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Recent questions tagged mathematics

Find the angle of intersection of the curve y=x-x^2 and y=x^2

asked Dec 5, 2018 by rajni.tomar903

0 answers

If the function $\; f(x) = \{ \begin{array} \large\frac{\sqrt{2+cos x}-1}{(\pi-x)^{2}} ,& x \neq \pi \\ k ,& x=\pi \end{array} \;$ is continuous at $\;x=\pi \;$ , then k equals :

asked May 25, 2014 by yamini.v

0 answers

If m is non - zero number and $\;\int \large\frac{x^{5m-1}+2x^{4m-1}}{(x^{2m}+x^{m}+1)^{3}} \normalsize dx= \normalsize f(x)+c\;$ , then $\;\normalsize f(x)\;$ is :

asked May 25, 2014 by yamini.v

0 answers

The contrapositive of the statement " If i am not feeling well , then i will go to the doctor " is :

asked May 25, 2014 by yamini.v

0 answers

The principal value of $\;tan^{-1}(cot \large\frac{43 \pi}{4})\;$ is :

asked May 25, 2014 by yamini.v

0 answers

The function $\;f(x)=|sin 4x|+|cos 2x|\;$ , is a periodic function with period :

asked May 25, 2014 by yamini.v

0 answers

Let $\;\overline{x}\;,M\;$ and $\;\sigma^{2}\;$ be respectively the mean ,mode and variance of n observations $\;x_{1},x_{2},...,x_{n}\;$ and $\;d_{i}=-x_{i}-a\;,i=1,2,...,n\;$, where a is any number.\[\] Statement I : Variance of $\;d_{1},d_{2},..,d_{n}\;$ is $\;\sigma^{2}\;$\[\] Statement II :Mean and mode of $\;d_{1},d_{2},..,d_{n}\;$ are $\;\overline{x}-a\;$ and $\;-M-a\;$, respectively

asked May 25, 2014 by yamini.v

0 answers

Let A and E be any two events with positive probabilities :\[\] Statement I : $\;\normalsize P(\large\frac{E}{A}) \geq \normalsize P(\large\frac{A}{E}) \normalsize P(E)\;$ \[\] Statement II : $\;\normalsize P(\large\frac{A}{E}) \geq \normalsize P(A \cap E)\;$ .

asked May 25, 2014 by yamini.v

0 answers

If $\;\overrightarrow{x}=3 \hat{i}-6 \hat{j}-\hat{k}\;, \overrightarrow{y}=\hat{i}+4 \hat{j}-3 \hat{k}\;$ and $\;\overrightarrow{z}=3 \hat{i}-4 \hat{j}-12 \hat{k}\;$ , then the magnitude of the projection of $\;\overrightarrow{x} \times \overrightarrow{y}\;$ on $\;\overrightarrow{z}\;$ is :

asked May 25, 2014 by yamini.v

0 answers

If the angle between the line $\;2(x+1)=y=z+4\;$ and the plane $\;2x-y+\sqrt{\lambda}z+4=0\;$ is $\;\large\frac{\pi}{6}\;$ ,then the value of $\;\lambda\;$ is :

asked May 24, 2014 by yamini.v

0 answers

Equation of the line of the shortest distance between the lines $\;\large\frac{x}{1}=\large\frac{y}{-1}=\large\frac{z}{1}\;$ ans $\;\large\frac{x-1}{0}=\large\frac{y+1}{-2}=\large\frac{z}{i}\;$ is :

asked May 24, 2014 by yamini.v

0 answers

The tangent at an extremely (in the first quadrant) of latus rectum of the hyperbola $\;\large\frac{x^{2}}{4}-\large\frac{y^{2}}{5}=0\;$ , meets x -axis and y -axis at A and B respectively .Then $\;(OA)^{2}-(OB)^{2}\;$ , where O is the origin , equals :

asked May 24, 2014 by yamini.v

0 answers

A chord is drawn through the focus of the parabola $\;y^{2}=6x\;$ such that its distance from the vertex of this parabola is $\;\large\frac{\sqrt{5}}{2}\;$ , then its slope can be :

asked May 24, 2014 by yamini.v

0 answers

The equation of the circle described on the chord $\;3x+y+5=0\;$ of the circle $\;x^{2}+y^{2}=16\;$ as diameter is :

asked May 24, 2014 by yamini.v

0 answers

If a line L is perpendicular to the line $\;5x-y=1\;$ , and the area of the triangle formed by the line L and the coordinate axes is 5 , then the distance of line L from the line $\;x+5y=0\;$ is :

