List of practice Questions

A small ball of mass \( M \) and density \( \rho \) is dropped in a viscous liquid of density \( \rho_0 \). After some time, the ball falls with a constant velocity. What is the viscous force on the ball?
A current of 10 A exists in a wire of cross-sectional area of \( 5 \times 10^{-6} \, \text{m}^2 \) with a drift velocity of \( 2 \times 10^{-3} \, \text{m/s} \). The number of free electrons in each cubic meter of the wire is:
Under the same load, wire A having length 5.0 m and cross-section \( 2.5 \times 10^{-5} \, \text{m}^2 \) stretches uniformly by the same amount as another wire B of length 6.0 m and a cross-section \( 3.0 \times 10^{-5} \, \text{m}^2 \) stretches. The ratio of the Young's modulus of wire A to that of wire B will be:
Mass numbers of two nuclei are in the ratio of 4:3. Their nuclear densities will be in the ratio of:
If it was a Friday on 1 January 2016, what was the day of the week on 31 December 2016?
In this question, there are three statements followed by conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follow from the three statements. 
Statements:
  • All books are ledgers.
  • All pens are keys.
  • Some pens are books.
Conclusions:
  • I. Some ledgers are keys.
  • II. Some keys are books.
In a class of 20 students, Alisha’s rank is 15th from the top. Manav is 4 ranks above Alisha. What is Manav’s rank from the bottom?
A is the brother of B. A is the brother of C. To determine the relation between B and C, what minimum information is necessary?
A man is facing west. He runs 45° in the clockwise direction and then another 180° in the same direction and then 270° in the anticlockwise direction. Which direction is he facing now?
In the following figure, how many educated people are employed
many educated people are employed
If NATION is coded as 467234 and EARN is coded as 1654, then ATTENTION should be coded as:
The monthly salary for a person who follows the same expense pattern, but has a petrol expense of Rs 500 p.m., is:
The annual saving for such a person will be approximately:
For a person, whose monthly salary is Rs 6,000 p.m., how many items are there on which he has to spend more than Rs 1,000 p.m.?
For real numbers \(x\) and \(y\), we define \(x R y\) iff \(x - y + \sqrt{5}\) is an irrational number. Then, relation \(R\) is:
In four schools \( B_1, B_2, B_3, B_4 \), the number of students is given as follows: \[ B_1 = 12, \quad B_2 = 20, \quad B_3 = 13, \quad B_4 = 17 \] A student is selected at random from any of the schools. The probability that the student is from school \( B_2 \) is:
Let \( f(x) \) be a polynomial function satisfying \[ f(x) \cdot f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{x}\right). \] If \( f(4) = 65 \) and \( I_1, I_2, I_3 \) are in GP, then \( f'(I_1), f'(I_2), f'(I_3) \) are in:
If \( z_r = \cos \frac{r\alpha}{n^2} + i \sin \frac{r\alpha}{n^2} \), where \( r = 1, 2, 3, ..., n \), then the value of \( \lim_{n \to \infty} z_1 z_2 z_3 ... z_n \) is:
Evaluate the limit: \[ L = \lim_{x \to 0} \frac{35^x - 7^x - 5^x + 1}{(e^x - e^{-x}) \ln(1 - 3x)} \]
If the roots of the quadratic equation $$ (a^2 + b^2) \, x^2 - 2 \, (bc + ad) \, x + (c^2 + d^2) = 0 $$ are equal, then: 
Let \( z \neq 1 \) be a complex number and let \( \omega = x + iy, y \neq 0 \). If \[ \frac{\omega -\overline{\omega}z}{1 -z} \] is purely real, then \( |z| \) is equal to
If A, B, C, D are the angles of a quadrilateral, then \[ \frac{\tan A + \tan B + \tan C + \tan D}{\cot A + \cot B + \cot C + \cot D} = \]
The points A(4, -2, 1), B(7, -4, 7), C(2, -5, 10), and D(-1, -3, 4) are the vertices of a:
The circle touching the y axis at a distance 4 units from the origin and cutting off an intercept 6 from the x axis is: (A) \(x^2 + y^2 \pm 10x - 8y + 16 = 0\)
The coordinates of the foot of perpendicular from the point \( (2, 3) \) on the line \( y = 3x + 4 \) is given by: