Recent questions in Class11

If in an AP , $\;a_{n}\;$ denotes the $\;n^{th}$ term and $\;a_{p}=\frac{1}{q}$ and $\;a_{q}=\frac{1}{p}$ the root of the equation

asked Jan 22, 2014 by yamini.v

1 answer

Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number” and r be the statement “x is a rational number iff y is a transcendental number”. \[\] S1 : r is equivalent to either q or p \[\] S2 : r is equivalent to $ ^{\sim}(p \leftrightarrow \: ^{\sim}q)$

asked Jan 22, 2014 by thanvigandhi_1

1 answer

S1:$ ^{\sim} (p \leftrightarrow\: ^{\sim} q)$ is equivalent to $p \leftrightarrow q.$ \[\] S2 :$ ^{\sim} (p\leftrightarrow \: ^{\sim} q)$ is a tautology.

asked Jan 22, 2014 by thanvigandhi_1

1 answer

If $\;a_{1},a_{2},\;....\;a_{n}$ are in HP then $\;\large\frac{a_{1}}{a_{2}+a_{3}+\;..\;+a_{n}}\;,\large\frac{a_{2}}{a_{1}+a_{3}+...+a_{n}}\;,\large\frac{a_{3}}{a_{1}+a_{2}+a_{4}+\;...\;+a_{n}}\;,.....\;\large\frac{a_{n}}{a_{1}+a_{2}+....+a_{n-1}}\;$ are in

asked Jan 22, 2014 by yamini.v

1 answer

Given : $P(x) =x^4 + ax^3 + bx^2 + cx + d$ such that $x=0$ is the real root of $P'(x)=0$. If $P(-1) < P(1)$, then in the interval $[-1, 1]$, which of the following statement is wrong.

asked Jan 22, 2014 by thanvigandhi_1

1 answer

Let A and B denote the statements \[ \] A: $ \cos \alpha + \cos \beta + \cos \gamma = 0$ \[\] B: $ \sin \alpha + \sin \beta + \sin \gamma = 0$ \[\] If $ \cos(\beta- \alpha) + \cos( \gamma- \alpha) + \cos( \alpha - \beta)= -\large\frac{3}{2}$, then

asked Jan 22, 2014 by thanvigandhi_1

1 answer

If a , b , c are in AP and A.G are arithmetic and geometric mean , between a and b while $\;A^{|}\;and\;G^{|}$ are A.M and G.M between B and C . then

asked Jan 22, 2014 by yamini.v

1 answer

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

asked Jan 22, 2014 by thanvigandhi_1

1 answer

The inverse of the converse of a conditional statement is the _______________.

asked Jan 22, 2014 by thanvigandhi_1

1 answer

What is true about the statement "If two angles are right angles, the angles have equal measure" and its converse "If two angles have equal measure then the two angles are right angles"?

asked Jan 22, 2014 by thanvigandhi_1

1 answer

If $a , b , c$ are three numbers in GP . and $\;a+x\;,b+x\;,c+x\;$ are in HP then $x$ equals

asked Jan 22, 2014 by yamini.v

1 answer

If a , b , c , d are in HP $\;\large\frac{d^{-2}-a^{-2}}{c^{-2}-b^{-2}}\;$ equals

asked Jan 22, 2014 by yamini.v

1 answer

In a class of 50 students, 18 take music, 26 take art, and 2 take both art and music. How many students in the class are not enrolled in either music or art?

asked Jan 22, 2014 by thanvigandhi_1

1 answer

If x , y , z are in GP then , $\;\large\frac{1}{x^2-y^2}+\frac{1}{y^2}\;$ equals

asked Jan 22, 2014 by yamini.v

1 answer

For $\;n \in N \;n \geq 25$ , Let A.G.H be A.M ,G.M and H.M of 25 and n . what is the least value of n such that A.G.H are all natural numbers greater than 25 .

