If $ i = \sqrt{-1} $ then $\text{Arg}\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right]=$
Let y = t2 - 4t -10 and ax + by + c = 0 be the equation of the normal L. If G.C.D of (a,b,c) is 1, then m(a+b+c) =
If the function f(x) = xe -x , x ∈ R attains its maximum value β at x = α then (α, β) =
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} sin^2xcos^2x(sinx+cosx)dx=\)
The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is
If f(x) is a function such that f(x+y) = f(x)+ f(y) and f(1) = 7 then \( \sum_{r=1}^{n}\) f(r) =
If A is a square matrix of order 3, then |Adj(Adj A2)| =
If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
The quadratic equation whose roots are
\(l = \lim_{\theta\to0} \frac{3sin\theta - 4sin^3\theta}{\theta}\)
m = \(\lim_{\theta\to0} \frac{2tan\theta}{\theta(1-tan^2\theta)}\) is
If Xn = cos \(\frac{ π}{2^n}\) + i sin\(\frac{ π}{2^n}\) , then
If A = \(\begin{bmatrix} 0 & 3\\ 0 & 0 \end{bmatrix}\)and f(x) = x+x2+x3+.....+x2023, then f(A)+I =
The quadratic equation whose roots are sin218° and cos2 36° is
The roots of the equation x4 + x3 - 4x2 + x + 1 = 0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such h are α and β, then 12(α - β)2 =
If x = log (y +√y2 + 1 ) then y =
A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls in the bag are white is
The period of function f(x) = \(e^{log(sinx)}+(tanx)^3 - cosec(3x - 5)\)is
lim n→∞ \(\frac{1}{n^3}\) \(\sum_{k=1}^{n} k^{2} =\)
If cosθ = \(\frac{-3}{5}\)- and π < θ < \(\frac{3π}{2}\), then tan \(\frac{ θ}{2}\) + sin \(\frac{ θ}{2}\)+ 2cos \(\frac{ θ}{2}\) =
If sin 2θ and cos 2θ are solutions of x2 + ax - c = 0, then
If ∫(log x)3 x5 dx = \(\frac{x^6}{A}\) [B(log x)3 + C(logx)2 + D(log x) - 1] + k and A,B,C,D are integers, then A - (B+C+D) =
\(∫\frac{dx}{(x2+1) (x2+4)} =\)
\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)
If order and degree of the differential equation corresponding to the family of curves y2 = 4a(x+a)(a is parameter) are m and n respectively, then m+n2 =
If l,m,n and a,b,c are direction cosines of two lines then