Recently Active Mathematics Questions

if x is real then prove that the expression (x2-2xcos2θ+1)/(x2-2xcos2φ+1) lies btween sin2θ/sin2φ and cos2θ/cos2φ. ...

The normal to the curve x=a(cos t + tsin t),y=a(sin t-tcos t)at any point t is such that-- A. it makes a constant angle with the X axis B. it passes through the origin. C. it is at a constant distance from the origin. D. none ...

If f:R→R is a monotonic,differentiable real valued function a,b are two real numbers and ∫f(x)+f(a))(f(x)-f(a))dx=I1 upper limit→ b and lower limit→a ∫x(b-f-1(x))dx=I2 upper limit→f(b) lower limit→f(a) I2/I1=___ ...

Ques1) Let a,b,c are respectively the sum of the first n terms, the next n terms, and the next n terms of a G.P. Show that a,b,c are in G.P. Ques2) Show that the sum of square of three consecutive odd no's increase by 1 is di ...

find out a four digit number M such that N=4xM and N has the following properties : i) it is also a four digit no. ii) the digits of N are in reverse order of those in M. ...

how to solve sin-1x≥0??????? ...

Here are a few good probs.Pls solve them. 1)What is the solution of the inequality |x+3|>|2x-1| 2)Find the solution of |x2+3x|+x2-2 ≥ 0 3)Find the solution of 2x+2|x| ≥ 2√2 ...

lim x→2 ( x-2 + x - 2 )/ x2-4 ...

Define a "valid n-bit binary word" as a n digit long sequence of 0's or 1's in which no two or more consecutive 1's are present. For example, for n = 3, we see that of all the 3-bit binary words possible: 000, 001, 010, 011, ...

pls solve 1)Σtan2(rΠ/16)=S and r varies from 1 to 7 wat is S? 2)let f(x+y)=f(x)2+f(y) for all x,y belongs R then find f(x) 3)If two distinct circles x2+y2-2ax+c=0 and x2+y2-2bx+c=0 and a2>c b2>c>0 cut equal interce ...

If T_n = \frac{4^n n^2}{(n+1)(n+2)} Find Sn where S_n = \sum_{i=1}^n T_n ...

please give the mistake in the following solution: I=∫ (ax+b)sec x tan x dx/4+tan2x dx (a,b>0) and lower limit 0 and upper limit π splitting the numerator, ∫ ax sec x tan x dx/3+sec2x = ∫ a(π-x)sec x tan x/3+sec2x ...

ysin2xdx=dy(1-k(y)^(1/2)cosx) here k is a known constant. ...

if a and b are two integers such that 7 divides a2+b2, prove that 49 divides a2+b2. HINT: try using euclid's division algorithm i must admit if presently i were in class ix-x, i would not even know how to approach it! ...

Prove the cos x2 is not periodic. ...

A Few reasoning and assertion questions -: f(x) = lim cos(n!2∩x) n is an integer . n--->∞ g(x) = lim cosn(2∩x) n--->∞ h(x) = lim {cos(n.x)+2}-n Range of f = R1 , Domain Of f is D1 Range of g = R2 , Domain Of g i ...

draw the graph of ---- (1)f(x)=2|x-2|-|x+1|+x (2)f(x)+x+|x| ...

Find the interval in which the function f(x)=loga(5x-2-2x2),where o<a<1 has an inverse. ...

The fuctions f(x)=x2-4x+3 and g(x)=2- 1+x are inverse functions of each other.Find any one root of the equation f(x)=g(x). ...

while solving an inequality, i got the interval of x as [-6,6] but there was another option as [-1,1] and the question was of one or more correct ans. type.should I mark both these options? ...

Prove that an infinite number of triangles can be inscribed in either of the parabolas y^2=4ax and x^2=4by whose sides touch the other ...

Show that (6!)5! is a divisor of (6!)!. ...

Prove that the roots of the equation (a4+b4)x2+4abcdx+(c4+d4)=0 cannot be different if real. ...

Ques1) If one Geometric mean G and two arithmetic means p & q are inserted between two quantities, then show that G2 = (2p-q)(2q-p) Ques2) Let a,b,c are respectively the sum of the first n terms, the next n terms, and the nex ...

10 women are sitting in a row. All of them get up and reseat themselves in a way such that each woman can sit either in the chair where she was previously sitting or in the chair right next to hers. In how many ways can the w ...

if one of the root of quadratic equation x2+ax+b=0 be the other root of x2+cx+d=0then prove that its other root is of the equation x2+(2a-c)x+(a2-ac+d) ...

if the angle of elevation of a cloud from a point 'h'metres above a lake is a and angle of depression of its reflection in the is b.Prove that the height of cloud is h( tan b + tan a )/( tan b - tan a ) .pls solve it by drawi ...

if α i a non real root of x7=1 , find the equation whose roots are :α+α6 ; α2+α5 ; α3+α4 . ...

y=sin(cos-1(tan(sec-1x))) find dy/dx ...

find ∫ x2 lnx/ 1-x2 dx lower limit =0 and upper limit = 1 ...