asked Jan 22, 2014 by yamini.v

1 answer

$\alpha$ & $\beta\;$are +ve roots of $\;x^2-2ax+ab=0\;$ then for $\;n \in N\;$$(0 \lt b \lt a)\;S_{n}=1+2(\large\frac{b}{a})$$+3(\large\frac{b}{a})^{\normalsize 2}$$+\;...+\;n$$(\large\frac{b}{a})^{n-1}\;$ can not exceed .

asked Jan 22, 2014 by yamini.v

1 answer

If a,b,c are real and $\;4a^2+9b^2+16c^2-6ab-12bc-8ac=0\;$ the a,b,c are in

asked Jan 22, 2014 by yamini.v

1 answer

$ If\;a_{1}=\frac{1}{2}\;,a_{k+1}=a_{k}^{2}+a_{k}\;\forall\;k\;\geq\;1\;and\;x_{n}=\large\frac{1}{a_{1}+1}+\large\frac{1}{a_{2}+1}+...\;\large\frac{1}{a_{n}+1}\;the \;value\;of\;[x_{50}]\;is\;([.]\;represents\;greatest\;integer\;function)$)

asked Jan 22, 2014 by yamini.v

1 answer

If $\;a_{1}=1\;,a_{n+1}=2a_{n}+1$ then , $\;a_{n+1}$ equals

asked Jan 22, 2014 by yamini.v

1 answer

Sum of n terms of series $\;S=1^2+2(2)^2+3^2+2(4)^2+5^2+\;....\;$ when n is even is :

asked Jan 22, 2014 by yamini.v

1 answer

If $\;a_{1},a_{2},a_{3}\;(a_{1}\;\geq\;0)$ are in GP with common ratio r . the value of r for which inequality $\;a_{3}\;\geq\;4a_{2}-3a_{1}$ holds is given by ,

asked Jan 22, 2014 by yamini.v

1 answer

If $\;px^2+\large\frac{q}{x}\;\geq\;r\;$ for every +ve x $\;(p>0 , q>0)\;,\;$ then $\;27pq^2\;$ can not be less than

asked Jan 22, 2014 by yamini.v

1 answer

$\;A_{1},A_{2}\;,....\;A_{n}\;$ are fixed +ve real number such that $\;A_{1}\;.A_{2}\;..\;A_{n}=k$ , then $\;A_{1}+2A_{2}+\;...\;nA_{n}$ can not be than :

asked Jan 22, 2014 by yamini.v

1 answer

If a,b,c,d are positive real number , then least value of $\;(a+b+c+d)\;(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d})\;$ is :

asked Jan 22, 2014 by yamini.v

1 answer

Ratio of sum of n terms of two AP's is $\;(5n+3)\;:\;(3n+4)\;,$ then the ratio of $\;15^{th}\;$ term will be :

asked Jan 22, 2014 by yamini.v

1 answer

Sum of first $n$ terms of an $AP$ is $kn^2$, sum of their squares will be

asked Jan 22, 2014 by yamini.v

1 answer

If $\;p=1+\frac{1}{2}+\frac{1}{3}+\;....\;+\frac{1}{n}\;$ then $\;S=\frac{1^2}{1^3}+\frac{1^2+2^2}{1^3+2^3}+\large\frac{1^2+2^2+3^2}{1^3+2^3+3^3}+\;....\;$ upto n terms equal to

asked Jan 22, 2014 by yamini.v

0 answers

If $p$ = $1$ + $\large\frac{1}{2}$ + $\large\frac{1}{3}$+....+$\large\frac{1}{n}$, then $S$ = $\large\frac{1^2}{1^3}$ + $\frac{1^2+2^2}{1^3+2^3}$ + $\large\frac{1^2+2^2+3^2}{1^3+2^3+3^3}$+.... upto $n$ terms equal to

asked Jan 22, 2014 by yamini.v

1 answer

Sum of n terms of series $(n^2-1^2)$ + $2\;.(n^2-2^2)$ + $3\;.(n^2-3^2)$+.....is

asked Jan 22, 2014 by yamini.v

1 answer

Sum of n terms of series $\;1.3.5+3.5.7+5.7.9+$.......is

asked Jan 22, 2014 by yamini.v

1 answer

Three positive numbers $p, q, r$ are in HP, $(r > p)$, then $log (p+r) + log (p-2q+r)$ is equal to

asked Jan 22, 2014 by yamini.v

1 answer

Given the following statement: All seats are hot. All belts are hot. Now, consider the claims: C1: Some seats are belts. C2: All hot are either seats or belts . Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.

