Answers posted by yamini.v

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Find n such that is $\large\frac{512}{729}\;$is the nth term of the GP 18,-12,8,-----------------

answered Jan 1, 2014

Answer : (d) 9Explanation :$ a=18 , r=\large\frac{-12}{18}=\large\frac{-2}{3}$$T_{n}=ar^{n-1}\qquad...

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Find n where 1536 is the nth term of the series 3,6,12---------------

answered Jan 1, 2014

Answer : (d) 10Explanation : 3,6,12---------is a GP where$a=3\;,r=\frac{6}{3}=\frac{12}{6}=2$$T_{n}=...

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What are next two terms of the GP $\sqrt{2},\;1/\sqrt{2},\;1/2\sqrt{2}$

answered Jan 1, 2014

Answer : $\frac{1}{4\sqrt{2}},\frac{1}{8\sqrt{2}}$Explanation : $r=\frac{T_{n}}{T_{n-1}}=\frac{1/\sq...

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If both the roots of the quadratic equation $(b-c)x^2+(c-a)x+(a-b)=0$ are equal. Then $a, b, c$ are in

answered Dec 31, 2013

Answer : (a) APExplanation : since both roots are equal,In a quadratic equation of type $lx^2+mx+n=0...

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If $a^2,b^2,c^2\;$ are in AP ,$\frac{1}{b+c},\frac{1}{a+c},\frac{1}{b+a}\;$ are in

answered Dec 31, 2013

Answer : (a) APExplanation : $check\;if\;\frac{1}{b+c},\frac{1}{a+c},\frac{1}{b+a} \;are\;in\;AP$$\f...

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The sum of terms of a series is $\frac{2^n-1}{3}$.What is the type of series AP or GP. What is the value of d or r (common difference of AP or common ratio of GP)

answered Dec 31, 2013

Answer : (b) GP ,r=2Explanation :$S_{n}=\frac{2^n-1}{3}\qquad\;S_{n-1}=\frac{2^(n-1)-1}{3}$$T_{n}=S_...

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Find the sum of series 4 + 44 + 444 + 4444 +------upto n terms.

answered Dec 31, 2013

Answer : (b) $\frac{4}{9}[\frac{10(10^n-1)}{9}-n]$Explanation: S=4+44+444+-------n terms$=4(1+11+11...

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In a GP, the ratio of the sum of first 3 terms to the sum of first 6 terms is 125/152. Find the common of the GP.

answered Dec 31, 2013

Answer : (c) 3/5$Explanation : S_{n}=a\;\frac{r^n-1}{r-1}\;in\;GP$$Given \;that $$\frac{S_{3}}{S_{6...

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The product of 3 numbers in a GP is 64 and the sum of product of numbers taken in pairs is 56. Find the three numbers in GP.

answered Dec 31, 2013

Answer : (c) $ both\;a\;\xi\;b$Explanation : Let the 3 numbers in GP be a/r, a, ar$a/r*a*ar=64\;\qq...

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If 4 positive numbers a, b, c and d are in HP, which of the following is true.

answered Dec 31, 2013

Answer : (c) $both\;(a)\;\xi\;(b)$Explanation: with any two numbers their AM >HMSince a,b,c,d are...

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Given that $\frac{S_{1}}{S_{2}}=\frac{3n+8}{7n+5}$, $\frac{S_{1}}{S_{2}}$ is the ratio of sum of two APs to n terms, find the ratio of the 11^th terms of the two APs.

answered Dec 31, 2013

Answer : (b) 71/152Explanation : $\frac{S_{1}}{S_{2}}=\frac{3n+8}{7n+5}$ $\frac{S_{1}}{S_{2}}=\frac{...

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Find the sum of the series -1 + 4 - 9 + 16 - 25 +-----+ 4008004.

answered Dec 31, 2013

Answer: (d) 4010006Explanation : The series can be written as $\;((-1)^2+2^2)-3^2+4^2--------+2002^2...

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Find the sum of the series $1^2$ - $2^2$ + $3^2$ - $4^2$ + $5^2$ - $6^2$.....$1000^2$.

answered Dec 31, 2013

Answer : (d) -500500Explanation : $S_{n}=1^2-2^2+3^2-4^2--------------------1000^2$$S_{n}=(1^2-2^2)+...

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In an AP, the sum of n terms is $n^2+1$. Find the 16th term.

answered Dec 30, 2013

Answer : (d) 31Explanation : In an AP$T_{n}=S_{n}-S_{n-1}\qquad\;S_{n}=n^2+1$$T_{n}=n^2+1-[(n-1)^2+1...

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In an AP, the sum of n terms is a function of n, $S_{n}=3n^2+2n.$ Find the rth term.

answered Dec 30, 2013

Answer : (b) 6r-1Explanation : $S_{n}=3n^2+2n$$For\; n=1\qquad\;S_{1}=3+2=5$$For\; n=2\qquad\;S_{2}...

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In a series -9,-6,-3,----, find the number of terms n to get a sum $S_{n}$ = 66.

answered Dec 30, 2013

Answer : (b) 11Explanation: Observe the series -9,,-6,-3-------It is an AP with a=-9 ,d=+3In an A...

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If the 7th term of an AP is 23 and the 12th term is 38, find the first term 'a' and common difference 'd'.

answered Dec 30, 2013

Answer :$ (b) a=5,\;d=3$$Explanation : T_{n}\; of\; AP=a+(n-1)d$$T_{7}=a+6d=23\qquad(1)$$T_{17}=a+11...

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Find the sum of the series 1, $\frac {7}{5}$, $\frac {13}{25}$, $\frac {19}{25}$,----,$\infty$.

answered Dec 30, 2013

Answer: (c) 25/8Explanation:$Let S=1+7/5+13/25+19/125--------\infty$Divide by 5S/5=1/5+7/25+13/125+-...

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Given that four positive numbers are in HP, which of the following is true.

answered Dec 30, 2013

Answer: (c) ad>bcExplanation :Sinc a,b,c,d are in HP$HM of a\;\xi\;c\; is\; b$$HM of b\;\xi\;d\;i...

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Among 5 numbers a, b, c, d and e the relationships are: a, b, c are in AP and b, c, d are in GP and c, d, e are in HP. Find b, c, d if a = 2 and e = 18.

answered Dec 30, 2013

Toolbox:Answer : (a) 4,6,9since a,b,c in AP$b=\frac{a+c}{2}=\frac{2+c}{2}\qquad(a=2)$c,d,e are in H...

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Among 5 numbers a, b, c, d and e the relationships are: a, b, c are in AP and b, c, d are in GP and c, d, e are in HP. Find b, c, d if a = 2 and e = 18.

answered Dec 30, 2013

Toolbox:Answer : (a) 4,6,9since a,b,c in AP$b=\frac{a+c}{2}=\frac{2+c}{2}\qquad(a=2)$c,d,e are in H...

0 votes

In a GP, the first term is $312\large\frac{1}{2}$, the common ratio is $\large\frac{1}{2}$. Find the sum of the series to $\infty$ terms.

answered Dec 30, 2013

answer is 625Hint:$ S_\infty=\large\frac{a}{1-r}$Answer: In a GP,$S _\infty=\large\frac{a}{1-r}$a=${...

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Find the area under the given curves and given lines: $ (ii)\:y = x^4, x = 1, x = 5 \: and\: x - axis$

answered Dec 23, 2013

Toolbox:Area of a region bounded by the curve $y=f(x)$,$x$-axis and the lines $x=a,x=b$ is given by ...

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Find the area of the smaller region bounded by the ellipse $ \frac{\large x^2}{\large 9} + \frac{\large y^2}{\large 4} =1$ and the line $ \frac{\large x}{\large 3}+ \frac{\large y}{\large 2}= 1$

answered Dec 21, 2013

Hence the required area is the area enclosed between the straight line and the ellipse. To find...

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Choose the correct answer in the the area bounded by the $y$ - axis, $y = \cos\: x$ and $y = \sin\: x$ when $0 \leq x \leq \frac{\large \pi}{2}$ is

answered Dec 21, 2013

Toolbox:Suppose we are given two curves represented by Y=f(x);y=g(x) where $f(x)\geq g(x)$ in [a,b] ...

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Find the area bounded by the curve $(y = \sin\; x) $ between $ (x = 0) $ and $(x = 2π).$

answered Dec 21, 2013

The required area ishttps://clay6.com/mpaimg/test27.png A=area of OAB+area of BCD$\;\;=\display...

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Choose the correct answer in the area bounded by the curve $ y = x^3$, the $x$ - axis and the ordinates $x = -2$ and $x = 1$ is

answered Dec 21, 2013

Toolbox: Whenever we consider areas on both the negative and positive side of the axes,we can sum...

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Find the area of the region lying in the first quadrant and bounded by $y = 4x^2, x = 0, y = 1$ and $y = 4$.

answered Dec 21, 2013

Toolbox: Clearly the shaded region is the region lying in the first quadrant and bounded by $y=4x^...

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Find the area under the given curves and given lines: $ (i) \: y = x^2, x = 1, x = 2 \: and\: x - axis$

answered Dec 21, 2013

Toolbox:Area of a region bounded by the curve $y=f(x)$,$x$-axis and the lines $x=a,x=b$ is given by ...

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Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).

answered Dec 21, 2013

Toolbox: Suppose three lines intersect at three different points the enclosed area will be the ar...

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Find the area between the curves $y = x$ and $y = x^2.$

answered Dec 21, 2013

Given two curves f(x)=x and g(x)=$x^2$.https://clay6.com/mpaimg/test22.png To find the limits,l...

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Using the method of integration find the area of the region bounded by lines: $2x + y = 4, 3x - 2y = 6$ and $x - 3y + 5 = 0$

answered Dec 21, 2013

Toolbox: Suppose three lines intersect at three different points,the enclosed area will be the ar...

