Recently Active Mathematics Questions

Ques) If Ck is a circle of eqn x2 + y2 = k2 ; k belongs to N, a point moves k units on Ck in anticlockwise direction then goes to C k+1 and so on. If point starts frm (1,0) and Ist time crosses the +ve x-axis on circle Cn , t ...

Well , how about some good questions to wake you up all night ? I think these are quite intriguing to attempt , so I will definitely post the solutions after a day or two ---- 1> ( a , 1 / a ) , ( b , 1 / b ) , ( c , 1 / c ...

PROVE : 2<f(n)<3 if n→N n ≥ 2 and f(n)=(1+1/n)n ...

Solve for x : (x+3)^{5}-(x-1)^{5}\geq 244 PS: the ans given is x \in (-infinity,-2] U [0,infinity) i thought of solving by taking x +1 = y ...so dat we can get some symmetry ...but ans nahi match hora ....pls see f any 1 can ...

find the values of 'a' for which the function f(x)=(a+2)x3 -ax2+9ax-1 is monotonically decreasing for x eR iknow its very easy but i m not getting the ans i did f'(x)≤0 and afetr taht D<=0 not getting ans with it any oth ...

A polynomial f(x) of n-th degree satis es f(k) = 2k for k = 0, 1, 2,.... n Find f(n + 1) (I was wondering if I should put it in the olympiad section.. but then with the last few discussions on polynomials that we have.. I tho ...

Prove (-1) x (-1) = 1 algebraically .... Soln. can be given by anyone other than ATGS :-) ...

Multi answer Q. Consider a curve 13[(x-2)2+(y-3)2] = (2x+3y-5)2. Tangents are drawn from (1,1) to this curve. If a conic S=0 having eccentricity half the eccentricity of the conic xy+x+y=0 always touches above tangents then t ...

Find the sum to n terms of the series : 3/4 + 15/16 + 63/64 + .......= (a) n-(4^n/3) + 1/3 (b) n-(4^n/3) - 1/3 (C) n-(4^-n/3) +1/3 (D) n-(4^-n/3) - 1/3 ...

Let there be a quotient of 2 natural nos in which the denominator is 1 less than the square of the numerator. If we add 2 to both numerator and denominator,the quotient will excess 2/3. If we subtract 3 from both numerator an ...

17 ants are roaming over the chess board of the area 8 X 8 (I.e is 64 square inches) then atleast two of them must always be closer than (a) 2 inches (b) 2 √2 inches (c) √2 inches (d) none of these ...

1. Find the number of solutions of the equation x+y+z=6 the answere is 28 Please explain this in detail 2. From 5 apples, 4 mangoes and 3 bananas, in how many ways can we select atleast two fruits of each variety if i) fruits ...

\begin{Bmatrix} x+y=2\lambda & \\ x+\lambd^2y=\mu & \end{Bmatrix} system has infinite solns and the position vectors of two points A and B are given as (1,λ,2μ),(1,μ,λ2) respectively.AB is line segment divided by XY plane ...

A : If P(x) is a polynomial of even degree with positive leading coefficient and P(x)-P''(x)≥0 for all xεR then P(x)≥0for all xεR R :lim P(x)= lim P(x)=+∞ x→∞ x→-∞ and min {P(x)} is finite number and at local ...

Some of the university lecturers here were interested in the question: Is it possible to divide a given square into n squares for any n≥6? (Obviously all squares neednt be the same size) ...

Well, here are some brainy problems you might want to have a look at only if you are not feeling too sleepy --- :) I am gonna post the solutions after one hour if I can --- 1> If y = x/x2+1 , then find x if d4/dx4 (y) = -3 ...

I think the following questions require good amount of thinking,but even after such a short stint with targetiit, i realized one thing and that is, no man made problem can escape from the axe of problem solving here :) [I hop ...

a,b,c be e R+ and form an AP and abc=4 find the minimum value of b ...

while solving this sum: find C0+C1/2 +C2 /3 +.............+Cn/n+1 there is an alternate method given in BT that is multiply and divide by( n+1) \frac{1}{n+1}[(n+1)(1+\frac{n}{2} + \frac{n(n-1)}{1.2.3}+...........] then the ex ...

At least two of the nonnegative real numbers $ a_{1},a_{2},...,a_{n} $ are nonzero. Decide whether a or b is larger if $ a=\sqrt[2002]{a_{1}^{2002}+a_{2}^{2002}+\ldots+a_{n}^{2002}} $ and $ b=\sqrt[2003]{a_{1}^{2003}+a_{2}^{2 ...

\int \frac{t(1-t^{2})^{-7/4}}{\sqrt{t+2\sqrt{1-t^{2}}+\sqrt{t+3\sqrt{1-t^{2}}}}}dt ...

sum 1 tel me...................... Sum of d factors of 10! which are odd and are of d form "3m+2", m belongs to N ...

cos 2φ/ sin 3φ < 0, if φ lies in: (a) {(13π/48),(14π/48)} (b) {(14π/48),(18π/48)} (c) {(18π/48),(23π/48)} (d) {(π/2),π} ...

The area that is outside the square |x| + |y| ≤1 and inside the circle x^2 + y^2 =1, is given by: (a) Π- 3 (b) Π- 2.5 (c)Π- 1 (d)Π- 2 ...

Ques) The equation (x2-a2) 2 + (y2-b2) 2 = 0 represents points (a) which are collinear (b) which lie on a circle with centre at (0,0) (c) which lie on a circle with centre at (a,b) (d) none of the above ...

Integrate \int \frac{1}{1+\cot x} \ dx ...

1 Three distinguishable dice are rolled. In how many ways can we get a total of 15. answere is 10 2 Rearrangements : In a match the column question. Column I has 10 questions and column II has 10 answeres written in arbitary ...

\sum_{i=0}^{\infty}{\sum_{j=0}^{\infty}{\sum_{k=0}^{\infty}{\frac{1}{3^i3^j3^k}}}}=?? ...

what is the equation of circle which pass thrugh the points A(-1,4), B(1,2) and which touch the line 3x-y-3=0???? ...

The no. of ways in which a score of 11 can be made from a throw by 3 persons, each throwing a die once is : A)45 B)18 C)27 D)68 Ans : C NO USE OF MULTINOMIALS PLEEEEEEAAAASE ...