
Limnâ†’ âˆž [ n2 . âˆ« ( tan1 nx)/( sin1 nx) dx Integration upper limit: ( 1/n ) Integration lower limit: { (1+ n ) / n } ...

If you flip a fair coin ten times, what is the probability there will be at least one sequence of three consecutive heads or three consecutive tails? ...

There are two drawers in each of three boxes that are identical in appearance. The first box contains a gold coin in each drawer, the second contains a silver in each drawer, but the third contains a gold in one drawer and a ...

P.T for any function f(x) and g(x) integrable on the interval (a,b).. \int_{a}^{b}f(x)g(x)dx\leq \sqrt{\int_{a}^{b}f^{2}(x)dx\int_{a}^{b}g^{2}(x)dx} ...

For an expression x2  5x + 6 = (x + a)(x + b), then ...

\hspace{16}$Determine all pairs $\bf{(a, b)}$ of natural numbers, for which the number\\\\ of $ \bf{a ^ 3 + 6ab + 1} $ and $ \bf{b ^ 3 + 6ab + 1}$ are cubes of natural numbers. ...

f(x) = âˆ« 1sin(2x) then f(Î /4) = ? will it be 2 or 0. because in the sheet that you gave the answer given at the back is (cosx + sinx)sgn(cosxsinx)+c ...

\hspace{16}$Calculation of real values of $\bf{(a,b,c)}$ such that $\bf{x^3ax^2+bxc =0}$\\\\ has a roots $\bf{a\;,b}$ and $\bf{c.}$ ...

\bf{\int\frac{1}{(x^2x+1)\sqrt{x^2+x+1}}dx} ...

\hspace{16}$factors of $\bf{a(bc)^3+b(ca)^3+c(ab)^3}$ ...

âˆ« dx/sec2x + tan2x ...

It is given that a1=1 and an=n(an1+1). Define a sequence pn as pn=(1+ 1/a1 )(1+ 1/a2 )...(1+ 1/an ). Find lim(nâ†’âˆž)pn. ...

Form the differential equation corresponding to y22ay+x2=a2 ...

if f(xy)=f(x)f(y) for all x and y and f(x)is continuous at x=1 ,prove that f(x)is continuous at all non zero x. ...

1. According to Euclid, a line is bounded by _________________ a. Points b. Surfaces c. Both d. None of these ...

1)If B, C be two points lying on the line joining A and D, between A and D, then a. AB = BD b. BC = CD c. AC = CD d. AC = AB how? ...

âˆš3âˆš4/âˆš3+âˆš4âˆš7 ...

4 persons r selected at random out of 3 men , 2 women, and 4 children. The probability that there r exactly 2 children in the selection is..??? ...

150 workers were engaged to finish a piece of work in a certain no. of days. four workers dropped the second day, 4 more workers dropped the third day and so on.....it takes 8 more days to finish the work now.. find the no. o ...

If (0,0),(a,11) and (b,37) are points of a equilateral triangle.....Find ab? ...

If Im,n = âˆ«cosmx.sin(nx).dx, then find 7I4,3  4I3,2. ...

Among all cyclic quadrilaterals inscribed in a circle of radius R with one of its angles equal to 120Â°, consider the one with maximum possible area. Its area is: (a) âˆš2R2 (b) 2R2 (c) âˆš3R2 (d) 2âˆš3R2 ...

if a1,a2,........,an+1 arev in ap,then 1/a1a2 + 1/a2a3 +...... 1/anan+1 is.....?????? ...

If the work done by (x2)men in (x+2)days to the work done by (x+3)men in (x2)days is 15:16 then x is.... ...

the maximum sum of the series 20+19 1/3 +18 2/3 +18+...is...?? how 2 find it....??? ...

The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m, 85 cm, 12 m 95 cm is??? ...

Given a polynomial of n degree such that f(x)+f(1/x)=f(x)*f(1/x) Find the polynomial ...

\hspace{16}$Solution for real $\bf{\left(a\;,b\;,c\right)}$ in \\\\ $\bf{[a]+c\{c\}b\{b\}=0.16}$\\\\ $\bf{b+a\{a\}c\{c\} = 0.25}$\\\\ $\bf{c[c]+b\{b\}a\{a\} = 0.49}$\\\\ Where $\bf{[x] =}$ Integer part of $\bf{x}$\\\\ and ...

If p(x) is an 11th degree polynomial such that p(x) = 1/1+x for x = 1, 2, 3,...11, then find p(12). ...

Two cogged wheels of which one has 32 cogs and other has 54 cogs , work into each other. If the latter turns 80 times in three quarters of a minute , how much the latter turns??? ...