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Find the area enclosed by the parabola $4y = 3x^2$ and the line $2y = 3x + 12.$

answered Dec 21, 2013

Given f(x) is 2y=3x+12$\Rightarrow y=\frac{3x+12}{2}$-----(1) and g(x) is 4y=3x^2$\Rightarrow y...

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Find the area of the smaller region bounded by the ellipse $\Large { \frac{ x^2}{ a^2}}+\Large { \frac{ y^2}{ b^2}} =\normalsize 1$ and the line $\Large { \frac{ x}{ a}}+\Large { \frac{y}{ b}} =\normalsize1$

answered Dec 21, 2013

The area of the smaller region bounded by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$and the...

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Choose the correct answer in the smaller area enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is \[ \begin{array}{1} (A)\;2(\pi - 2) \qquad & (B)\;\pi - 2 \qquad &(C)\;2\pi - 1 \qquad & (D)\;2 ( \pi + 2) \end{array} \]

answered Dec 21, 2013

Toolbox: If we are given two or more curves represented by y=f(x) and y=g(x),where $f(x)\geq g(x)...

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Find the area of the circle $4x^2 + 4y^2 = 9$ which is interior to the parabola $x^2 = 4y$.

answered Dec 21, 2013

Toolbox: If we are given two curves represented by y=f(x),y=g(x) where $f(x)\geq g(x)$ in [a,b],t...

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Using integration find the area of region bounded by the triangle whose vertices are $(-1, 0), (1, 3) $ and $(3, 2)$.

answered Dec 21, 2013

<div class="clay6-toolbox"><b>Toolbox:</b><ul><li class="clay6-basic" i...

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Find the area bounded by curves $(x - 1)^2 + y^2 = 1$ and $x^2 + y^2 = 1$.

answered Dec 21, 2013

Toolbox: If we are given two curves represented by y=f(x);y=g(x),where $f(x)\geq g(x)$ in [a,b],t...

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Find the area of the region bounded by the curves $y = x^2 + 2, y = x, \: x = 0$ and $x = 3.$

answered Dec 21, 2013

Toolbox: If we are given two curves represented by y=f(x);y=g(x),where $f(x)\geq g(x)$ in [a,b],t...

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Using integration find the area of the triangular region whose sides have the equations $y = 2x + 1, y = 3x + 1$ and $x = 4.$

answered Dec 21, 2013

Toolbox: If we are given two or more curves represented by y=f(x) and y=g(x),where $f(x)\geq g(x)...

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Choose the correct answer in the area lying between the curves $y^2 = 4x$ and $y = 2x$ is

answered Dec 21, 2013

Toolbox: If we are given two curves represented by y=f(x) and y=g(x),where $f(x)\geq g(x)$ in [a,...

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Choose the correct answer in the area of the region bounded by the curve $y^2 = 4x,\; y$ - axis and the line $y = 3$ is

answered Dec 20, 2013

Toolbox: The area bounded by the curve g(y),y axis and the ordinate y=c,y=d is given by,\[A=\int_...

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Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x$ - axis.

answered Dec 20, 2013

Toolbox: To find the area bounded by the curve y=f(x),x-axis and the ordinates x=a and x=b,then t...

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Choose the correct answer in area lying in the first quadrant and bounded by the circle $x^2 + y^2 = 4 $ and the lines $x = 0$ and $x = 2$ is

answered Dec 20, 2013

Toolbox:The area bounded by the curve f(x),x-axis and the ordinate x=a,x=b is given by\[A=\int_a^by\...

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Find the area of the region bounded by $y^2 = 9x,\; x = 2,\; x = 4$ and the $x$ - axis in the first quadrant.

answered Dec 20, 2013

Toolbox: To find the area bounded by the curve y=f(x),x-axis and the ordinate x=a,x=b then the re...

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Find the area of the region in the first quadrant enclosed by $x$ - axis, line $x = \sqrt {3}\: y$ and the circle $x^2 + y^2 = 4$.

answered Dec 20, 2013

Toolbox: Area of the region bounded between a curve y=f(x) and a line is given by \[A=\int_a^by\;...

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Find the area of the region bounded by the curve $y^2 = 4x$ and the line $x = 3$.

answered Dec 20, 2013

Toolbox: If we are given two curves represented by y=f(x),y=g(x),where $f(x)\geq g(x)$ in [a,b],t...

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Find the area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$.

answered Dec 20, 2013

Toolbox: If we are given two curves represented by y=f(x),y=g(x),where $f(x)\geq g(x)$ in [a,b],t...

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Find the area of the smaller part of the circle $x^2 + y^2 = a^2$ cut off by the line $x =\Large { \frac{a}{\sqrt 2}}$.

answered Dec 20, 2013

Toolbox: Area of the region bounded between a curve and a line is given by \[A=\int_a^by\;dx=\int...

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Find the area of the region bounded by the ellipse $\frac{\Large x^2}{\Large 4 } + \frac{\Large y^2}{\Large 9} = 1$

answered Dec 20, 2013

Toolbox:Area of the region bounded by the ellipse is 4 times the area bounded by it in the first qua...

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