Recently Active Mathematics Questions

i know this is not directly integrable, bt i'm nt getting any way to directly derive this relationship if \int_{0}^{1}{\frac{e^{t}}{t+1}} =a and \int_{3}^{4}{\frac{e^{t}}{t-5}} =b then find the relation btw a and b??? ...

Q1 If roots of x3-px2-r=0 are tanα,tanβ,tanγ ,find value of sec2α.sec2β.sec2γ I did by converting secx into tanx and then using equation to solve ......any better method ?? Q2 Prove that sinx/cos3x + sin3x/cos9x + sin9x ...

give the full solution 4 pipes fill a cisern in 15,20,30 and 60 hrs .The first was opened at 6 am,the second at 8am,and the thrid at 10 am and the fourth at noon .When will the reservoir be full? ...

*Image* ...

Find the locus of point of chord of contact of tangents from which to the ellipse x2/a2 +y2/b2=1 touches the circle x2+y2=c2 couldnt understand what question wants ??? ...

\sum_{r=0}^{9}{\left(-1 \right)^r\cos^{10}\frac{r\pi}{10}} any short solution using complex? ...

A variable st. line is drawn thru the point A(10,-8) to intersect the curve x^2-xy+y^2+4x-5y-2=0 at the points B and C. A point P is on the chord BC such that AB, AP,AC are in HP., then P moves on a) a line b) a circle C) a p ...

f(x)=ax^2+bx+c Given |f(x)| \le 1 \forall x \epsilon [0,1] . Find maximum value of \left|a \right|+|b|+|c| . ...

Find all real values of the parameter a for which the equation (a-1)z^{4}-4z^{2} +a+2=0 has only pure imaginary roots. ...

If x, y \varepsilon ( 0, \pi ) and (sin 3 x + sin 4 y) + 3 cosec x + 4 cosec y - 9 =0, then no. of solutions of the equation sin x sin y = 1/2 in ( 0, \pi ) is A) 0 B) 1 C) 2 D) infinite ...

k= \lim_{n\to\infty}\frac{(2n+1)\int_{0}^{1}x^{n-1}\sin\left(\frac{\pi}{2}x\right)dx}{(n+1)^{2}\int_{0}^{1}x^{n-1}\cos\left(\frac{\pi}{2}x\right)dx}\ \ (n=1,\ 2,\ \cdots). find k ...

If x+\frac{1}{x}=5 then the numerical value of x^{7}+\frac{1}{x^{7}} is, A) 57965 B) Is a multiple of 7 C) 57695 D) Is a multiple of 5 [ multiple options correct] ...

Number of solutions of the equation \mid x-1\mid + \mid x\mid + \mid x+1\mid = \mid sinx\mid + \mid cosx\mid is, A) 1 B) 0 C) 2 D) 4 ...

evaluate !!!!!!!!!!!!!! 1. \int \frac{3x ^2 - 7 dx}{ (x^2 -4) ( x^2 + 1 ) } 2 . \int \frac{ dx}{ x.\sqrt{x^6 + 1} } 3. \int \frac{ \sqrt{x} dx}{(1+ x^2)^{\frac{7}{4}}} just practice problems [1] ...

Q1: If a,b,c are digits ,then rational number represented by 0.cababab.... is ? Q2: Calculate sum of products of ten numbers ±1,±2,±3,±4,±5 taking two at a time. Q3: Sum of series 1/ 3 + 7 + 1/ 7 + 11 + 1/ 11 + 15 ..... ...

INTEGER ANS TYPE QS 1) Let F (x) be a non- negative continuous function defined on R such that F (x) + F ( x+1/2) = 3 and the value of ∫[0--->1500] F(x)dx is 9000/a . Then the numerical value of ' a ' is . ...

1) If A and B are any two different square matrices of order n with A - B is non-singular A3 = B3 and A(AB) = B(BA) , then a) A2 + B2 = 0 b) A2 +B2 = I c) A2 + B3 = I d) A3 + B3 = 0 ...

INTEGER ANS TYPE 1) Let f(x) = 30 - 2x - x3 , then find the number of positive integral values of x which satisfies f ( f ( f ( x ) ) ) > f ( f ( -x ) ) . ...

*Image* ans d Post the solution also......... ...

Some might-be-too-easy-type integrals, i don't know exactly :P. *Image* ...

*Image* ans c Plz post the soln......... ...

*Image* ans b ...

\\\texttt{Given\; that\;} \\H_k=\frac{k(k-1)}{2}cos\left ( \frac{k(k-1)\pi}{2} \right )\\\texttt{Find \;teh\; value}\; of\\\;H_{19}+H_{20}+H_{21}......H_{98} try it..for practice ...

If S=1+2+4+8+16+...∞.Then S is a positive number.Multiply both sides by 2,then it is found that 2S=S-1 which leads to conclusion that S=-1 which is certainly negative.Do you agree with conclusion?Give a suitable explainatio ...

TRY THIS QUESTION: A recurrence satisfies a_{n+1}=a_{n}+\sqrt{1+a_{n}} then Obtain an explicit formula for a_{n} i.e. find a function f(n) such that a_{n}=F(n) (given that a_{0}=0 ) ...

Q) A Square ABCD of diagonal 2a is folded along the diagonal AC so that the planes DAC and BAC are at right angles. The shortest distance between DC and AB is a) √2a b) 2/3 a c) 2/√5 a d) √3/2 a ...

1) If the normal at one end of the latus rectum of an ellipse x2/a2+y2/b2=1 passes through the one end of the minor axis then A. e4-e2+1=0 B. e2-e+1=0 C. e2+e+1=0 D. e4+e2-1=0 2) In an ellipse the eccentric angle of any point ...

If (4k1,k1^2,1) and (4k2,k2^2,1) are two points lying on the plane in which 1,2,1 are mirror image to each other then k1k2 equals a) -3/2 b) -5/2 c) -7/2 d) -9/2 ...

Q)→Assertion: Function f(x)=1/1-x is a continous function. Reason: A continous function is that which is continous in its domain with no breaks and hence in the function f(x)=1/1-x x=1 is not in the domain of this function. ...

If n line segments of length 1,2,3,4....,n units are given,Calculate number of triangles that can be formed using them ( I saw a ques in which four line segments were given..and answer was caclulated using triangle inequality ...