The formula of a metal oxide is M0.96 O1. The fractions of metal that exists as M3+and M2+ ions in that oxide are respectively
An engine is dragging a mass of 5000 kg with a velocity of 5 ms-1 along a smooth inclined plane of inclination 1 in 50. Then the power of the engine is
The rate of diffusion of a gas A is √5 times more than of gas B. If the molar mass of A is x gmol-1, the molar mass of B ( in g mole-1) is
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) =
Arrange the following in the correct order of their reactivity towards nucleophilic addition reactions
Identify the correct statement about the oxidation states of group 14 elements
if |a| = 4, |b| = 5, |a - b| = 3 and θ is the angle between the vectors a and b, then cot2 θ =
At 50 °C, the vapour pressure of pure benzene is 268 torr. The number of moles of non-volatile solute per mole of benzene required to prepare a solution having a vapour pressure of 167 torr at the same temperature 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 the radical center of the given three circles x2 + y2 = 1, x2 + y2 -2x - 3 =0 and x2 + y2 -2y - 3 = 0 is C(α,β) and r is the sum of the radii of the given circles, then the circle with C(α,β) as center and r as radius is
In △ABC, if a : b : c = 4 : 5 : 6, then the ratio of the circumference to its in radius is
The ratio of lone pair of electrons to bond pair of electrons in ozone molecule is:
If A = \(\begin{bmatrix} 0 & 3\\ 0 & 0 \end{bmatrix}\)and f(x) = x+x2+x3+.....+x2023, then f(A)+I =
The radius of a circle touching all the four circles (x ± λ)2 + (y ± λ)2 = λ2 is
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) =
\(∫\frac{dx}{(x2+1) (x2+4)} =\)
If the function f(x) = xe -x , x ∈ R attains its maximum value β at x = α then (α, β) =
A tangent PT is drawn to the circle x2 + y2 = 4 at the point P(√3, 1). If a straight line L which is perpendicular to PT is a tangent to the circle (x- 3)2 + y2 = 1, then a possible equation of L is
If ∫ \(\frac{x^{49} Tan^{-1} (x^{50})}{(1+x^{100})}\)dx = k(Tan-1 (x50))2 + c, then k =
If l,m,n and a,b,c are direction cosines of two lines then
\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)
The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of:
A cylindrical vessel, open at the top, contains 15 liters of water. Water drains out through a small opening at the bottom. 5 liters of water comes out in time t1, the next 5 litre in further time t2, and the last 5 litre in further time t3. then:
If sin 2θ and cos 2θ are solutions of x2 + ax - c = 0, then