Recent questions in Mathematics

Let P be the probability of happening any event and Q its failure, then the total chance of $r$ success in $n$ trials is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

The probability that a non - leap year has 53 sundays is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

The chance of throwing a total of 3 or 5 or 11 wih two dice is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

The range of the function $f(x) = \large\frac{x^2+x+2}{x^2+x+1}$ , $x \in (-\infty, \infty)$ is:

asked Jan 6, 2014 by sreemathi.v

1 answer

A and B are two events such that $P(A) > 0, P(B) \neq 1$ then $P( \overline A / \overline B )=$

asked Jan 6, 2014 by thanvigandhi_1

1 answer

If the function $f(x)=\left\{\begin{array}{1 1}(\cos x)^{1/x}&x\neq 0\\k&x=0\end{array}\right.$ is continuous at $x=0$ then value of $K$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

If $P(A)=0.65\: P(B)=0.80$ then $P(A \cap B)$ lies in the interval

asked Jan 6, 2014 by thanvigandhi_1

1 answer

A fair coin is tossed 100 times. The probability of getting tails on odd number of times is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

A line with direction ratio $(2,1,2)$ meets the lines $x=y+a=z\:\;and\:\:x+a=2y=2z$ . The coordinates of the points of intersections are ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The value of $f(0)$ so that $f(x)=\large\frac{(4^x-1)^3}{\sin\big(\Large\frac{x}{4}\big) \normalsize {\log}(1+\Large\frac{x^2}{3}\big)}$ is continuous everywhere is

asked Jan 6, 2014 by sreemathi.v

1 answer

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

let $\alpha$ and $\beta$ be the distinct roots of $ax^2+bx+c=0$ then $\lim\limits_{x\to \alpha}\large\frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}$ is equal to

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\large\frac{\sin(e^x-1)}{\log x}$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

Let A,B,C be three equally likely and collectively exhaustive events. If the odds 8 : 3 against A, 5:2 against B then the odds against C are

asked Jan 6, 2014 by thanvigandhi_1

1 answer

The probability of guessing correctly atleast 8 out of 10 answers on a true - false examination is :

asked Jan 6, 2014 by thanvigandhi_1

1 answer

$\lim\limits_{x\to \infty}\cos(\large\frac{x}{2})$ $\cos(\large\frac{x}{4})$ $\cos(\large\frac{x}{8})$ $........\cos(\large\frac{x}{2^n})$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

If $X$ follows a binomial distribution with parameters $n$ and $p$ . $p \lt 0 \lt 1$ If $P(X=r)/P(X=n-r)$ is independent of $n \:$ and $\: r$ , then value of p is :

asked Jan 6, 2014 by thanvigandhi_1

1 answer

Two dice are thrown, the probability that the sum of the points on the dice is 7 is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

If $\alpha,\beta$ are roots of $ax^2+bx+c=0$ then $\lim\limits_{x\to \alpha}\large\frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to a}\bigg($ $\bigg[$ $\big(\large\frac{a^{1/2}+x^{1/2}}{a^{1/4}-x^{1/4}}\big)^{-1}$ $-$ $\frac{2(ax)^{1/4}}{x^{3/4}-a^{1/4}x^{1/2}+a^{1/2}x^{1/4}-a^{3/4}}\bigg]^{-1}$ $-$ $(\sqrt 2)^{\large\log_4 a}\bigg)^8$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

A variable plane is at a distance $k$ from origin and meets the coordinate axes at the points $A,B,C$ respectively. then the locus of centroid of the $\Delta\:ABC$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

Ram shares a photo link on facebook with 3 persons and requests each of them to share with 3 more persons and continue the chain. For every share of the photo link if Rs 100 is donated to the Adyar Cancer society, what is the total amount collected by the society till the $b^{th}$ set of shares.

asked Jan 6, 2014 by yamini.v

1 answer

The equation of the plane passing through the point $(1,1,1)$ and having direction ratios $b,c,a$ $(a < b < c)$ , where $a,b,c$ are prime factors of $2001$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The set of points where the function $f(x)=\sqrt{1-e^{-x^2}}$ is differentiable is

asked Jan 6, 2014 by sreemathi.v

1 answer

Given $4$ numbers, the first $3$ numbers are in $AP$ and the last $3$ numbers are in $GP$ . The $1^{st}$ and $3^{rd}$ terms add upto $2$ and the $2^{nd}$ and $4^{th}$ terms add to $17$ . Find the numbers.

asked Jan 6, 2014 by yamini.v

1 answer

At the point $x=1$ the function $f(x)=\left\{\begin{array}{1 1}x^3-1&1 < x < \infty\\x-1&-\infty < x \leq 1\end{array}\right.$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

If $P(0,1,0)\:and\:Q(0,0,1)$ are two points in space, then the projection of $PQ$ on the plane $x+y+z=3$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $a, b, c$ are in $AP, a, x, b$ and $b, y, c$ in $GP$ , what is the progression type for $x^2,b^2,y^2$ ?

