List of practice Questions

Answer the following questions in about 40 words each:
(b) What did Roosevelt say about fear in the lesson 'Deep Water'?

A wheel of mass $ 4M $ and radius $ R $ is made of a thin uniform distribution of mass $ 3M $ at the rim and a point mass $ M $ at the center. The spokes of the wheel are massless. The center of mass of the wheel is connected to a horizontal massless rod of length $ 2R $, with one end fixed at $ O $, as shown in the figure. The wheel rolls without slipping on horizontal ground with angular speed $ \Omega $. If $ \vec{L} $ is the total angular momentum of the wheel about $ O $, then the magnitude $ \left| \frac{d\vec{L}}{dt} \right| = N(MR^2 \Omega^2) $. The value of $ N $ (in integer) is:

What is equivalent lens? Derive an expression for equivalent focal length of two lenses of focal lengths $f_1$ and $f_2$ kept at a distance $d$.

Consider the following code:

int a;
int arr[] = {30, 50, 10};
int *ptr = arr[10] + 1;
a = *ptr;
(*ptr)++;
ptr = ptr + 1;
printf("%d", a + arr[1] + *ptr);

Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.

Radha's friend says that Radha is deeply hurt and has ........................ weight.

At a dinner party, six members (A, B, C, D, E, F) are sitting around a circular table. A is sitting next to B, but C is not sitting next to A and B. D is sitting opposite E, and E is sitting next to C. Who is sitting to the left of D?

From the following details, calculate Cash Flow from Investing Activities: - Purchase of Machinery Rs 1,50,000
- Sale of Land Rs 80,000
- Purchase of Investments Rs 50,000
- Interest received Rs 8,000

A double-ended ranging drum (DERD) shearer uni-directionally cuts coal in a longwall panel having the following details:
Shearer drum diameter = 1.4 m
Panel dimension = 1200 m × 200 m × 2.4 m
Web depth = 0.6 m
Average cutting speed = 5 m/minute
Average retreating speed = 10 m/minute
Average operational delay between cuts is 2 hour. There are two production shifts, each of 8 hour duration. The number of days required for complete extraction of the panel is:

The antonym of 'ancient' is

Appreciation of the poem:
Read the following poem and write an appreciation of it with the help of the points given below:
Stopping by Woods on a Snowy Evening
Whose woods these are I think I know.
His house is in the village, though;
He will not see me stopping here
To watch his woods fill up with snow
My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.
He gives his harness bells a shake
To ask if there is some mistake.
The only other sound’s the sweep
Of easy wind and downy flake.
The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.
Robert Frost

A string of length 2 m is vibrating with 2 loops. The distance between its node and adjacent antinode is ............

Colour origin from

What will come in the place of the question mark in the question figure?

The screened nuclear charge of neutral Helium atom is given as $ 1.7e $, where $ e $ is the magnitude of the electronic charge. Assuming the Bohr model of the atom for which the energy levels are $ E_n = - \frac{Z^2}{2n^2} $ atomic units (where $ Z $ is the atomic number), the first ionization potential of Helium in atomic units is:

How many numbers are divisible by 3 between 50 and 500?

Change any one of the following into indirect speech:
(i) She said, "Brother, I shall give you my watch."

If the sequence of one strand of DNA is written as follows: 5' - ATGC ATGC ATGC ATGC ATGC - 3', write down the sequence of the complementary strand in 3' → 5' direction.

Write a note on Intra-Uterine Devices (IUD’s) and their applications.

Give a brief account of different components of a nucleotide.

Give names of any two artificial ecosystems.

What is the number of chromosomes in a female honeybee? What is sex determination system called in them?

The directional derivative of a function $ f(x, y, z) = 4x^2 + 8y^2 + 9z^2 $ at the point $ P(3, 4, 5) $ in the direction vector $ \vec{b} = 2\hat{i} - 3\hat{j} + 4\hat{k} $ is _______ (rounded off to 1 decimal place).

Change any one of the following into indirect narration:
(i) He said to me, "I shall help you today."

Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.