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Recent questions tagged sec-b

If $a,b,c,d$ are in G.P. then show that $(a^n+b^n),(b^n+c^n),(c^n+d^n)$ are in G.P.

asked Mar 31, 2014 by rvidyagovindarajan_1

1 answer

If $a\bigg(\large\frac{1}{b}+\frac{1}{c}\bigg)$$,\:b\bigg(\large\frac{1}{c}+\frac{1}{a}\bigg)$$,\:c\bigg(\large\frac{1}{a}+\frac{1}{b}\bigg)$ are in A.P., then prove that $a,b,c$ are in A.P.

asked Mar 31, 2014 by rvidyagovindarajan_1

1 answer

If $p^{th},\:q^{th}\:\:and\:\:r^{th}$ terms oa an A.P. are $a,\:b\:and\:c$ respectively, then show that $(q-r)a+(r-p)b+(p-q)c=0$

asked Mar 31, 2014 by rvidyagovindarajan_1

1 answer

If $\large\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}$$\:(x\neq0)$, then show that $a,b,c\:and\:d$ are in G.P.

asked Mar 30, 2014 by rvidyagovindarajan_1

1 answer

The sum of first four terms of an A.P. is $56$. The sum of last four terms is $112$. If its first term is $11$ then find the number of terms.

asked Mar 30, 2014 by rvidyagovindarajan_1

1 answer

A G.P. consists of even number of terms. If the sum of all the numbers is $5$ times the sum of terms occupying the odd places, then find the common ratio.

asked Mar 30, 2014 by rvidyagovindarajan_1

1 answer

The sum of three numbers in G.P. is $56$. If we subtract $1,7,21$ from the numbers in that order, we obtain an A.P. Find the numbers.

asked Mar 30, 2014 by rvidyagovindarajan_1

1 answer

The first term of a G.P. is $1$. The sum of third term and fifth term is $90$. Find the common ratio of the G.P.

asked Mar 30, 2014 by rvidyagovindarajan_1

1 answer

The sum of some terms of a G.P. is $315$ whose first term and the common ratio are $5$ and $2$ respectively. Find the last term and number of terms of the series.

asked Mar 30, 2014 by rvidyagovindarajan_1

1 answer

If $f$ is a function satisfying $f(x+y)=f(x).f(y)\:\:\forall x,y\in N$ such that $f(1)=3\:\:and\:\:\displaystyle\sum ^{n}_{x=1} f(x)=120$, then find the value of $n$.

asked Mar 29, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of all two digit numbers which when divided by $4$ yields $1$ as remainder.

asked Mar 29, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of all the integers from $1$ and $100$ that are divisible by $2$ or $5$.

asked Mar 29, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of all the numbers between $200$ and $400$ which are divisible by $7$.

asked Mar 28, 2014 by rvidyagovindarajan_1

1 answer

If the sum of $n,2n\:and\:3n$ terms of an A.P. are $S_1,S_2\:and\:S_3$ respectively, then show that $S_3=3(S_2-S_1)$

asked Mar 28, 2014 by rvidyagovindarajan_1

1 answer

If the sum of three numbers in A.P. is $24$ and their product is $440$, then find the numbers.

asked Mar 28, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series whose $n^{th}$ term is $(2n-1)^2$

asked Mar 27, 2014 by rvidyagovindarajan_1

1 answer

Find the value of p, so that the lines $ l_1 : \large\frac{1-x}{3} $$= \large\frac{7y-14}{p} $$= \large\frac{z-3}{2}$ and $l_2 : \large\frac{7-7x}{3p} $$= \large\frac{y-5}{1} $$ = \large\frac{6-z}{5}$ are perpendicular to each other. Also find the equations of a line passing through a point ( 3, 2, -4 ) and parallel to line $l_1$.

asked Mar 25, 2014 by thanvigandhi_1

0 answers

Find the particular solution of the differential equation $ log \bigg( \large\frac{dy}{dx} \bigg) =3x+4y,$ given that $ y=0$ when $x=0$

asked Mar 25, 2014 by thanvigandhi_1

1 answer

If $ x = \cos\: t ( 3-2 \: \cos^2 t)\: and \: y = \sin \: t ( 3-2 \sin^2\: t)$ find the value of $ \large\frac{dy}{dx} $ at $ t = \large\frac{\pi}{4}$

asked Mar 25, 2014 by thanvigandhi_1

1 answer

Using properties of determinants, prove that, \[\] $\begin{vmatrix} 1+a & 1 & 1 \\[0.3em] 1 & 1+b & 1 \\[0.3em] 1 & 1 & 1+c \end{vmatrix} = abc +bc+ca+ab$

asked Mar 25, 2014 by thanvigandhi_1

0 answers

If $ y = Pe^{ax}+Qe^{bx}$, show that \[\] $\large\frac{d^2y}{dx^2}$$-(a+b) \large\frac{dy}{dx}$$+aby=0$

asked Mar 25, 2014 by thanvigandhi_1

0 answers

An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least three successes

asked Mar 25, 2014 by thanvigandhi_1

1 answer

If $ \tan^{-1} \bigg( \large\frac{x-2}{x-4} \bigg) $$+ \tan^{-1} \bigg( \large\frac{x+2}{x+4} \bigg) $$ = \large\frac{\pi}{4}$ find the value of x.

asked Mar 25, 2014 by thanvigandhi_1

0 answers

prove that : \[\] $ \tan^{-1} \bigg[ \large\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}} \bigg]$$ = \large\frac{\pi}{4}$$- \large\frac{1}{2}$$ \cos^{-1}x , \large\frac{-1}{\sqrt 2}$$ \leq x \leq 1$

asked Mar 25, 2014 by thanvigandhi_1

0 answers

If the function $ f : R \rightarrow R $ be given by $ f(x) = x^2+2$ and $ g : R \rightarrow R $ be given by $ g(x) = \large\frac{x}{x-1} , x \neq 1$, find fog and gof and hence find fog (2) and gof (-3)

asked Mar 25, 2014 by thanvigandhi_1

0 answers

Find the equations of the tangent and normal to the curve $ \large\frac{x^2}{a^2}$$ - \large\frac{y^2}{b^2} = 1$ at the point $ ( \sqrt 2a, b)$

asked Mar 25, 2014 by thanvigandhi_1

0 answers

Find the value(s) of $x$ for which $y = [x(x-2)]^2$ is an increasing function.

asked Mar 25, 2014 by thanvigandhi_1

0 answers

Evaluate : \[\] $\int \large\frac{x+2}{\sqrt{x^2+5x+6}} dx$

asked Mar 25, 2014 by thanvigandhi_1

0 answers

Evaluate : \[\] $ \int_0^{\pi} \large\frac{4x \sin x}{1+ \cos^2x} dx$

asked Mar 25, 2014 by thanvigandhi_1

0 answers

The scalar product of the vector $ \overrightarrow a = \hat i + \hat j + \hat k$ with a unit vector along the sums of vectors $ \overrightarrow b = 2 \hat i + 4\hat j - 5 \hat k$ and $ \overrightarrow c = \lambda \hat i + 2 \hat j + 3 \hat k\;$ is equal to one. Find the value of $ \lambda $ and hence find the unit vector along $ \overrightarrow b + \overrightarrow c$

asked Mar 25, 2014 by thanvigandhi_1

1 answer

Show that the four points A, B, C and D with position vectors $ 4\hat i + 5 \hat j + \hat k, \: \: -\hat j - \hat k, \: \: 3\hat i + 9 \hat j + 4\hat k,$ and $ 4(-\hat i + \hat j + \hat k) $ respectively are coplanar.

asked Mar 25, 2014 by thanvigandhi_1

0 answers

Solve the differential equation $(1+x^2) \large\frac{dy}{dx}$$ +y = e^{ tan^{-1}}x$

asked Mar 25, 2014 by thanvigandhi_1

0 answers

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

asked Mar 24, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series whose $n^{th}$ term is given by $n(n+1)(n+4)$

asked Mar 24, 2014 by rvidyagovindarajan_1

1 answer

If $x=a\:cos\theta+b\:sin\theta$ and $y=a\:sin\theta-b\:cos\theta$, then show that $y^2.\large\frac{d^2y}{dx^2}$$-x\large\frac{dy}{dx}$$+y=0$

asked Mar 23, 2014 by rvidyagovindarajan_1

1 answer

Three cards are drawn at random (without replacement) from a well shuffled pack of 52 playing cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution.

asked Mar 23, 2014 by rvidyagovindarajan_1

1 answer

Show that $cot^{-1}7+cos^{-1}8+cot^{-1}18=cot^{-1}3$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Solve: $cos(tan^{-1}x)=sin(cot^{-1}(\large\frac{3}{4}))$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Integrate the function $(3x-2)\sqrt{x^2+x+1}$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Solve the differential equation $(x^2-yx^2)dy+(y^2+x^2y^2)dx=0$ Given $y=1$ when $x=1$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Find a unit vector perpendicular to each of the vector \( \overrightarrow a + \overrightarrow b\) and \( \overrightarrow a - \overrightarrow b\), where \( \overrightarrow a = \hat i + \hat j + \hat k\) and \( \overrightarrow b = \hat i + 2\hat j +3\hat k\)

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Evaluate: $\large \int \limits_0^1$$ x\;e^{x^2}\; dx$

asked Mar 21, 2014 by balaji

1 answer

Find the distance between the two lines $l_1$ and $l_2$ where $l_1: \overrightarrow r=(\hat i+2\hat j-4\hat k)+\lambda(2\hat i+3\hat j+6\hat k)$ and $l_2: \overrightarrow r=(3\hat i+3\hat j-5\hat k)+\mu(4\hat i+6\hat j+12\hat k)$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a^2&bc&ac+c^2 \\ a^2+ab&b^2&ac \\ ab&b^2+bc&c^2 \end{vmatrix} = 4a^2b^2c^2\]

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Find the sum of 20 terms of the series. $5^2+6^2+7^2+.....20^2$

asked Mar 12, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $1\times 2+2\times 3+3\times 4+4\times 5+.............$

asked Mar 7, 2014 by rvidyagovindarajan_1

1 answer

What will Rs. 500 amounts to in $10$ years after its deposit in a bank which pays annual interest of $10%$ compounded annually?

asked Mar 6, 2014 by rvidyagovindarajan_1

1 answer

If $a,b,c,d$ are in G.P, then show that $(a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+bc+cd)^2$

asked Mar 3, 2014 by rvidyagovindarajan_1

1 answer

Show that the ratio of the first $n$ terms of a G.P. to the sum of the terms from $(n+1)^{th}$ to $(2n)^{th}$ term is $1:r^n$

asked Mar 2, 2014 by rvidyagovindarajan_1

1 answer

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