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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.
answered Jan 6, 2014
Answer : (b) 5 hours$Explanation\;:\;Let\;number\;of\;hours\;be\;n\;distance\;covered\;by\;1^{st}\...
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Given an AP, if the sum of first 5 terms is 175 and the sum of first 10 terms is 700, find the sum of the first 7 terms.
answered Jan 6, 2014
Answer : (c) 343$Explanation :\;S_{n}=\frac{n}{2}\;[2a+(n-1)d ]$$S_{5}=\frac{5}{2}\;[2a+4d]=175$$...
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Find the sum of all natural numbers between 45 and 300 that are exactly divisible by 7.
answered Jan 5, 2014
Answer : (b) 6174Explanation : $1^{st}\;term\;greater\;than\;or\;equal\;to\;45\;that\;is\;divisibl...
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How many 3 digit numbers leave a remainder of 2 when divided by 7 ?
answered Jan 5, 2014
Answer : (d) 129 Explanation : 3 digit numbers are between 100 and 999. First 3 digit number to...
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How many 3 digit numbers are divisible by 5?
answered Jan 5, 2014
Answer : (d) 180Explanation : $1^\;{st}\;3\;digit\;no\;divisible\;by\;5\;=>\;100$$Last\;3\;digit...
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How many two digit numbers are divisible by 4?
answered Jan 5, 2014
Answer : (c) 22Explanation : 2 digit numbers 10 to 99 first 2 digit number divisible by 4 is 12...
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Which term of the sequence 130,126,122----- is the first negative term.
answered Jan 5, 2014
Answer : (c) -2Explanation : $t_{n}=130-4(n-1)\;<\;0$$130\;<\;4(n-1)$$\frac{65}{2}\;<\;n-...
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Find the value of $n$ such that the $n^{th}$ term of the sequences 27,24,21------- and 2,4,6----- are equal.
answered Jan 5, 2014
Answer : (b) n=6Explanation : $a_{1}=27\;,d_{1}=-3\;,t_{n}=27-3(n-1)$$a_{2}=2\;,d_{2}=2\;,t_{n}...
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The $n^{th}$ term of a progression is $2n+3$. What is the type of progression and what is its $15^{th}$ term.
answered Jan 5, 2014
Answer : (d) AP,33Explanation : $T_{n}=2n+3$$T_{n-1}=2(n-1)+3=2n-2+3$$d=T_{n}-T_{n-1}=2n+3-2n-1=2$...
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For what value of n is $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ the GM of 4 and 16.
answered Jan 3, 2014
Answer : (c) $\frac{-1}{2}$Explanation : $\frac{4^{n+1}+16^{n+1}}{4^n+16^n}=\sqrt{4*16}=\sqrt{64}=8...
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Find the value of n such that $\frac{5^{(n+1)}+17^{(n+1)}}{5^n+17^n}$ is the AM of 5 and 17
answered Jan 3, 2014
Answer : (c) n=0Explanation : AM of 5 and 17 is $\frac{5+17}{2}=\frac{22}{2}=11$$\frac{5^{n+1}+17^...
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Given that $a\;\xi\;b$ are not equal , find the value of n so that $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the GM of $a\;\xi\;b$
answered Jan 3, 2014
Answer : (d) $n=\frac{-1}{2}$$Explanation :\; Since\quad\;\frac{a^n+1+b^n+1}{a^n+b^n}\;is\;the\;GM\...
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If n arithmetic means are interested between $0$ and $32$ such that the $2^{nd}$ mean is one-seventh of the $(n-1)^{th}$ mean, find the value of $n$.
answered Jan 3, 2014
Answer : (c) 15$Explanation \; : \;n\;AMs\;between\;0\;\xi\;32 $$2^{nd}\;mean=a+2d$$=0+2d=2d$$(n-1)...
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Insert k arithmetic means between 1 and $k^2$ . what is the resulting series?
answered Jan 3, 2014
Answer : (c) $1,k,2k-1,3k-2\;-------\;k^2-k+1,k^2$Explanation : k arithmetic means between $\;1...