asked May 24, 2014 by yamini.v

0 answers

The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points $\;(a^{2}+1,a^{2}+1)\;$ and $\;(2a ,-2a)\;, a \neq 0\;$.Then for any a , the orthocentre of this triangle lies on the line :

asked May 24, 2014 by yamini.v

0 answers

If $\;\large\frac{dy}{dx} + y tan x=sin 2x\;$ and $\;y(0)=1\;$ , then $\;y(\pi)\;$ is equal to :

asked May 24, 2014 by yamini.v

0 answers

The area of the region above the x - axis bounded by the curve $\;y=tan x\;,0 \leq x \leq \large\frac{\pi}{2}\;$ and the tangent to the curve at $\;x= \large\frac{\pi}{4}\;$ is :

asked May 24, 2014 by yamini.v

0 answers

Let function F be defined as $\;F(x) =\int \limits_{1}^{x} \large\frac{e^{t}}{t} dt\;$ , x > 0 then the value of the integral $\;\int \limits_{1}^{x} \large\frac{e^{t}}{t+a} dt\;$ , where a > 0 , is :

asked May 24, 2014 by yamini.v

0 answers

If the volume of a spherical ball is increasing at the rate of $\;4 \pi \;cc/sec\;$ , then the rate of increase of its radius (in cm/sec) , when the volume is $\;288 \pi\;cc\;$ , is :

asked May 24, 2014 by yamini.v

0 answers

If non - zero real numbers b and c are such that min f(x) > max g(x) , where $\;f(x)=x^{2}+2bx+2c^{2}\;$ and $\;g(x)=-x^{2}-2cx+b^{2}\;(x \in R)\;$ ;then $\;|\large\frac{c}{b}|\;$ lies in the interval :

asked May 24, 2014 by yamini.v

0 answers

Let $\;f: R \to R\;$ be a function such that $\;|f(x)| \leq x^{2}\;$ , for all $\;x \in R\;$.Then , at x= 0 , f is :

asked May 24, 2014 by yamini.v

0 answers

Let $\;f(n)=[\large\frac{1}{3} + \large\frac{3n}{100}]n\;$ , where [n] denotes the greatest integer less than or equal to n .Then $\;\sum_{n=1}^{56} f(n)\;$ is equal to :

asked May 24, 2014 by yamini.v

0 answers

The number of terms in an A.P. is even ; the sum of the odd terms in it is 24 and that the even terms is 30 . If the last term exceeds the first term by $\;10 \large\frac{1}{2}\;$, then the number of terms in the A.P. is :

asked May 24, 2014 by yamini.v

1 answer

The coefficient of $\;x^{1012}\;$ in the expansion of $\;(1+x^{n}+x^{253})^{10}\;$,(where $\;n \leq 22\;$ is any positive integer),is :

asked May 24, 2014 by yamini.v

0 answers

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants .If the number of games that the men played between them - selves exceeds the number of games that the men played with the women by 66 , then the number of men who participated in the tournament lies in the interval :

asked May 24, 2014 by yamini.v

1 answer

If $\;\bigtriangleup_{r}=\begin{vmatrix} r & 2r-1 & 3r-2 \\[0.3em] \large\frac{n}{2} & n-1 & a \\[0.3em] \large\frac{1}{2}n(n-\normalsize 1) & (n-\normalsize 1)^{2} & \large\frac{1}{2} (n-\normalsize 1)(\normalsize 3n-\normalsize 4)\end{vmatrix}\;$ , then the value of $\;\sum_{r=1}^{n-1} \bigtriangleup_{r}\;$ :

asked May 24, 2014 by yamini.v

0 answers

Let A and B be any $\;3 \times 3\;$ matrices . If A is symmetric and B is skewsymmetric , then the matrix AB - BA is :

asked May 24, 2014 by yamini.v

0 answers

The equation $\;\sqrt{3x^{2}+x5}=x-3\;$ , where x is real , has :

asked May 24, 2014 by yamini.v

0 answers

For all complex numbers z of the form $\;1+i \alpha\;, \alpha \in R\;$ , if $\;z^{2}=x+iy\;$ , then :

asked May 24, 2014 by yamini.v

1 answer

Let $\;f: R \to R \;$ be defined by $\;f(x) = \large\frac{|x|-1}{|x|+1}\;$ then f is :

asked May 24, 2014 by yamini.v

0 answers

Let p,q,r denote arbitrary statements . Then the logically equivalent of the statement $\;p \Rightarrow (q \lor r)\;$ is :

asked May 21, 2014 by yamini.v

0 answers

If $\;f(\theta) = \begin{vmatrix} 1 & cos\theta &1 \\[0.3em] -sin\theta & 1 & \cos \theta \\[0.3em] -1 & sin \theta & 1\end{vmatrix}\;$ and A and B are respectively the maximum and the minimum values of $\;f(\theta)\;$ , then (A ,B) is equal to :

asked May 21, 2014 by yamini.v

0 answers

Statement I : The equation $\;(sin^{-1} x)^{3} + (cos^{-1} x)^{3} - a \pi^{3}=0\;$ has a solution for all $\;a \geq \large\frac{1}{32}\;$ .\[\] Statement II : For any $\;x \in R\;, sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}\;$ and $\; 0 \leq (sin^{-1}x - \large\frac{\pi}{4})^{2} \leq \large\frac{9 \pi^{2}}{16}\;$ .

