Recently Active Mathematics Questions

f(x) is a periodic fn with pd λ and f(x-\frac{\lambda }{2})=-f(x) ,then show thta g(x+\lambda)=g(x) where g(x)=\int_{0}^{x}{f(t)dt} ...

Q1 If a1,a2,..a101 is an arrangement of the numbers 1,2,...101 then prove that the product of (1-a1)(2-a2)...(101-a101) is an even integer I wasnt in favour of starting aonther revision thread on P&C beocz already many exist. ...

FInd the sum of inifnite series a1+a2+a3+..... where a_n=(log3)^n\sum_{k=1}^{n} \frac {2k+1}{k!(n-k)!} ALso it is known that a0,a1,a2.... be the coefficients in the expasion of (1+x+x2)n in ascending power of x i have calcula ...

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sininverse((2x+2/( 4x2+8x+13 ))) ...

if p1 and p2 are the probability of speaking the truth of two independent witnesses A and B then find the probabilty that der combined statement is true ...

Find the last three digits of 17256 ...

1/(sinx+cosx) ...

If a0,a1,a2.... be the coefficients in the expasion of (1+x+x2)n in ascending power of x then prove that 1) (r+1)a_{r+1}=(n-r)a_r+(2n-r+1)a_{r-1};0<r<2n 2) (a_0+a_3+a_6+...)=(a_1+a_4+a_7+...)=(a_2+a_5+a_8+...)=3^{n-1} i ...

If there are 'm' non concurrent and non parallel lines, then what is the maximum number of points which are equidistant from all the 'm' lines? from another IIT JEE forum ;) ...

q)the lengths of the tangents drawn from vertices A,B,C to the incircle of triangle ABC are 5,3,2 respectively.IF THE LENGTHS OF THE PARTS OF THE TANGENTS WITHIN THE TRIANGLE WHICH ARE DRAWN PARALLEL TO THE SIDES BC,CA,AB OF ...

(1)there are 24 balls of 6 different sizes in a bag, there being 4 balls of each size in four different colours .in how many ways 4 balls can be selected so that they are of differnt colours?????? (2) how many 5 digit nos. of ...

Q1 Find the no. of rational and irrational roots of x^3+1=2(2x-1)^{1/3} Q2 Let P(x) be a polynomial such that P(x^2+2)=x^{17}-3x^5+x^3-3 then find roots of P(x) Q3 Let a,b,c ε R and a≠0 be such that (a+c)2<b2 the nfind ...

(1) Prove that \left C(2n,n \right)/(n+1)=Integer where n\ \epsilon Integer ...

(1)If no of ordered pairs (x,y) satisfying lyl = cosx & y = sin-1(sinx) is m when l x l≤2∩ & n when l x l ≤ 3∩ Then A)m+n = 0 B)m+n =2 C)m+n =10 D)n-m =0 E)n-m=2 (2)If the no of solutions of ln l sinx l = -x2 + 2x , x ...

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Well ,let's make mincemeats of these --- :) 1 > Do try to find the remainder when 21990 is divided by 1990 . I have found a way without using binomial but , still it would good to see the other ways too ---- maybe an easie ...

If x is real, the maximum value of - y = 2\left(a-x\right) \{ x+ \sqrt{x^2 + b^2} \} is ________ ? ...

Ques1) Let f(n) = 10 n + 3.4 n+2 + 5 , where n belongs to N. The greatest value of the integer which divides f(n) for all n is (a) 27 (b) 9 (c)3 (d) none Ques2) If m and n are any two odd positive integers with n < m , the ...

Q1 Find the real values of a,b,p,q for which (2x-1)^{20}-(ax+b)^{20}=(x^2+px+q)^{20} Q2 Find Sum of series S=C_1-(1+ 1/2)C_2 +(1+ 1/2 +1/3)C_3+...+(-1)^{n-1}(1+ 1/2+....+1/n)C_n Q3 Sum of series S=\sum_{r=0}^{n}\frac{3^{r+4}. ...

6 apples and 6 oranges are to be distributed among 10 boys. Find the number of ways in which this can be done . Ans : (10+6-1 C6 )2 How can this be possible ?????????? ...

A circle S=0 passes thru the common pts of intersection of family of circles x^2+y^2+λx-4y+3=0 & have min area then (A) area of S=0 is Πsq units (B) radius of director circle of S=0 is 2 (C) length of intercept made by S=0 ...

S[n]= 3/4 +15/16 +63/64+...... find S[n] a) n - 1/3*4^(n) -1/3 b) n + 1/3*4^(-n) -1/3 c) n + 1/3*4^(n)- 1/3 d) n-1/3*4^(-n) +1/3 ...

*Image* In the given figure, u have the road plan of a city. A man standing at X wants to reach the cinema hall at Y by the shortest path. (i) Find the no. of different paths that he can take. (ii) Find the no. of shortest ro ...

A parallelogram OABC ,s.t a,b,c respectively are position vectors of A,B,C wrt O (origin).A poin P is taken on BC which divides it in ration 2:1.Also line segment AP intersects the line bisecting angle O internally in point Q ...

1) Last two digits of 3100 are .... 2)Last three digits of 17256 are... 3)The remainder when (a) 597 is divided by 52 (b) (106)85 - (85)106 is divided by 7 (c) 3100 is divided by 100 ...

Be sure to read the problem clearly. A bag contains 6 balls of different unknown colors. Probability for A and B speaking truth are p and q respectively. A ball is drawn and both cofirm it to be RED. What is the probability t ...

prove that the straight lines ax+(b+c)y+d=0,bx+(c+a)y+d=0 and cx+(a+b)y+d=0 are concurrent? ...

find the magnitude of the angle which the line y=-x makes with the positive direction of the x-axis? ...

find the condition that the lines xcosα+ysinα=p,xcosβ+ysinβ=q and y=xtanθ may be concurrent? ...