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)
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
The rate law for the decomposition of hydrogen iodide is - = d[HI]/dt = k[HI]2. The units of rate constant k are:
Consider the following statements about the oxides of halogens A. At room temperature, OF2; is thermally stable B. Order of stability of oxides of halogens is I > Br > Cl C. I2O5 is used in the estimation of CO D. ClO2; is used as a bleaching agent The correct statements are
If \(\int_{0}^{3} (3x^2-4x+2) \,dx = k,\) then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is
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 =
The general solution of the differential equation (x2 + 2)dy +2xydx = ex(x2+2)dx is
If a man of mass 50 kg is in a lift moving down with a acceleration equal to acceleration due to gravity, then the apparent weight of the man is:
If n is a positive integer and f(n) is the coeffcient of xn in the expansion of (1 + x)(1-x)n, then f(2023) =
Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire C be F. If the wire B is removed without disturbing the other two wires, then the force per unit length on wire A is:
According to MO theory, the molecule which contain only π-Bonds between the atoms is
In which if the following changes there is no change in hybridization of the central atom?
If $ i = \sqrt{-1} $ then $\text{Arg}\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right]=$
Let $ X = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \middle| a, b, c, d \in \mathbb{R} \right\} $. If $ f: X \to \mathbb{R} $ is defined by $ f(A) = \det(A) $ for all $ A \in X $, then $ f $ is
Let a = i + 2j -2k and b = 2i - j - 2k be two vectors. If the orthogonal projection vector of a on b is x and orthogonal projection vector of b on a is y then |x - y| =
In a triangle BC, if the mid points of sides AB, BC, CA are (3,0,0), (0,4,0),(0,0,5) respectively, then AB2 + BC2 + CA2 =
If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g (x)= (16-x)C(2x-1) is
The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} sin^2xcos^2x(sinx+cosx)dx=\)
\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)
\(∫\frac{dx}{(x2+1) (x2+4)} =\)
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) =
If ∫ \(\frac{x^{49} Tan^{-1} (x^{50})}{(1+x^{100})}\)dx = k(Tan-1 (x50))2 + c, then k =