asked May 21, 2014 by yamini.v

0 answers

A number x is chosen at random from the set $\;\{ 1,2,3,4,...,100\}\;$ .Define the event : A= the chosen number x satisfies $\;\large\frac{(x-10)(x-50)}{(x-30)} \geq 0\;$ Then P(A) is :

asked May 21, 2014 by yamini.v

0 answers

Let $\;\overline{x}\;$ M.D. be the mean and the mean deviation about $\;\overline{x}\;$ on n observations $\;x_{i} , i=1,2,...,n\;$.If each of the observations is increased by 5 , then the new mean and the mean deviation about the new mean , respectively , are :

asked May 21, 2014 by yamini.v

0 answers

If $\;\hat{x} , \hat{y}\;$ and $\;\hat{z}\;$ are three unit vectors in three - dimensional space , then the minimum value of $\;|\hat{x} + \hat{y}|^{2} + |\hat{y} + \hat{z}|^{2} + |\hat{z} + \hat{x}|^{2}\;$ :

asked May 21, 2014 by yamini.v

0 answers

If the distance between planes , $\;4x - 2y -4z+1=0\;$ and $\;4x - 2y -4z+d=0\;$ is 7 , then d is :

asked May 21, 2014 by yamini.v

0 answers

A symmetrical form of the line of intersection of the planes $\;x=ay+b\;$ and $\;z=cy+d\;$ is :

asked May 21, 2014 by yamini.v

0 answers

The minimum area of a triangle formed by any tangent to the ellipse $\;\large\frac{x^{2}}{16}+\large\frac{y^{2}}{81} =1\;$ and the co - ordinate axes is :

asked May 21, 2014 by yamini.v

0 answers

Two tangents are drawn from a point (-2 ,-1) to the curve , $\;y^{2}=4x\;$ . If $\;\alpha\;$ is the angle between them , then $\;|tan \alpha|\;$ is equal to :

asked May 21, 2014 by yamini.v

0 answers

For the two circles $\;x^{2}+y^{2}=16\;$ and $\;x^{2}+y^{2}-2y=0\;$ , there is/are :

asked May 21, 2014 by yamini.v

1 answer

If the three distinct lines $\;x+2ay+a=0\;,x+3by+b=0\;$ and $\;x+4ay+a=0\;$ are concurrent , then the point (a,b) lines on a :

asked May 21, 2014 by yamini.v

0 answers

If a line intercepted between the coordinate axes is trisected at a point $\;A(4,3)\;$ , which is nearer to x - axis, then its equation is :

asked May 21, 2014 by yamini.v

0 answers

The general solution of the differential equation , $\;sin 2x (\large\frac{dy}{dx} - \sqrt{tanx})-y=0 \;$, is :

asked May 21, 2014 by yamini.v

0 answers

If for a continuous function f(x) , $\;\int \limits_{\pi}^{t} (f(x)+x) dx = \pi^{2}-t^{2}\;$ , for all $\;t \geq -\pi\;$ , then $\;f(- \large\frac{\pi}{3})\;$ is equal to :

asked May 21, 2014 by yamini.v

0 answers

If [] denotes the greatest integer function , then the integral $\;\int \limits_{0}^{\pi} [cos x] dx\;$ is equal to :

asked May 21, 2014 by yamini.v

1 answer

The integral $\;\int \large\frac{sin^{2}x cos^{2}x}{(sin^{3} x +cos^{3} x )^{2}} dx\;$ is equal to :

asked May 21, 2014 by yamini.v

0 answers

If $\;1+x^{4}+x^{5} = \sum_{i=0}^{5} a_{i} (1+x)^{i}\;$, for all x in R , then $\;a_{2}\;$ is :

asked May 21, 2014 by yamini.v

0 answers

Let f and g be two differential functions on R such that $\;f^{'}(x) > 0\;$ and $\;g^{'}(x) > 0\;$ for all $\; x \in R\;$. Then for all x :

asked May 21, 2014 by yamini.v

0 answers

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