Let \(S_n = \sum_{K=1}^{4n} (-1)^{K(K+1)/2} \cdot K^2\). Then Sₙ can take value(s):

If the polynomial 3x² − x³ − 3x + 5 is divided by another polynomial x − 1 − x², the remainder comes out to be 3, the quotient polynomial is:

Rearrange the parts of the sentence in correct order.

P. despite pandemic-related travel complications, the

Q. governments of India and France facilitated interactions

R. NPCIL a binding techno-commercial offer on 22 April 2021

S. between EDF and NPCIL which allowed EDF to submit to

X, Y and Z enter into a partnership. X invests some money at the beginning. Y invests thrice the amount of X after 4 months and Z invest double the amount of Y after a month from the beginning. If the annual gain be Rs. 450000, then what is the share of Y?

If (10)⁹ + 2(11)¹(10)⁸ + 3(11)²(10)⁷ + .... + 10(11)⁹ = K(10)⁹, then K is equal to:

Let α and β be the roots of the equation px² + qx + r = 0, p ≠ 0. If p, q, r are in A.P. and $\frac{1}{α}$ + $\frac{1}{β}$ = 4, then the value of |α − β| is:

Let −$\frac{π}{6}$ < θ < − $\frac{π}{12}$. Suppose α₁ and β₁ are the roots of the equation x² − 2x sec θ + 1 = 0 and α₂ and β₂ are the roots of the equation x² + 2x tan θ − 1 = 0. If α₁ > β₁ and α₂ > β₂, then α₁ + β₂ equals:

The number of values of x lying in the interval (−π, π) which satisfy the equation 8^{1+|cos x|+cos²x+|cos³x|+....∞} = 4³ is:

The value of \(\cos^3(\pi/8)\cdot\cos(3\pi/8) + \sin^3(\pi/8)\cdot\sin(3\pi/8)\) is: