \\[0.3em] a & b& c \\[0.3em] 1 & 1 & 1 \end{vmatrix}\;,\lambda \neq 0\;$ , then k is equal to :

asked May 21, 2014 by yamini.v

0 answers

8 - digit number are formed using the digits 1,1,2,2,2,3,4,4.The number of such numbers in which the odd digits do not occupy odd places , is :

asked May 20, 2014 by yamini.v

0 answers

The sum of the roots of the equation ,$\;x^{2}+|2x-3|-4=0\;$ is :

asked May 20, 2014 by yamini.v

1 answer

Let $\;z \neq -i\;$ be any complex number such that $\;\large\frac{z-i}{z+i}\;$ is a purely imaginary number . Then $\;z+ \large\frac{1}{z}\;$ is :

asked May 20, 2014 by yamini.v

0 answers

A relation on the set $\;A=\{x:|x| < 3 , x \in Z\}\;$ where Z is the set of integers is defined by $\;R=\{(x,y) : y=|x| , x \neq -1\}\;$. Then the number of elements in the power set of R is :

asked May 20, 2014 by yamini.v

0 answers

The proposition $\;\sim (p \vee \sim q) \vee \sim (p \vee q)\;$ is logically equivalent to :

asked May 10, 2014 by yamini.v

0 answers

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be $\;\alpha\;$ . After moving a distance 2 meters from P towards the foot of the tower , the angle of elevation changes to $\;\beta\;$. Then the height (in meters) of the tower is :

asked May 10, 2014 by yamini.v

0 answers

If $\;2 cos \theta + sin \theta =1 \;(\theta \neq \large\frac{\pi}{2})\;$ , then $\;7 cos \theta + 6 sin \theta\;$ is equal to :

asked May 10, 2014 by yamini.v

0 answers

If X has a binomial distribution , B(n , p) with parameters n and p such that P(X=2)=P(X=3) , then E(x) , the mean of variable X , is

asked May 10, 2014 by yamini.v

0 answers

A set contains 7 elements . A non - empty subset A of S and an element x of S are chosen at random . Then the probability that $\; x \in A\;$ is :

asked May 10, 2014 by yamini.v

0 answers

If $\;|\overrightarrow{a}|^{2} =60 \;$ and $\;\overrightarrow{c} \times (\hat{i} + 2 \hat{j} +5 \hat{k}) = \overrightarrow{0}\;$ , then the value of $\;\overrightarrow{c}\;.(-7 \hat{i} + 2 \hat{j} +3 \hat{k}) \;$ is :

asked May 10, 2014 by yamini.v

0 answers

The plane containing the line $\;\large\frac{x-1}{1}=\large\frac{y-2}{2}=\large\frac{z-3}{3} \;$ and parallel to the line $\;\large\frac{x}{1}=\large\frac{y}{1}=\large\frac{z}{4}\;$ passes through the point :

asked May 10, 2014 by yamini.v

0 answers

Let $\;A (2 , 3 , 5)\;,B(-1 ,3 , 2)\;$ and $\;C(\lambda , 5 , \mu)\;$ be the vertices of a $\;\bigtriangleup ABC\;$ . If the median through A is equally inclined to the coordinate axes , then :

asked May 10, 2014 by yamini.v

0 answers

Let $\;P(3 sec \theta , 2 tan \theta)\;$ and $\;Q( 3sec \phi ,2 tan \phi)\;$ where $\;\theta + \phi = \large\frac{\pi}{2}\;$ , be two distinct points on the hyperbola $\;\large\frac{x^{2}}{9} - \large\frac{y^{2}}{16}= 1\;$ . Then the ordinate of the point of intersection of the normals at P and Q is :

asked May 10, 2014 by yamini.v

0 answers

Let $\;L_{1}\;$ be the length of the common chord of the curves $\;x^{2}+y^{2}=9\;$ and $\;y^{2}=8x\;$ , and $\;L_{2}\;$ be the length of the latus rectum of $\;y^{2}=8x\;$, then :

asked May 10, 2014 by yamini.v

0 answers

The set of all real values of $\;\lambda\;$ for which exactly two common tangents can be drawn to the circles $\;x^{2}+y^{2}-4x-4y+6=0\;$ and $\;x^{2}+y^{2}-10x-10y+\lambda=0\;$ is the interval :

asked May 10, 2014 by yamini.v

0 answers

The base of an equilateral triangle is along the line given by $\;3x+4y=9\;$. If a vertex of the triangle is (1,2) , then the length of a side of the triangle is :

asked May 10, 2014 by yamini.v

0 answers

A stair - case of length l rests against a vertical wall and a floor of a room , let P be a point on the stair - case , nearer to its end on the wall , that divides its length in the ratio 1:2 . If the stair - case begins to slide on the floor , then the locus of P is :

asked May 10, 2014 by yamini.v

0 answers

If the general solution of the differential equation $\;y^{'}=\large\frac{y}{x} +\Phi (\large\frac{x}{y})\;$, for some function $\;\Phi\;$ , is given by $\;y ln |cx| = x\;$ , where c is an arbitrary constants , $\;\Phi(2)\;$ is equal to :

asked May 10, 2014 by yamini.v

0 answers

If for $\; n \geq 1\;,P_{n} = \int_{1}^{e} (log x)^{n} dx\;$ , then $\;P_{10} - 90 P_{8}\;$ is equal to :

asked May 10, 2014 by yamini.v

0 answers

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

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