Recent questions tagged sec-b

If the first and $n^{th}$ term of a G.P. are $a$ and $b$ respectively and if $P$ is the product of the $n$ terms then prove that $P^2=(ab)^n$

asked Mar 2, 2014 by rvidyagovindarajan_1

1 answer

If the $p^{th},q^{th}\:\:and\:\:r^{th}$ terms of G.P.are $a,b\:\:and\:\:c$ respectively then prove that $a^{q-r}.b^{r-p}.c^{p-q}=1$

asked Mar 1, 2014 by rvidyagovindarajan_1

1 answer

Find the four numbers forming a G.P. in which the $3^{rd}$ term is greater than the $1^{st}$ term by $9$ and the $2^{nd}$ term is greater than the $4^{th}$ term by $18$.

asked Mar 1, 2014 by rvidyagovindarajan_1

1 answer

Find the sum to $n$ terms of the sequence $8,88,888,.............$

asked Feb 27, 2014 by rvidyagovindarajan_1

1 answer

If the $4^{th},10^{th}\:\;and\:\:16^{th}$ terms of a G.P. are $x,y\:\;and\:\:z$ respectively. Prove that $x,y,z$ are in G.P.

asked Feb 27, 2014 by rvidyagovindarajan_1

1 answer

Find the G.P. the sum of whose first two terms is $-4$ and the $5^{th}$ term is $4$ times the $3^{rd}$ term.

asked Feb 27, 2014 by rvidyagovindarajan_1

1 answer

The sum of first three terms of a G.P. is $16$ and the sum of next three terms is $128$. Find the $1^{st}$ term, common ratio and the sum of $n$ terms of the G.P.

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

The sum of first $3$ terms of a G.P is $\large\frac{39}{10}$ and their product is $1$. Find the common ratio and the terms of the G.P.

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

Evaluate $\sum\limits_{k=1}^{11} (2+3^k)$

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

The difference between any two consecutive interior angles of a polygon is $5^\circ$. If the smallest angle is $120^ \circ$, then find the number of sides of the polygon.

asked Feb 24, 2014 by rvidyagovindarajan_1

1 answer

Between $1\:\:and\:\:31$ $m$ numbers are inserted so that the resulting sequence is an $A.P.$ and the ratio of $7^{th}\:\;and\:\:(m-1)^{th}$ numbers is $5:9$. find the value of $m$.

asked Feb 24, 2014 by rvidyagovindarajan_1

1 answer

If $\large\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b$, then find the value of $n$

asked Feb 24, 2014 by rvidyagovindarajan_1

1 answer

The ratio of the sums of $m\:\:and\:\:n$ terms of an $A.P.$ is $m^2:n^2$. Show that the ratio of $m^{th}\:and\:n^{th}$ term is $(2m-1):(2n-1)$

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

Sum of first $p,q\:\:and\:\:r\:terms$ of an $A.P.$ are $a,b\:\:and\:\:c$ respectively. Prove that $\large\frac{a}{p}$$(q-r)+\large\frac{b}{q}$$(r-p)+\large\frac{c}{r}$$(p-q)=0$

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

If the sum of first $p$ terms of an $A.P.$ is equal to sum of first $q$ terms, then find the sum of first $p+q$ terms of the $A.P.$

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

The sum of $n$ terms of two $A.P.s$ are in the ratio $5n+4:9n+6$ Find the ratio of their $18^{th}$ terms.

asked Feb 22, 2014 by rvidyagovindarajan_1

1 answer

If the sum of certain number of terms of the A.P., $25,22,19................$ is $116$, then find the last term.

asked Feb 20, 2014 by rvidyagovindarajan_1

1 answer

In an $A.P.$ if $p^{th}$ term is $\large\frac{1}{q}$ and $q^{th}$ term is $\large\frac{1}{p}$, then prove that the sum of first $pq$ terms is $\large\frac{1}{2}$$(pq+1)$ where $p\neq q$

asked Feb 20, 2014 by rvidyagovindarajan_1

1 answer

How many terms of the A.P. $-6,-\large\frac{11}{2}$$, -5........$ are needed to give the sum $-25$

asked Feb 20, 2014 by rvidyagovindarajan_1

1 answer

In an $A.P.$ the first term is $2$ and the sum of first $5$ terms is one-fourth of the next five terms. Find its $20^{th}$ term.