asked Jan 6, 2014 by yamini.v

1 answer

$f(x)=\left\{\begin{array}{1 1}\large\frac{1-\cos 4x}{x^2}&x < 0\\a&x=0\\\large\frac{\sqrt x}{\sqrt{[16+\sqrt x]-4}}&x > 0\end{array}\right.$ If the function be continuous at $x=0$ then $a=$

asked Jan 6, 2014 by sreemathi.v

1 answer

Find the sum of the series upto 20 term 1+(1+2)+(1+2+3)+--------

asked Jan 6, 2014 by yamini.v

1 answer

Find the sum of 8 terms of the series whose $n^{th}$ term is given by $n^2+2^n$

asked Jan 6, 2014 by yamini.v

1 answer

The function $f(x)=\left\{\begin{array}{1 1}x+a\sqrt 2\sin x&0\leq x < \large\frac{\pi}{4}\\2x\cot x+b&\large\frac{\pi}{4}\normalsize \leq x < \frac{\pi}{2}\\a\cos 2x-b\sin x&\large\frac{\pi}{2}\normalsize < x \leq \pi\end{array}\right.$ is continuous for $0 \leq x \leq \pi$ then a,b are

asked Jan 6, 2014 by sreemathi.v

1 answer

For what value of n , the $n^{th}$ term of the GPs 2560,1280,640 ----- and 10,20,40 ------ are equal.

asked Jan 6, 2014 by yamini.v

1 answer

The first term of a $GP$ is $4$ and the sum of its $3^{rd}$ and $5^{th}$ terms is $360$ . Find the common ratio.

asked Jan 6, 2014 by yamini.v

1 answer

$\lim\limits_{x\to 0}\large\frac{x(1+a\cos x)-b\sin x}{x^3}$ $=1$ then $a,b$ are

asked Jan 6, 2014 by sreemathi.v

1 answer

Find three numbers in AP whose sum is 33 and the sum of whose squares is 395

asked Jan 6, 2014 by yamini.v

1 answer

If $\lim\limits_{x\to \infty}\big(1+\large\frac{a}{x}+\frac{b}{x^2}\big)^{2x}$ $=e^2$ then the value of a and b are

asked Jan 6, 2014 by sreemathi.v

1 answer

Two cars start at a point A at the same time. The first car goes with a uniform speed of 100 Km/hr and the second car starts at 80 for the first hour and increases the speed by 10 km/hr every hour. After how much time does the second car overtake the first car, assuming these are no stops in between.

asked Jan 6, 2014 by yamini.v

1 answer

Distance of a point $P(\overrightarrow c)$ from the the line $\overrightarrow r=\overrightarrow a+\lambda \overrightarrow b$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

Let $f(a)=g(a)=k$ and their $n^{th}$ derivatives $f^{(n)}(a),g^{(n)}(a)$ exist and are not equal for some n. Further if $\lim\limits_{x\to a}\large\frac{f(a)g(x)-f(a)-g(a)f(x)+g(a)}{g(x)-f(x)}$ $=4$ then the value of K is

asked Jan 6, 2014 by sreemathi.v

1 answer

Given an AP, if the sum of first 5 terms is 175 and the sum of first 10 terms is 700, find the sum of the first 7 terms.

asked Jan 6, 2014 by yamini.v

1 answer

If $f(x)=\cot^{-1}\big[\large\frac{3x-x^3}{1-3x^2}\big]$ and $g(x)=\cos^{-1}\big[\large\frac{1-x^2}{1+x^2}\big]$ then $\lim\limits_{x\to a}\large\frac{f(x)-f(a)}{g(x)-g(a)}$ $\quad0 < a < \large\frac{1}{2}$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

If the vectors $\overrightarrow a+\lambda \overrightarrow b+3\overrightarrow c,\:-2\overrightarrow a+3\overrightarrow b-4\overrightarrow c\:and\:\overrightarrow a-3\overrightarrow b+5\overrightarrow c$ are coplanar and $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are non coplanar, then $\lambda=?$

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $\lim\limits_{x\to a}\large\frac{a^x-x^a}{x^x-a^a}$ $=-1$ and $a > 0$ then $a$ =?

asked Jan 6, 2014 by sreemathi.v

1 answer

Let $f(x+y)=f(x)f(y)$ $\forall x,y\in R$ . Suppose that $f(3)=3$ and $f'(0)=11$ , then $f'(3)$ is given by

asked Jan 6, 2014 by sreemathi.v

1 answer

If $\alpha$ is a repeated root of $ax^2+bx+c=0$ , then $\lim\limits_{x\to \alpha}\large\frac{\sin(ax^2+bx+c)}{(x-\alpha)^2}$ =

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\bigg[\large\frac{1^x+2^x+3^x+.........n^x}{n}\bigg]^{\Large\frac{1}{x}}$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

Find the sum of all natural numbers between 45 and 300 that are exactly divisible by 7.

asked Jan 5, 2014 by yamini.v

1 answer

How many 3 digit numbers leave a remainder of 2 when divided by 7 ?

asked Jan 5, 2014 by yamini.v

1 answer

How many 3 digit numbers are divisible by 5?

asked Jan 5, 2014 by yamini.v

1 answer

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