List of practice Questions

Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1=7$ and common difference 8. Let $T_1, T_2, T_3, \ldots$ be such that $T_1=3$ and $T_{n+1}-T_n=a_n$ for $n \geq 1$. Then, which of the following is/are TRUE ?

Which element has more electron gain enthalpy among chalcogen group?

Study the following table and answer the questions based on it. Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.

Year	Item of Expenditure
Year	Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98

Correct the sentence – Vanilla ice cream is very cold to eat.

Identify tense of the sentence: I had called him over lunch last week.

Convert in reported speech - The teacher, “do you know how to write an essay?”

Pick the compound word.

Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAⁿ + mB^m = I} is _______.

A van is moving with a speed of 108 km/hr on a level road where the coefficient of friction between the tyres and the road is 0.5. For the safe driving of the van, the minimum radius of curvature of the road shall be (Acceleration due to gravity, g=10 m/s²)

Considering only the principal values of the inverse trigonometric functions, the value of $\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^2}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^2}+\tan ^{-1} \frac{\sqrt{2}}{\pi}$ is ___

Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}$ If $\sin (\alpha+\beta)=\frac{1}{3}$ and $\cos (\alpha-\beta)=\frac{2}{3}$, then the greatest integer less than or equal to $\left(\frac{\sin \alpha}{\cos \beta}+\frac{\cos \beta}{\sin \alpha}+\frac{\cos \alpha}{\sin \beta}+\frac{\sin \beta}{\cos \alpha}\right)^2$ is ____.

The maximum speed of a particle in S.H.M. is V. The average speed is

A galvanometer of resistance G has voltage range V_g. Resistance required to convert it to read voltage up to V is

Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A :Cߏ∩B ≠ φ} is _____________.

An ideal gas of density $\rho=02 \,kg \, m ^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=08 \,kg \,s ^{-1}$ from its lower end, and escapes through the upper end as shown in the figure The cross-sectional area of the lower end is $A_1=01 \, m ^2$ and the upper end is $A_2=04 \, m ^2$ The pressure and the temperature of the gas at the lower end are $600 \,Pa$ and $300 \,K$, respectively, while its temperature at the upper end is $150 \,K$ The chimney is heat insulated so that the gas undergoes adiabatic expansion Take $g=10 \,ms ^{-2}$ and the ratio of specific heats of the gas $\gamma=2$ Ignore atmospheric pressure Which of the following statement(s) is(are) correct?

Let the matrix $A=\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$ and the matrix $B_0=A^{49}+2 A^{98}$ If $B_n=\text{Adj}\left(B_{n-1}\right)$ for all $n \geq 1$, then $\text{det}\left( B _4\right)$ is equal to :

Which of the following statement is correct ?

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Two identical balls A and B thrown with same velocity ’u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height h₁ and h₂ respectively, then

$R=\sqrt{4ℎ1ℎ2}.$

Reason R: Product of said heights.

$h_1h_2=(\frac{u^2sin^2θ}{2g}).(\frac{u^2cos^2θ}{2g})$

The graph between $\frac 1u$ and $\frac 1v$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5, and its both the surfaces have the same radius of curvature R. The value of R will be______cm.
(where u = object distance, v = image distance)

The graph between 1/u and 1/v for a thin convex lens

Let $z$ be a complex number with non-zero imaginary part If $\frac{2+3 z+4 z^2}{2-3 z+4 z^2}$ is a real number, then the value of $|z|^2$ is ___ .

Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis of MO Theory, by removal of an electron?
(A) NO
(B) N₂
(C) O₂
(D) C₂
(E) B₂
Choose the most appropriate answer from the options given below :

Outermost electronic configurations of four elements A,B,C,D are given below:
(A) 3s² (B) s²3p¹ (C) 3s²3p³ (D) 3s²3p⁴
The correct order of fist ionization enthalpy for them is:

For the reaction H₂F₂(g) → H₂(g) + F2(g), ΔU = –59.6 kJ mol^–1 at 27°C. The enthalpy change for the above reaction is (–) _______ kJ mol–1 [nearest integer] Given: R = 8.314 J K–1 mol^–1.

The correct decreasing order of priority of functional groups in naming an organic compound as per IUPAC system of nomenclature is

The major product of the following reaction is