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In the series 2,10,50 ------ the number of terms required to make a sum of 7812 is
answered Jan 3, 2014
Answer : (b) 6Explanation : 2,10,50 ------ is a with a=2 , r=5$S_{n}=\frac{a(r^n-1)}{r-1}=\frac{...
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Which term of the series $\frac{16}{9}$, $\frac{4}{3}$, $1$, $\frac{3}{4}$------is $\frac{243}{1024}$
answered Jan 3, 2014
Answer : (b) $7^{th}$Explanation : The series is a GP with $a=16/9\;,r=3/4$$ar^n=\large\frac{243...
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The angles of a quadrilateral are in AP whose common difference is $10^0$. Find the angles.
answered Jan 3, 2014
Answer : (d) 75,85,95,105$Explanation :\; Let\;the\;4\;angles\;be\;a,a+d,a+2d,a+3d $$a+a+10+a+20+a+...
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Divide 44 into 4 parts following an AP such that the ratio of the product of extremes to the product of the means is 5:14.
answered Jan 3, 2014
Answer : (d) 2,8,14,20Explanation : Let the 4 terms in AP = $a-3d\;,a-d\;,a+d\;,a+3d$$sum=44$$a+3d...
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If the $3^{rd}$ term of a GP is 18 and the $10^{th}$ term is 39366 , find the $7^{th}$ term of the GP.
answered Jan 3, 2014
Answer : (d) 1458Explanation : $T_{3}=ar^2=18$$T_{10}=ar^9=39366$$\frac{T_{10}}{T_{3}}=\frac{ar^9}...
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Find the sum of the series 1.4 + 2.5 + 3.6----- upto 20 terms.
answered Jan 3, 2014
Answer : (d) 3500$Explanation : \;T_{n}=n(n+3)$$=n^2+3n$$S_{n}=\sum\;T_{n}=\sum\;n^2+3\;.\sum\;n$$=...
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Find the sum of the series $3^2$ + $5^2$ + $7^2$ +-----upto 10 terms
answered Jan 3, 2014
Answer : (c) 1770Explanation : $T_{n}=(2n+1)^2$$\sum\;T_{n}=(2n+1)^2$$=\sum\;(4n^2+4n+1)$$S_{n}=\...
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If $\large\frac{1}{x+y}$, $\large\frac{1}{xy}$, $\large\frac{1}{y+z}$ are in AP, $x, y, z$ are in
answered Jan 3, 2014
Answer : (b) GPExplanation : $\;\large\frac{1}{x+y}\;,\;\large\frac{1}{xy}\;,\;\large\frac{1}{y+z...
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The sum of three numbers in GP is 26. If 2,2,-6 are added to them respectively they form as.n AP . Find the number
answered Jan 3, 2014
Answer : (b) 18,6,2$Explanation \;:\; Let\;the\;three\;numbers\;in\;GP\;be\;a\;,ar\;,ar^2$$a+ar+a...
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The product of $3$ numbers in $GP$ is $1000$. If $6$ and $7$ are added to the $2^{nd}$ and $3^{rd}$ terms respectively, the terms form an $AP.$ Find the $GP$.
answered Jan 3, 2014
Answer : (c) 5,10,20$Explanation : \;Let\;the\;3\;numbers\;be\;\frac{a}{r},a,ar.$$\frac{a}{r}*a*ar=...
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Find the sum of n terms of the series 2.4 + 5.6 + 8.8 + 11.10 +---------
answered Jan 3, 2014
Answer : (c) $ n(2n^2+5n+1) $Explanation : $T_{n}=(3n-1)(2n+2)$$=6n^2+6n-2n-2=6n^2+4n-2$$S_{n}=\su...
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Find the sum of n terms of the series 1.5+3.8+5.11+---------------n
answered Jan 3, 2014
Answer : (c) $\frac{4n^3+7n^2-n}{2}$Explanation : $T_{n}=(2n-1)(3n+2)$$S_{n}=\sum\;T_{n}=\sum\;[6n...
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Find the sum of n terms of the series 2.4+5.7+8.10+------------
answered Jan 3, 2014
Answer : (d) $ \frac{n}{2}\;(6n^2+9n+1)$Explanation : 2.4 +5.7 +8.10 +-------------$T_{n}=(3n-1)(3n+...
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If a, b, c, d are in GP, what is the progression of $a^n + b^n$, $b^n + c^n$, $c^n + d^n$.
answered Jan 3, 2014
Answer : (c) GP$Explanation\;:To\;check\;if\;it\;is\;in\;GP-$$a=a\;,b=ar\;,c=ar^2\;,d=ar^3$$if\;a^n...
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If a, b, c are in GP, find the value of $a^2b^2c^2(\large\frac{1}{a^3}+\large\frac{1}{b^3}+\large\frac{1}{c^3})$
answered Jan 3, 2014
Answer : $(d)\;a^3+b^3+c^3$Explanation : a,b,c are in GP $ \;b^2=ac$$a^2b^2c^2\;(\large\frac{1}{a^3}...
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Find 3 Geometric means between $\large\frac{1}{3}$ and 432.
answered Jan 3, 2014
Answer : (d) 2,12,72Explanation : $\large\frac{1}{3},\large\frac{r}{3},\large\frac{r^2}{3},\large\f...
0 votes
Insert two geometric means between 4 and 256 .
answered Jan 3, 2014
Answer : (d) 16,64Explanation : $4,g_{1},g_{2},256\; are\;in\;GP$$4,4r,4r^2,256.$$4\;.r^3=256$$r^3=\...
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If $a, b, c$----$l$ is a GP, find the sum of the series.
answered Jan 3, 2014
Answer : (d) $\large\frac{bl-a^2}{b-a}$$Explanation :\;r=\large\frac{b}{a}\quad\;l=a\;(b/a)^{n-1} $...
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How many terms of the series $6, 3, \large\frac{3}{2}$------ will make a sum of $\large\frac{765}{64}$.
answered Jan 2, 2014
Answer : (b) 8Explanation : In a GP$S_{n}=\large\frac{a(r^n-1)}{r-1}\quad\;a=6,r=\large\frac{1}{2}$$...
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How many terms of the series $\sqrt2$, 2, $2\sqrt2$,------- will make a sum of $62+31\sqrt2$ ?
answered Jan 2, 2014
Answer : (c) 10Explanation : $\sqrt2,2,2\sqrt2$ is a GP with $a\sqrt2\quad\;r=\sqrt2$$S_{n}=\larg...
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If the sum of n terms of the AP 55, 57, 59------ is equal to the sum of first 2n terms of the AP 1, 4, 710--------then n equals
answered Jan 2, 2014
Answer : (c) 11Explanation : Sum of 2n terms of AP 1,4,7----$=\large\frac{2n}{2}\;[2*1+(2n-1)3]$$=...
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What is the harmonic mean of the two roots of the following equation $(5+\sqrt2)x^2-(4+\sqrt5)x+8+2\sqrt5=0$
answered Jan 2, 2014
Answer : (b) 4$Explanation: Let\;the\;two\;roots\;of\;the\;quadratic\;equation\;be\;\alpha\;\xi\;\b...
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In an AP of 10 numbers and a HP of 10 numbers, the first term and last term are the same and equal to 2 and 3. Find the value of product of fourth term of the AP and the seventh term of the HP.
answered Jan 2, 2014
Answer : (d) 6Explanation : Let the AP = $a_{1},a_{2},a_{3}--------a_{10}$$HP\;=h_{1},h_{2},h_{3}--...
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The third term of a GP is 2. Calculate the product of the first 5 terms.
answered Jan 2, 2014
Answer : (c) 32Explanation : Let terms of GP= $a,ar,ar^2,ar^3,ar^4$$ar^2=2$$product \;of\; 5 terms\q...
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If the p and q are roots of the equation $x^2-7x+A=0\;\xi\;r\;\xi\;s$ are roots of equation $x^2-19x+B=0,$ find the values of $A\;\xi\;B$ if p,q,r,s are in AP.
answered Jan 2, 2014
Answer : (d) A=10 , B=88 Explanation : Equations $\;x^2-7x+A=0\qquad\;x^2-19x+B=0$ $p+q...
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The sum of integers from 1 to 200 that are divisible by 2 or 5 is
answered Jan 2, 2014
Answer : (d) 12100Explanation : Integers divisible by 2 are {2,4,6----------200}$sum S_{1}=2(1+2+3+-...
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If $a, b, c$ are in $AP$ and $a^2,b^2,c^2$ are in $HP$, how are $a, b$ and $\large\frac{-c}{2}$ related?
answered Jan 2, 2014
Answer : (d) $a,b,\frac{-c}{2}\;are\;in\;GP$Explanation :$a,b,c\;are\;in\;AP$$2b=a+c$. Squaring, you...
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If the $ i^{th},j^{th}\; and\; k^{th} $ term of an AP and a GP are equal and are $x,y,z$ find the value of $x^{(y-z)}\;.y^{(z-x)}\;.z^{(x-y)}$
answered Jan 2, 2014
Answer : (c) 1Explanation : $x=a+(i-1)d=b\;r^{i-1}$$y=a+(j-1)d=b\;r^{j-1}$$z=a+(k-1)d=b\;r^{k-1}$$x-...
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If a$\xi\;b$ are two positive integers,x is their AM and $y\;\xi\;z$ are two GMs then calculate the value of $\frac{y^3+z^3}{xyz}$
answered Jan 2, 2014
Answer : (b) 2Explanation : $x=\frac{a+b}{2}\quad\;a,y,z,b\;are\;in\;GP\quad\;b=ar^3\;\quad\;r=(b/a)...
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If the harmonic mean H and geometric mean G of two positive numbers a and b are in ratio 3:5, then a and b are in the ratio
answered Jan 2, 2014
Answer : (a) 1:9Explanation :$ H=\large\frac{2ab}{a+b}$$G=\sqrt{a}{b}$$\frac{H}{G}=\large\frac{2ab/...
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In a triangle $\bigtriangleup ABC$,a,b,c are its sides ,A,B $\xi\;$ C are its angles, if $\cot A,\cot B\;\xi\;\cot C$ are in AP , the a,b, and c are in which progression?
answered Jan 2, 2014
Answer : (a) APExplanation : $\cot A,\cot B \;\xi\;\cot C$ are in AP$2 \cot B=\cot A+\cot C$$2\sqrt...
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An infinite GP has its first term as x and sum is 6 , then which of the following is true?
answered Jan 2, 2014
Answer : (c) 0 < x < 12Explanation : $S_{\infty}\;of\;a\;GP$ $S_{\infty}=\frac{a}{1-r}$$6=\fr...
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If 5, x, y, z, 1280 are in GP, what are the values of x, y, z.
answered Jan 2, 2014
Answer : $(b) \pm20,80,\pm320$Explanation : $In \;a\; GP ,a=5$$ar^4=1280\qquad\;r^4=\large\frac{1280...
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If the $4^{th}$ term of a GP is the square of its second term and the first term is -2. Find the $7^{th}$ term of the GP.
answered Jan 2, 2014
Answer : (d) -128Explanation : $Given\;T_{4}=T_{2}^2$$ar^3=a^2r^2$$a=-2$$r=a$$r=-2$$T_{7}=ar^6=(-2)(...
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Given that a,b$\xi$ c are in AP,which of the following is true?
answered Jan 2, 2014
Answer : (c) $ (a-c)^2=4(b^2-ac)$Explanation : Given a,b,c are in AP$2b=a+c$$(a+c)^2=(2b)^2$$a^2+c^2...
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Find 3 numbers in AP whose sum is 18 and the sum of its cube is 972.
answered Jan 1, 2014
Answer : (c) 3,6,9Explanation : Let the three numbers in AP be a-d,a,a+d$a-d+a+a+d=18$$3a=18$$a=6$$m...
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