asked Feb 19, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of all the natural numbers lying between $100\:\: and\:\: 1000$ which are multiples of $5$

asked Feb 19, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of odd integers from $1 $ to $2001$

asked Feb 18, 2014 by rvidyagovindarajan_1

1 answer

A beam of light consisting of two wavelength $6500 A^{\circ}$ and $5200 A^{\circ}$ is used to obtain interference fringes in a young's double slit exp. Then what is the distance from central maxima where the bright fringes due to both wavelength coincides? The distance between slits is 2 mm and distance between plane of slits and screen is 120 cm

asked Feb 13, 2014 by meena.p

1 answer

If $ \sqrt{1-y^2}-\sqrt{1-x^2}=a(x-y),\normalsize$ then find $\large\frac{dy}{dx}$

asked Feb 5, 2014 by rvidyagovindarajan_1

1 answer

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

asked Feb 4, 2014 by rvidyagovindarajan_1

1 answer

If O be the origin and the coordinates of P be (1, 2, – 3), then find the equation of the plane passing through P and perpendicular to OP.

asked Feb 3, 2014 by rvidyagovindarajan_1

1 answer

By using the properties of definite integrals,evaluate the integral $ \int\limits_{-10}^{10}\mid x+2 \mid\;dx$

asked Jan 31, 2014 by balaji

1 answer

If $x,y,z$ are all distinct and $\begin{vmatrix}x&x^2&1+x^3\\y&y^2&1+y^3\\z&z^2&1+z^3\end{vmatrix}=0$ then the value of $\;\large\frac{-1}{xyz}$ is

asked Jan 30, 2014 by balaji.thirumalai

1 answer

Suppose you roll 5 dice and sum up the highest 3 numbers. What is the probability that the sum is 18?

asked Jan 30, 2014 by balaji

1 answer

Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

asked Jan 30, 2014 by balaji

1 answer

Let $(f:R \to R)$ be defined as $(f(x)=2x+3.)$Find the function $(g(x):R \to R)$ such that $(g\;o\;f = f\;o\;g = I_R.)$

asked Jan 29, 2014 by balaji

1 answer

Find the value of $\tan({\frac{1}{2}}\sin^{-1}{\frac{1}{4}})$

asked Jan 28, 2014 by rvidyagovindarajan_1

1 answer

If $\ast$ is a binary operation on the set $(\{0, 1, 2, 3, 4, 5\})$ defined as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] then draw the composition table for the operation and find the identity element and inverse of $4$ if exists.

asked Jan 27, 2014 by rvidyagovindarajan_1

1 answer

Find the equation of the tangent and normal to the curve $ \;y=\large\frac{1+\sin x}{\cos x}$ at $\;x=\large\frac{\pi}{4}$

asked Dec 23, 2013 by balaji.thirumalai

1 answer

Find the area enclosed by the curve $y^2+1=x,x\leq 2$ and the line $x=2$.

asked Dec 22, 2013 by balaji.thirumalai

1 answer

If $( x = \sqrt {a^{\large sin^{-1}t}}, \: y = \sqrt {a^{\large cos^{-1}t}} ),$ what is the value of $\frac {\large dy}{\large dx}$

asked Dec 22, 2013 by balaji.thirumalai

1 answer

Evaluate: $ \begin{vmatrix} (x-2)^2 & (x-1)^2 & x^2 \\ (x-1)^2 & x^2 & (x+1)^2 \\ x^2 & (x+1)^2 & (x+2)^2 \end{vmatrix}$

asked Dec 22, 2013 by balaji.thirumalai

1 answer

Evaluate $\large \int \frac{2\sin 2 x -\cos x }{6-\cos^2x -4\sin x }$$dx$.

asked Dec 22, 2013 by balaji.thirumalai

1 answer

$\int \large\frac{(2\sin 2x-\cos x)}{(6-\cos 2x -4\sin x) }$$dx$

asked Sep 12, 2013 by anonymous

1 answer