asked Jan 21, 2014 by thanvigandhi_1

1 answer

Given the following statement: All doors are windows. Some windows are clips. Now, consider the claims: C1 :Some clips, if they are doors, they are also windows C2: All clips which are not widows are also not doors. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.

asked Jan 21, 2014 by thanvigandhi_1

1 answer

Given the following statement: Some paints are red. AIl red which are paints are yellow. Now, consider the claims: C1 :C1: Some paints are yellow. C2: Some yellow are red. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.

asked Jan 21, 2014 by thanvigandhi_1

0 answers

Given the following statement: Statements: No shoe is a chappal. Some chappals are sandals. Now, consider the claims: C1: Some sandals are not chappals.. C2: Sandals which are not chappals are shoes. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.

asked Jan 21, 2014 by thanvigandhi_1

1 answer

Given the following statement: All doors are windows. Some windows are dips. Now, consider the claims: C1: Some clips are doors. C2: Some windows are doors. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.

asked Jan 21, 2014 by thanvigandhi_1

0 answers

The ratio of the coefficient of $x^{10}$ in $(1-x^2)^{10}$ and the term independent of $x$ in $(x-\large\frac{2}{x}$$)^{10}$ is ?

asked Jan 21, 2014 by rvidyagovindarajan_1

1 answer

$ \displaystyle\sum_ {i=o} ^{{m} ^{10}} C_i ^{20}C_{m-i}$ is maximum when $m=?$

asked Jan 21, 2014 by rvidyagovindarajan_1

1 answer

If $A,B,C$ are three points on $x\:axis,\:y\:axis\:and\:z\:axis$ respectively which are at the distances $a,b,c$ from origin respectively and $P$ is a point which is equidistant from $A,B,C,O$ then the coordinates of $P$ is?

asked Jan 21, 2014 by rvidyagovindarajan_1

1 answer

Which of the following is not a false statement?

asked Jan 21, 2014 by thanvigandhi_1

1 answer

Which of the following is a true statement?

asked Jan 21, 2014 by thanvigandhi_1

1 answer

Find $\frac{1}{3}+\frac{1}{15}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}$ +....upto n terms

asked Jan 21, 2014 by yamini.v

1 answer

Let A={2,3,5,7}. For which of the sets, truth value is true?

asked Jan 21, 2014 by thanvigandhi_1

1 answer

If $1$, $log_{b}^{a}$, $log_{c}^{b}$, $-15\;log_{a}^{c}$ are in AP, then

asked Jan 21, 2014 by yamini.v

1 answer

$p, q, r$ are three unequal numbers in AP. If $q-p$, $r-q$ and $p$ are in GP, the $p\;:\;q\;:\;r$ equals

asked Jan 21, 2014 by yamini.v

1 answer

For an AP with first term a and sum of first m terms 0, the sum of next n terms will be

asked Jan 21, 2014 by yamini.v

1 answer

If p, q, r are in increasing AP, then common difference will be

asked Jan 21, 2014 by yamini.v

1 answer

If the numbers $a, b, c, d, e$ are in AP, the value of $a-4b+6c-4d+e$ is

asked Jan 21, 2014 by yamini.v

1 answer

Sum of 20 terms of the series 1+2+3+4+5+8+7+16+9+....... is

asked Jan 21, 2014 by yamini.v

1 answer

The sum $1+\frac{3}{x}+\frac{9}{x^2}+\frac{27}{x^3}+....\infty$, ($x\neq\;0$) is finite if

asked Jan 21, 2014 by yamini.v

1 answer

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