Recent questions in Class11

If $a, b, c$ are in $GP$ and equations $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$ have a common root, then $\large\frac{d}{a}$, $\large\frac{e}{b}$, $\large\frac{f}{c}$ are in

asked Jan 24, 2014 by yamini.v

1 answer

If $\large\frac{a_{2}a_{3}}{a_{1}a_{4}}$ = $\large\frac{a_{2}+a_{3}}{a_{1}+a_{4}}$ = $3\;(\large\frac{a_{2}-a_{3}}{a_{1}-a_{4}})$, then, $a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$ are in

asked Jan 24, 2014 by yamini.v

1 answer

If $(m+n)^{th}$, $(n+1)^{th}$, $(r+1)^{th}$ term of an AP are in GP and $m, n, r$ are in HP, then ratio of first term of AP to common difference is

asked Jan 24, 2014 by yamini.v

1 answer

$a^x=b^y=c^z=d^t$ and $a, b, c, d$ are in GP, then $x, y, z, t$ are in

asked Jan 24, 2014 by yamini.v

1 answer

$ ^{\sim}(p \leftrightarrow q)$ is equivalent to

asked Jan 23, 2014 by thanvigandhi_1

1 answer

$(p \wedge\: ^{\sim}q) \wedge (^{\sim}p V q)$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

$ ^{\sim}[(p \wedge q) \rightarrow (^{\sim}p V q)]$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If p,q,r are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true, then

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If p, q, r are simple propositions with truth values T,F,T then the truth value of $ [(^{\sim}p Vq) \wedge ^{\sim}r] \Rightarrow p$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The statement $ p V q \Rightarrow \: p \wedge q$ is a

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If sides of $\bigtriangleup ABC \;(a, b, c)$ are in AP, $cot\;{\large\frac{c}{2}}$ equals

asked Jan 23, 2014 by yamini.v

1 answer

If AM and GM of two numbers are in ratio $p : q$, then the ratio of two numbers is

asked Jan 23, 2014 by yamini.v

1 answer

The contrapositive of $ (p V q) \Rightarrow r$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

Given $\large\frac{1}{1^4}+\large\frac{1}{2^4}+\large\frac{1}{3^4}$+.....$\infty$ = $\large\frac{{\pi}^{4}}{90}$, then the value of $\large\frac{1}{1^4}+\large\frac{1}{3^4}+\large\frac{1}{5^4}$+....$\infty$ is

asked Jan 23, 2014 by yamini.v

1 answer

If a,b,c are the sides of a triangle, then the statement, “$ \large\frac{1}{(b+c)},\: \large\frac{1}{(c+a)},\: \large\frac{1}{(a+b)}$ are also the sides of the triangle”, is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If $a_{1}, a_{2}, a_{3},.....$ are in HP and $f (k)$ = $\displaystyle\sum_{r=1}^{n}\;a_{r}-a_{k}$, then $\large\frac{a_{1}}{f (1)}$, $\large\frac{a_{2}}{f (2)}$, $\large\frac{a_{3}}{f (3)}$,...,$\large\frac{a_{n}}{f (n)}$ are in

asked Jan 23, 2014 by yamini.v

1 answer

A survey shows that 63% of the Americans like cheese whereas 76% like apples. The statement, “x% of Americans like both cheese and apples” is true for

asked Jan 23, 2014 by thanvigandhi_1

1 answer

$a_{1}=50$ and $a_{1}+a_{2}+....+a_{n}=n^2a_{n}$ $\forall\;n \geq 1$, value of $a_{50}$ equal to

asked Jan 23, 2014 by yamini.v

1 answer

If p : It rains today. q : I go to school. r : I shall meet my friends. s : I shall go for a movie. Then which of the following is the proportionate representation of the statement, If it does not rain or if I do not go to school, then I shall meet my friends and go for a movie.

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If 1 , 3 , 8 are first three terms of an arithmetic - geometric progression (with +ve common difference ) , the sum of next three terms is :

asked Jan 23, 2014 by yamini.v

1 answer

Consider the statement $ \log \bigg(\large\frac{5c}{a} \bigg),\: \log \bigg(\large\frac{3b}{5c} \bigg)$ and $ \log \bigg(\large\frac{a}{3b} \bigg)$ are in AP, where a,b,c are in GP. The statement is true only if a,b,c are the lengths of sides of

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The proposition $ (p \Rightarrow \: ^{\sim}p) \wedge (^{\sim}p \Rightarrow p)$ is a

asked Jan 23, 2014 by thanvigandhi_1

1 answer

Sum of n terms of the series $\large\frac{1}{4}+\large\frac{7}{16}+\large\frac{37}{64}+\large\frac{175}{256}$+... is

asked Jan 23, 2014 by yamini.v

1 answer

Which one of the following is a fallacy?

