Recently Active Mathematics Questions

if α,β are d roots of x2 -x-1 =0 and An = αn +βn then A.M of An-1 and An is ........... ...

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1. Show that the point M(-3,2) outside the triangle whose sides are given by the equations x+y-4=0, 3x-7y+8=0 and 4x-y-31=0 2. One diagonal of a square is the portion of the line 7x+5y=35 intercepted by the axes. Obtain the e ...

Let h(x)=f(x)-(f(x))2+(f(x))3 for every real no x. Then- (a)h is increasing whenever f in is increasing. (b)h is increasing whenever f is decreasing. (c)h is decreasing whenever f is decreasing. (d)nothing can be said in gene ...

The function f(x)=sin4x+cos4x increases if (a)0<x<pi/8 (b)pi/4<x<3pi/8 (c)3pi/8<x<5pi/8 (d)5pi/8<X<3pi/4 ...

Q1 - If cos4 (θ + α) , sin4(θ + α) are the roots of the equation x2 +b(2x+1) = 0 and cos2(θ+β),sin2(θ+β) are the roots of the equation x2+4x+2 = 0 then b is equal to ? Q2 - (Sinθ / sin δ)2 = tan θ / tanδ = 3 then ...

let d(n) denote no. of divisors of n,then prove that d(n)<2 n ...

∫sinx/sin4x ...

Q) If the nth term of a certain series,whose first three terms are 2,1 and -3 is of the form a+bn+c.2n ,where a,b,c are constants,then show that a,c,b are in AP.Also find the sum of first 'n' terms of the series ...

1. f(x)= sin-1 (sin x)...find its period.... 2. 2f(x2) + 3f(1/x2) = x2 -1......for all x belonging to R - {0} then f(x2) = ????? pls ans urgently required...!!!! ...

∫ (3cosx+2) dx/(sinx+2cosx+3) Please give me a solution to this problem..... And these too. ∫(tanx)^(1/6)dx ∫√sin^-1(x) dx it's integration of root under sin inverse x . ...

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i'm very weak at algebra. So can anyone plz say me if (x+1/x)=4 then (x-1/x)=? nd why?? ...

pls solve these sums for me in detail: 1) What is the period of the function |sin2x|+|cos8x| 2) If f(x)=ln( x2+e/x2+1 ),then find the range of f(x) 3) Let f:R→R be defined by f(x)=(ex-e-x)/2.Is f(x) invertible?.If so find i ...

If α and β are the zeroes of the quadratic polynomial f(x)=ax2+bx+c, then evaluate: a(α2/β+β2/α)+b(α/β+β3/α) I think there is some mistake in the problem. If yes, then pls tell me. Otherwise pls solve the problem fo ...

Easy one I guess, but i want to see the method. The odd numbers are arranged as shown below: (1) (3,5) (7,9,11) (13,15,17,19)... Find the sum of terms in the nth bracket as a function of n. ...

Find the intervals in which the function f(x)=3cos4x+10cos3x+6cos2x-3,0≤x≤pi;is monotonically increasing or decreasing. ...

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\int dx/sinx+cosx ...

If f(x)=x3+bx2+cx+d and 0<b2<c, then in (-∞,∞) ,f(x) (a)is increasing. (b)is decreasing. (c)has local maxima. (d)is bounded. ...

The domain of defination of the function f(x)= 22x+64(x-2)/3-2-1(72+22x) i m not givin the options coz u'll be able to eliminate it(option) easily.solve wid proper method. ...

if α,β are d roots of ax2+ bx +c =0 den d roots of a(x+1)2+b(x+1)(x-2)+c(x-2)2=0 are...........?? ...

For any natural number n≥2, find out which of the real positive numbers a and b is greater, knowing that an=a+1 and b2n=b+3a. ...

This time's Pan-African Olympiad had a problem that goes: If, 1 \le i \le 2000, \ x_i \in \{-1,1\} is it possible to have x_1 x_2 + x_2x_3+x_3x_4+....+x_{2000} x_1 = 999 ...

If (1+x)^{n}=C_{0}+C_{1}x+C_{2}x^{2}+.......C_{n}x^{n} then prove that \sum_{0\leq i}^{}{\sum_{<j\leq n }^{}{}}C_{i}C_{j}(i+j)=n(2^{2n-1}-\frac{1}{2}. ^{2n}C_{n}) ...

The first violet leaflet that you sent on maths has several errors.The answer to question no.1 under 'DIVISIBILITY' is given 'a' and 'b'.It should actually be 'b' and 'e'.Then in question no.9 under 'DIVISIBILITY' the answer ...

we have functions from {1,2,3..n} to {1,2,3..n}, find the probability that the function is, 1)increasing 2)Non decreasing juniors try it out, seniors, im not sure, but i think this one has already been discussed (i think so), ...

Let f be a continuous function on [0,1] such that for all x\in[0,\,1] , \int_x^1 f(t)\ \mathrm{d}t \geq \dfrac{1-x^2}{2} Prove that \int_0^1 f^2(t)\ \mathrm{d}t \geq \dfrac{1}{3} Here, f2(x) means (f(x))2. Also, determine the ...

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*Image* ans. given is false.................can u tell y? ...