If the line x cos α + y sin α = 2√3 is tangent to the ellipse \(\frac{x^2}{16} + \frac{y^2}{8} = 1\) and α is an acute angle then α =
If $ i = \sqrt{-1} $ then $\text{Arg}\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right]=$
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 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 cosθ = \(\frac{-3}{5}\)- and π < θ < \(\frac{3π}{2}\), then tan \(\frac{ θ}{2}\) + sin \(\frac{ θ}{2}\)+ 2cos \(\frac{ θ}{2}\) =
A straight line parallel to the line y = √3 x passes through Q(2,3) and cuts the line 2x + 4y - 27 = 0 at P. Then the length of the line segment PQ is
A random variable X has the following probability distribution
For the events E = {x/x is a prime number} and F = {x/x <4} then P(E ∪ F)
If (h,k) is the image of the point (3,4) with respect to the line 2x - 3y -5 = 0 and (l,m) is the foot of the perpendicular from (h,k) on the line 3x + 2y + 12 = 0, then lh + mk + 1 = 2x - 3y - 5 = 0.
If a point P moves so that the distance from (0,2) to P is \(\frac{1}{√2 }\) times the distance of P from (-1,0), then the locus of the point P is
Which of the following does not form a buffer solution?
The ratio of lone pair of electrons to bond pair of electrons in ozone molecule is:
Ziegler-Natta Catalyst is used in the manufacture of
XeF4 + O2F2 → X + O2 X + H2O → Y +2HF The shape of the molecules of X and Y respectively are:
The aromatic compound/species with maximum number of x - electrons is
The following molecule with the structure acts as
A current of 15.0 amperes is passed through a solution of CrCl2, for 45 minutes. The volume of Cl2 , (in I) obtained at the anode at 1 atm and 273 K is around (IF=96500 Cmol-1, At. wt. of Cl=35.5, R=0.082 L-atmK-1 mol-1)
The number of electrons with (n+1) values equal to 3,4 and 5 in an element with atomic number (z) 24 are respectively (n = principal quantum number and l = azimuthal quantum number)
Which one of the following has the same number of atoms as are in 6g of H2O
Arrange the following in the correct order of their reactivity towards nucleophilic addition reactions