Recently Active Mathematics Questions

\int \frac{\sqrt{x}dx }{1- x} another for practice 2. \int_{0}^{\frac{\pi }{2}}{ \frac{sinx cosx dx }{ cos^2x + 3cosx + 2}} ...

1) \\\textit{Find the values of }\left | a \right |+\left | b \right |\textit{such that the identity }\\ \left | ax+by \right |+\left | bx+ay \right |=\left | x \right |+\left | y \right |\emph{holds } \forall x ,y\epsilon R ...

\texttt{the number of ordered triplet(x,y,z) such that LCM(x,y)=3375,LCM(y,z)=1125,LCM(z,x)=3375 is} ...

If two circles passing through the point (0,a) and (0,-a),cut each other orthogonally and touch the straight ine y=mx+c then------- Prove---c2=a2(2+m2) ...

\int \frac{ dx}{ (a^2 sin^2x + b^2 cos^2x ) ^2} ...

Statement 1: f(x) = \left | x \right |cosx is NOT differentiable at x=0 Statement 2: Every Absolute value functions are NOT differentiable. EXPLAIN YOUR ANSWER. ...

Q. For some Natural No. N the no. of positive integral 'x' satisfying the equation 1! + 2! + 3! + ....... + (x!) = (N)2 is: A) None B) one C) two D) infinite I've found the values of x as 3 and 1. So total of 2 values is poss ...

Lim\; n\to \infty \; \frac{1}{n^{2}} \; \sum_{k=0}^{n-1}\: \: \begin{bmatrix} k\int_{k}^{k+1}((x-k)(k+1-x))^{1/2} \end{bmatrix} A) π/32 B) π/16 C) π/8 D) π/4 ...

Find: \lim_{x\to\infty} \left(\dfrac{ex}{2}+x^2\left\{\left(1+\dfrac{1}{x}\right)^x-e\right\}\right) Note that {.} is NOT the fractional part. ...

Positive value of a so that the definite integral \int_{a}^{a^{2}} \frac{dx}{x+x^{\frac{1}{2}}} achieves the smallest value is: A) tan2(Ï€/8) B) tan2(3Ï€/8) C) tan2(Ï€/12) D) 0 ...

If (x1,y1) and (x2,y2) be the two vertices of an equilatera triangle then the third vertex is x=( (x1+x2)+ 3 (y2-y1)) / 2) y=( (y1+y2)+ 3 (x1-x2)) / 2) Can someone give me he proof for this theorem?plz ...

True/ False: If f is differentiable then f\left | f \right | is also differentiable. Give Reason. ...

f(x)=(x^{2}-1)\left | x^{2}-3x+2 \right | + cos\left | x \right | is NOT differentiable at x= A) -1 B) 0 C) 1 D) 2 ...

Consider the polynomials f(x) =a_1 +a_2x+a_3x^2+a_4x^4 and g(x) =b_1 +b_2x+b_3x^2+b_4x^4 where all coefficients are real It is known that \forall \ x \in \mathbb{R} \ \ [f(x)] = [g(x)] Is it necessary that f(x) = g(x)? ...

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\\\textsl{let N be sum of all the roots of the equation }\left (\frac{1}{2x} -1 \right )^{2009}=-1\\ \textit{find the last digit of N} ...

find the min possible value of \left|z \right|^2+\left|z -3\right|^2+\left|z -6i\right|^2 ...

Q1 min value of f(x)= a2cos2x+b2sin2x + a2sin2x+b2cos2x Q2 What is condition so that f(x)=ax3+bx2+cx+dsinx is one one fn ...

Multiple Correct Answer Type Let f(x)=\left\{\begin{matrix} x^{2}sin\frac{1}{x}\; \; x\neq0 \\ 0\; \; \; \; \; \; x=0 \end{matrix}\right. then: A) f and f' are continuous at x=0 B) f is derivable at x=0 C) f is derivable at x ...

Is \; the\; function\; f(x)=e^{-\left | x \right |} \; \; differentiable \; at \; x=0 Give Reason. ...

1.Statement I : gof : A → C is one one Statement II - gof : A → C is onto 2. let A nd B be two events such that P(A ∩ B) =1/4 and P(A)=1/2 and P(B)= 1/2 then A- A and B are independent events R- P(A ∩ B) ≠P(A).P(B) ...

Q1 The statement ~(p q) is logically equivalent to p ^ ~q and plzz someone explain all this logic things in detail...or provide a few links from where i can learn more about them Q2 If we have in options a){3} b)3 which to ch ...

Find teh sum of all four digit palindromes............. u must be knowing wat a palindrome is if not *Image* it is a word or number that reads the same backwards as forwards i want a soln :) ...

The shortest normal chord of the parabola y2 = 4ax is a) 3 a (b) 2 3 a (c) 3 3 a (d) 6 3 a ...

Let n is a positive integer greater than 7 and let f(x) is a biquadratic polynomial with *Image* and *Image* .Let *Image* and remainder when g(x) is divided by f(x) is *Image* then find the value of a b and c in terms of n ...

if an=Σ 1 / nCr,then Σ (n-2r) / nCr=??{answer in terms of an} ...

∫ 1/√3 sin x + cos x dx (there is no square root on sinx it's just √3 sin x is outside root.) [ ans - 1/2 log l tan ( x/2 + pi/12 ) + c ] ...

PROVE THAT (( a/b )α +1)1/α < (( a/b ) β+1)1/β where α > β ...

A triangle ABC with vertices A(-1,0) B(-2, 3/4) C(-3, -7/6) has its orthocentre at H. Then the orthocentre of triangle BCH will be A) (-3,-2) B) (1,3) C) (-1,2) D) None of these ...

Prove that nCm+n-1Cm+n-2Cm+.....+mCm=n+1Cm+1 ...