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If $ \phi(x) = f(x) + f(1-x), f’(x)<0 \: for\: 0 \leq x \leq 1$, then the tautology among the following is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

Sum of the series $\;\large\frac{2}{5}+\large\frac{3}{5^2}+\large\frac{4}{5^3}+\large\frac{2}{5^4}+\large\frac{3}{5^5}+\large\frac{4}{5^6}+...$ equals:

asked Jan 23, 2014 by yamini.v

1 answer

The proposition $ p \Rightarrow ^{\sim}(p \wedge\: ^{\sim}q)$ is

asked Jan 23, 2014 by thanvigandhi_1

1 answer

$\sqcap_{n=2}^{\infty}\;\large\frac{n^3-1}{n^3+1}$ equals

asked Jan 23, 2014 by yamini.v

1 answer

S1 : The function $f(x)=|x|$ is not one-one.\[\] S2: The negative real numbers are not the images of any real numbers. \[\] If the statement S1 holds true then,

asked Jan 23, 2014 by thanvigandhi_1

1 answer

The first two terms of a geometric progression add up to 12. The terms of the G.P. are alternately positive and negative.The statement - The sum of the third and the fourth terms is 48 holds true for the first term being

asked Jan 23, 2014 by thanvigandhi_1

1 answer

If $S_{n}=\large{1}{6}\;n(n+1)(n+2)$ $\forall\;n\;\geq\;1$, then $\displaystyle\lim_{n \to \infty}\;\displaystyle\sum_{r=1}^{n}\;\large\frac{1}{a_{r}}$ equals

asked Jan 23, 2014 by yamini.v

1 answer

Given $1^2+2^2+3^2+....+2003^2$ = $(2003)(4007)(334)$ and $(1)(2003)+(2)(2002)+(3)(2001)+....+(2003)(1)$ = $(2003)(334)(x)$ then value of $x$ is

asked Jan 23, 2014 by yamini.v

1 answer

If $a_{n}=\displaystyle\sum_{k=1}^{n}\;\large\frac{1}{k(n+1-k)}$, then for $n\;\geq\;2$

asked Jan 23, 2014 by yamini.v

1 answer

If $f_{1}=f_{2}=1$ and thereafter $f_{n+2}=f_{n+1}+f_{n}$ for all $n \in N$. Find $\displaystyle\sum_{n=2}^{\infty}\;\large\frac{1}{f_{n+1}\;.f_{n-1}}$

asked Jan 23, 2014 by yamini.v

1 answer

$S_{1}, S_{2},.....S_{n}$ are sums of infinite geometric series with first term $1,2,3,...n$ and common ratio $\large\frac{1}{2}$, $\large\frac{1}{3}$,...$\large\frac{1}{n+1}$ respectively. Find $\displaystyle\sum_{r=1}^{n}\;S_{r}$.

asked Jan 23, 2014 by yamini.v

1 answer

Find sum upto n terms: $\large\frac{3}{1^2.2^2}+\large\frac{5}{2^2.3^2}+\large\frac{7}{3^2.4^2}$+....

asked Jan 23, 2014 by yamini.v

1 answer

Find the sum of the numbers in the $n^{th}$ set: $(1)$, $(2,3)$, $(4,5,6)$, $(7,8,9,10)$.....

asked Jan 23, 2014 by yamini.v

1 answer

Find sum of first n terms of series : $\;1+\large\frac{1}{1+2}+\large\frac{1}{1+2+3}+\;....$

asked Jan 23, 2014 by yamini.v

1 answer

Evaluate sum to n terms $\;1.1+2.01+3.001+\;.....$

asked Jan 23, 2014 by yamini.v

1 answer

For an AP with first term $a$ and common difference $d$, if $\large\frac{S_{nx}}{S_{x}}\:(S_{r}$ denotes sum upto $r$ term$)$ is independent of $x$ then,

asked Jan 23, 2014 by yamini.v

1 answer

If $log\:_{5.2^{x}+1}^{2}$, $log\:_{2^{x-1}+1}^{4}$ and 1 are in HP, then

asked Jan 23, 2014 by yamini.v

1 answer

If the sum of first n terms of an AP is half the sum of next n terms, then $\large\frac{S_{4n}}{S_{n}}$ equals

asked Jan 23, 2014 by yamini.v

1 answer

Sum of the series $\;S=\large\frac{4}{7}-\large\frac{5}{7^2}+\large\frac{4}{7^3}-\large\frac{5}{7^4}+.....\;\infty\;$ is :

asked Jan 23, 2014 by yamini.v

1 answer

Given $a_{n}=\displaystyle\sum_{k=1}^{n}\;\sqrt{1+\large\frac{1}{k^2}+\large\frac{1}{(k+1)^2}}\;$ the value of $\;a_{5}\;$ is

asked Jan 23, 2014 by yamini.v

1 answer

$a,x,y,z,b$ are in AP such that $x+y+z=15$ and $a$, $\alpha$, $\beta$, $y$, $b$ are in HP such that $\large\frac{1}{\alpha}+\large\frac{1}{\beta}+\large\frac{1}{\gamma}=\large\frac{5}{3}$. Find $a$, $(a > b)$.

asked Jan 23, 2014 by yamini.v

1 answer

The sum of three terms of a strictly increasing GP is $\alpha S$ and sum of their squares is $S^{2}$. $\alpha^{2}$ lies in

asked Jan 23, 2014 by yamini.v

1 answer

Given for every $n \in N \;(1^2-a_{1})+(1^2-a_{2})+.......+(n^2-a_{n})=\large\frac{1}{3}n(n^2-1)\;the\;a_{n}$ equals

asked Jan 23, 2014 by yamini.v

1 answer

Given $\;t_{r}=1^2+2^2+.......\;r^2$ and $t_{1}+t_{2}+t_{3}+...\;t_{n}=\large\frac{k}{12}\;n\;(n+1)\;(n+2)\;$ the value of k will be

asked Jan 23, 2014 by yamini.v

1 answer

Four geometric means are inserted between $\;2^{9}-1\;and \;2^{9}+1\;.$ The product of these means is :

asked Jan 22, 2014 by yamini.v

0 answers

$p\;(x)=\large\frac{1+x^2+x^4+\;...\;x^{2n-2}}{1+x+x^2+\;...\;+x^{n-1}}\;$ is a polynomial in x , then n must be

asked Jan 22, 2014 by yamini.v

1 answer

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