List of practice Questions

$∫_{-\pi}^{\pi} \frac{2x(1+sinx)}{1+cos^2x}dx $ is equal to?

The molar conductivities of a divalent cation (M²⁺) and monovalent anion (A^-) are 57 S cm^-1 mol^-1 and 73 S cm^-1 mol^-1 respectively. Then find the total molar conductivity shown by their compound in S cm^-1 mol^-1

Consider the following statements:
Statement I: Stability of +1 oxidation state increases down the group in group-13.
Statement II: Atomic radius of Ga is greater than that of Al.

In which of the following compounds Mn has the highest oxidation state?

Let f(x) = $x^2 - 5x$ and $g(x) = 7x - x^2$, then the area between the curves equals to:

Which metal shows the highest and maximum number of oxidation states?

A rectangle ABCD with ABCD with AB = 2 and BC = 4 is inscribed in rectangle PQRS such that vertices of ABCD lie on sides of PQRS then maximum possible area(in sq. unit) of rectangle PQRS is :

Two lines passing through (2, 3) parallel to coordinate axes. A circle of unit radius touches both the lines and lies on the origin side. Then the shortest distance of point (5,5) from the circle is:

Identify the change occuring in oxidation state of Mn in cell reaction of dry cell of clock during its use

Sum of the number π and nt bonds in the ethylene molecule is x. The value of x is

Which of the following cation will give green colour in Borax bead test

If the number of neutrons in the most abundant isotope of boron is 'x' and its highest oxidation state in unsaturated compound is 'y', then find the value of (x+y).

What is the correct order of strength of following ligands according to the spectrochemical series?

Assertion: Trans But-2-ene is less polar than cis But-2-ene
Reason: Trans But-2-ene has zero dipole moment

Consider the reaction:
Fe₂0₃(s) + 3CO(g) = 2Fe(s) + 3CO₂(g)
Which of the following will not affect the equilibrium state:
(I) Addition of Fe₂O₃
(II) Addition of CO₂
(III) Decreasing mass of Fe₂O₃
(IV) Removal of CO

Match the column. [Given: mass of sun = $M_s$ | mass of earth = $M_e$ | Radius of earth = R | Distance between the Sun and the Earth = a]

List-I		List-II
(A)	Kinetic energy of Earth	(I)	$-\frac{GM_sM_e}{a}$
(B)	Potential energy of Earth and Sun	(II)	$\frac{GM_sM_e}{2a}$
(C)	Total energy of Earth and Sun	(III)	$\frac{GM_e}{ R}$
(D)	Escape energy from surface of Earth per unit mass	(IV)	$\frac{GM_sM_e}{2a}$

Choose the correct answer from the options given below:

In YDSE for wavelength $λ = 5000 A$ , slit distance $d = 3 mm$ and screen distance of $2 m$, the intensity at a point which is $3 cm$ away from central maxima (assume intensity of light for each source is $I_0$) is $xl_0$ then x is

$ \lim_{t \rightarrow x} \frac{t^2f(x) - x^2 f(t)}{t-x} = 1$, then 2f(2) + 3f(3) equals to:

Three helium atoms from carbon at high temperature due to fusion. Masses of helium and carbon nuclei a.m.u are 4.0002 and 12 respectively . Find energy released in the process

Find the current I in the given circuit

Two concentric conducting rings of radius a and b are placed as shown in diagram (a < < b). Find coefficient of mutual inductance of rings

Find dimension of \(\sqrt{G}\).𝞵, where G is universal gravitational constant and 𝞵 is energy gradient

The ratio of radius of gyration of uniform hollow sphere and uniform solid sphere about its diameter is _______ (both have the same radius)

The maximum amplitude of an amplitude-modulated wave is found to be 15V while its minimum amplitude is found to be 3V. The modulation index is: