Recently Active Mathematics Questions

Maybe this is pretty easy -- but I liked it a lot -- so here goes -- Find the remainder when 1003 x 1009 x 1017 is divided by 119. ...

tan2 (pi/7) + tan2 (2pi/7) + tan2 (3pi/7) ...

\mathfrak{Evaluate-} \boldsymbol{\sum_{i=1}^{100}{\binom{100}{i}}\left ( 2^{i-1} \right )\left ( 1+3^{100-i} \right )} ...

Q1 Find F(x)=limn→∞( x2nf(x)+g(x)/x2n+1 ) when: a)x<-1 b)-1<x<0 c)0<x<1 d)x>1 where f(x) and g(x) are continuous functions Q2 limn→∞ an/n! ; a ε R Q3 limn→∞ (1+ 1/a1 )(1+ 1/a2 )(1+ 1/a3 )...(1+ ...

Find f(x) which is a continuos fuction such that f(x)=\frac{e^{2x}}{2(e-1)}\int_{0}^{1}e^{-y}f(y)dy+\int_{0}^{\frac{1}{2}}f(y)dy+\int_{0}^{\frac{1}{2}}\sin^{2}(\pi y)dy for practice. ...

(1) No. of solution of the equation C(2n,n)=163 C(2n,n)=\frac{(2n)!}{n!*n!} ans= 0 ,1 2 , Infinity (2)No. of (+ve) Integral solution (x,y) of \frac{(6x)!}{(x!)^{6}}=y is eual to ans=0 ,1 , 2 , infinity ...

xy(d^2y/dx^2)+x(dy/dx)^2+y(dy/dx)=0 ...

A line intersencts hte ellipse x2/a2 +y2/b2=1 at P and Q and the parabola y2=4d(x+a) at R and S.The line segment PQ subtend right angle at the centre of ellipse.Find the locus of hte point of intersection of tangents to the p ...

(1) If S=\sum_{k=1}^{80}{\frac{1}{\sqrt{k}}} Then \left[S \right]= where [ .] Greatest Integer function. ...

IF f(x)=e-ln x and f(2m2 + m +1) < f(3m2 - 4m + 1) then m belongs to A. (0,5) B. (-7,-3) C. (3,17) D. none of these. ...

1..THE POSITIVE REAL FUNCTION SATISFIES F(X)/F(Y) ≤7(X-Y)2 FOR X , Y BELONG TO ITS DOMAIN ,F(3/2)= Π/4 THEN 1.F(X)= X +X3 2.F'(7)=0 3.F(X)=∫sin-1 t dt +∫ cois-1 t dt (in 3--limit for sin-1 t is from 0 to sin2x while fo ...

There are three sets of objects. One group contains n elements of one kind Other contains n elements of another kind Last grp contains n different elements All 3n elements are mixed together. Find the number of ways in which ...

find : \ \int_{0}^{\pi}\frac{\cos nx}{2-\cos x}dx\ (n = 0,\ 1,\ 2,\ \cdots) ...

(1) find all Integral value of x for which the expression x^{2}+7x+13 is a perfect square. i have got only one solution x= - 4 is there is any other Integral value of x which satisfy this expression? ...

If a(70a - 12b + 2c)> 0 and the quadratic equation ax^2 + bx + c = 0 has real roots alpha and beta, then which of the following statement is always false? alpha< beta < -7 alpha < beta<= - 8 alpha > beta> ...

A ball is drawn at random from a bag containing 3 balls and it is found to be black. If it is equally likely that it may contain 1 or 2 or 3 black balls, the probability that the ball drawn is the only black ball is...is the ...

draw d graph of [y]=[x]... ...

please solve it asap *Image* x ...

It is given that tan A and tan B are the roots of t2-pt+q=0. Find in terms of p and q: i) sin2(A+B) ii)cos 2(A+B) ...

Q1 f:R→ R ;f(x) is continuous funciton satisfying f(x)+f(x2)=2 for all x ε R,the f(x) is a)into b)many one c)constatn d)periodic Q2 If [x] denotes GINT and f(x) =[n+p.sinx],0<x<π ,n ε I and p is a prime no., If p=1 ...

1. If a,b are the roots of x2=x+1 , prove that a5=5a+3 2. Two candidates attempt to solve a quadratic eqn of the form x2+px+q=0 . One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a w ...

someone plzz see the miscelaaneous exercise on chapter8, q no.10, ncert for class XII.... the ans is wrong at the back of ncert...it ought to be 5/6 ...

Q1. Let f(x) = ax^4+bx^3+cx^2+dx+e where a,b,c,d,e\; \; \epsilon \; R , a≠0, b2>8ac/3 and g(x) = lf(lxl)l , then maximum possible no. of points at which g(x) is non-differentiable is _______ Q2. \int_{0}^{\infty }{\left[ ...

\\\texttt{If} \: f_{n}=\sum_{k=0}^{n}\binom{n-k}{k} \\\texttt{evaluate}\\ \\ \begin{vmatrix} f_{n}& f_{n+1}&f_{n+2} \\ f_{n+1}& f_{n+2}&f_{n+3}\\ f_{n+2}&f_{n+3}& f_{n+4} \end{vmatrix} ...

prove: \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n} is not an integer for any value of n. ...

Solve 1. 4x -3x- 1/2 = 3x+ 1/2 - 22x-1 2. 2x2 : 2x =8:1 ans1 is x=1+- 13 /2 ans 2 is x=3/2 ...

Q1- A: if f(x) is discontinous at a point c and g(x) is continous at c and f(x).g(x) is continous at c then f(x) must be 0 at point c. B: if f(x) and g(x) are two continous function in their domain then f(x).g(x) must be cont ...

\int_{0}^{2\pi }{e^{\cos \theta }cos(sin\theta )d\theta }= ...

If A(1,p2) , B(0,1), C(p,0) are the co-ordinates of the three points then the value of p for which the area of the triangle ABC is minimum is : A) 1/√3 B) - 1/√3 C) 1/√3 or -1/√3 D) None of these Ans: D ...

A student appears for test I, II and II. The student is successful if he passes either in tests I and II or test I and III. The probabilities of the student passing in tests I, II and III are p, q and 1/2 respectively. If the ...