Recently Active Mathematics Questions

\hspace{-16}$Calculate value of \\\\\\ $\mathbf{(1)::I_{1}=\int_{0}^{\pi}\frac{\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\\\ $\mathbf{(2)::I_{2}=\int_{0}^{\pi}\frac{x.\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\ \hspace{-16}$Ans\; :: $I_{ ...

\hspace{-16}\int\frac{x^2}{\left(1+\sin 2x\right)}dx ...

sorry for multiple posting ...

Please post a detailed explanatory solution to the following. *Image* Thanks ...

Solve 1 +x2 +y2 +x2 y2 + xy dy/dx = 0 ...

Q. Let f(x) and g(x) be differentiable functions such that f'(x)g(x)\neq f(x)g'(x) for any real x. Show that between any two real solutions of f(x)=0 , there is atleast one real solution of g(x)=0 . ...

the argument of (1- i 3 ) is (1+ i 3 ) A) 60° B) 120° C) 210° D) 240° i got the answer as 240° but the book ans says it is 60°.... 'am baffled!! ...

\hspace{-16}$If $\mathbf{f(x)}$ is a defined function in such a way such that\\\\\\ $\mathbf{f(x+1)=\frac{f(x).\cos\left(\frac{\pi}{67}\right)+\sin\left(\frac{\pi}{67}\right)}{\cos\left(\frac{\pi}{67}\right)-f(x).\sin\left(\f ...

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Integrate: 1) ∫ 1/sinx+sec x dx Please show me the steps also. ...

if (a+2)sinx + (2a-1)cosx = (2a+1) find tanx. the options were (a) 3/4 (B) 4/3 (C) 2a/(a2+1) (D) 2a/(a2-1) well we can see that option B holds. i want the solution. ...

Express (1+x2) (1+y2) (1+z2) as sum of two squares. ...

If a,b,c and d are real positive such that : a + b + c + d = 1 Show that : 4a+1 + 4b+1 + 4c+1 + 4d+1 < 6 ...

Prove that [√n + √(n+1)] = [√(4n+1)] = [√(4n+2)] [.] here is used to denote greatest integer/floor function. ...

Find the sum of [x]+[x+ 1/n ]+[x+ 2/n ]+......+[x+ n-1/n ] if 'x' is real and 'n' is natural. [.] represents the greatest integer function. ...

let f1(x) = x for 0≤x≤1 1 for x>1 0 otherwise and f2(x) = f1(-x) for all x f3(x) = -f2(x) for all x f4(x) = f3(-x) for all x Which of the following in necessarily true? 1. f4(x) = f1(x) for all x 2. f1(x) = - f3(-x) fo ...

Sorry. Mistakes that the question repeated ...

*Image* just focus... its simple.. !! ...

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Q: Given a,b,c and d ε R satisfying a+b=8 ; ab+c+d=23 ; ad+bc = 28 ; cd = 12 , Find a) a+b+c+d b) ab+cd c) ac+bd d) ab (It's matrix type but I didn't wrote the options as it was taking more time) Q: The no. of values of ' k ...

PROVE: n!/r! (n-r)! + n!/(r-1)!(n-r+1)! = (n+1)!/r! (n-r+1)! ...

1.find the number of ways in which m boys and n girls may be arranged in a row so that no two girls are together . given that m>n 2. In an exam,10 candidates have to appear. 4 candidates are to appear in maths and rest in ...

prove that - tan 2pi/13 + 4sin 6pi/13 = √(13+2√13) ...

1. A= \begin{bmatrix} 1& 0 &1 \\ 0 & 1 &1 \\ 0& -2 & 4 \end{bmatrix} 6A-1=A2+cA+dI,then c,d = [a nice method will do,without working a lot] 2. Assertion and Reason: Consider the system of equations: x-2y+3z=-1;x-3y+4z=1;-x+y- ...

1. Prove that (n!)! is divisible by (n!)^{(n-1)!} . 2. Show that 1!+2!+3!+ \dots + n! cannot be a perfect square for any n \in \mathbb{N}, \: n\geq 4 . ...

let P1(x)= ax^2-bx-c, P2(x)=bx^2-cx-a,P3(x)= cx^2-ax-b, be 3 quadritic polynomials where a,b,c are non zero real numbers suppose there exists a real number k such that P1(k) = P2(k)= P3(k). then prove that a=b=c. please do it ...

can someone help me solve , 2cosα - 1 = sinα - cosα*tan( α/2 ) ...

nishant sir could you please provide some link or source from where we can study geometry which helps solve coordinate . ...

*Image* sine rule can help too... ...

Little Einstein writes the numbers 2 , 3 , … N on a blackboard. He chooses any two of them, say X and Y, scratches both of them and replaces them by the single number T given by the relation : T = XY – X – Y + 2 He repe ...