Recently Active Mathematics Questions

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This qsn came in FIITJEE AITS 2day. I_n=\int_{\frac{\pi}{2}}^{\propto}{e^{-x}cos^{n}xdx}=\frac{720}{3145}e^{-\frac{\pi}{2}} This holds for n=2m, where m is a natural number. Find it. ...

AA A>0 + BB B>0 CDC All A,B,C are digits. Find D A.4 B.3 C.2 D.1 ...

what is the unit digit of N if N = (289)5 *(587)7 *(1156)9 *(17)15 without actual multiplying A.8 B.5 C.3 D.6 show me how to do this 1 step by step ...

if xy=yx and x2=y, where x and y are dinstinct positive real integers then the value of of x+2y is ...

y2 = 2c(x+ c ) find order and degree iit qsn After double differentiation im getting yy''+y'2=0 from this order is 2 and degree is 1 but it's wrong Ican not understand why it's wrong Hel[p me in solving this Q. ...

This is a brilliant brilliant proof i read today... *Image* This is from a book called problem solving strategies... (it is a brilliant read!) ...

statement 1: 0∫Π1/1+5cosx=Π/2 statement 2:0∫af(x)dx=0∫af(a-x)dx ...

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1. a box contains 8 pairs of shoes. if 4 shoes are selected at random then find the probabilty that exactly one pair of shoes is selected?? 2.neha's tv has only 4 channels; all of them quite boring,hence it is not suprising t ...

1) find maxima of xy2z3 provided : x + y + z = 6. 2) find maxima of (x-3)2 + (y-2)2 provided : (x+3)2 + (y+2)2 = 4 ...

∫(x7m+ x2m + xm).(2x6m + 7xm + 14)1/m.dx (Have seen these sort of Qn(s) b4 too,,,A hint to start wud be enuf...) ...

how to find the locus of a point P outside a circle, when the angle between the tangets frm that point to the circle is given...??? plz giv me the entire algorithm... ...

(1) A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white? ...

How many terms are perfect square in the sequence 4,44,444,4444,44444............................ and why? give the appropriate reason also ...

1) cos (x+y) dy = dx 2) x+y dy/dx /y-x dy/dx = (1 + x2/y2 ) ( ln ( x2+y2 )) 3) dy/dx = (4x + y + 1)2 4) 2x3y3 + x4y2 dy/dx = -b2/a2 y - b2/a2 x dy/dx [ GUYS POST THE SOLN. FULL AS I CANNOT CONFIRM UR ANS. SINCE I DON'T HAVE T ...

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S = 1.3.4 + 4.5.5 + 7.7.6 + 10.9.7 + .............. Find sum to n terms ??? (In terms of n) I have a method but want some time saving one So post ur methods ...

I want the expansion of different expressions like 1/(1-x) sq. root of above then, √1-a2x2 etc.... if u hav good link for this kind of expansions, pls post here... ...

Saw this in some coaching institute material. Its easy, but their method seemed tedious. Lets see how targetiitians fare: x,y \in \mathbb{R} and x+iy = \frac{3}{\cos \theta + i \sin \theta+2} Evaluate 4x-x^2-y^2 ...

two numbers 'a' and 'b' are selected at random from the set {1,2,3,4,5............3n}. find the probabilty that a2-b2 is divisible by 3 ...

\int \frac{1}{(2sinx+secx)^{4}}dx for practice ...

A bag contains 5 balls of unknown colour. A ball is drawn and replaced twice , and in each case it is found to be red.: if two balls are drawn simultaneously .find the chances that it is red. ...

f(x)=|x-x2| What is the maximum value of this fn? ans is 6 but i got as 1 ...

prove that (k-1)2=(n-1)2+(m-1)2+(f-1)2 have infinitely many solutions when all the variables are natural numbers[1] hey forgot one constraint they r distinct for obvious reasons.....[1][1] ...

TMH iit jee for 2008: pg-21.16 , f(x)=sin(2x+1) f:R→[-1,1] domain is restricted to [-3Π/4 - 1/2 , -Π/2-1/2] In this case find onto or not? Can u pls explain with the help of graph? *Image* /hide] I think it is not onto .. ...

Q1. Let \LARGE\!\phi (x) = sinx\int_{0}^{x}{costdt} + 2\int_{0}^{x}{tdt} + cos^2x - x^2 . If \LARGE\!x^2 - 2x +3 \geq \phi (x) \vee x\epsilon R, then greatest area bounded by xφ(x) and coordinate x=0 and x=5 is (a) 16 (b) 25 ...

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P (3,1), Q (6,5) and R(x,y) are three points such that the angle PRQ is a right angle and the area of PRQ is 7, then the number of such points R is...???? Please give a detailed solution. ...

\int \frac{1}{(x+\sqrt{x^{2}-1)}^{2}}dx far practize ...