List of practice Questions

Find the mean of the following data using the direct method:

If \( \tan A = \frac{3}{4} \), find \( \sin A \) and \( \sec A \).

Solve the quadratic equation: \( 2x^2 + 5x - 3 = 0 \)

Find the coordinates of the point which divides the line segment joining A(3, –2) and B(5, 4) in the ratio 2:3.

The sum of the first 20 terms of an AP is 820. If the first term is 5, find the 20th term and the common difference.

Rearrange the following parts to form a meaningful sentence:
P. technological advancement
Q. has led to
R. in many fields
S. a significant leap

The expression given below shows the variation of velocity \( v \) with time \( t \): \[ v = At^2 + \frac{Bt}{C + t}. \] The dimension of \( ABC \) is:

An aqueous solution of NaOH was made and its molar mass from the measurement of osmotic pressure at 27°C was found to be 25 g mol$^{-1$.}
Calculate the percentage dissociation of NaOH in this solution.

Solve the equation \(4x^2 - 9x + 3 = 0\), using quadratic formula.

A small conducting sphere A of radius \( r \) charged to a potential \( V \), is enclosed by a spherical conducting shell B of radius \( R \). If A and B are connected by a thin wire, calculate the final potential on sphere A and shell B.

How many grams of sodium chloride (NaCl) are produced when 2.0 moles of sodium (Na) react with excess chlorine gas (Cl\(_2\)? The balanced chemical equation for the reaction is: \[ 2 \, \text{Na} (s) + \text{Cl}_2 (g) \rightarrow 2 \, \text{NaCl} (s) \]

You are Mrs. Savita Manjrekhar, a professor in English. You are invited to be one of the judges for the inter-school debate competition by the Principal of J.M. Public School, Cochin. Write a formal letter expressing your inability to accept the invitation.

The input voltage \( v(t) \) and current \( i(t) \) of a converter are given by, \[ v(t) = 300 \sin(\omega t) \, {V} \] \[ i(t) = 10 \sin\left(\omega t - \frac{\pi}{6}\right) + 2 \sin\left(3\omega t + \frac{\pi}{6}\right) + \sin\left(5\omega t + \frac{\pi}{2}\right) \, {A} \] where \( \omega = 2\pi \times 50 \) rad/s. The input power factor of the converter is closest to:

A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find the probability that
(i) it bears a 2-digit number
(ii) the number is a perfect square.

If $6 + 2 = 16$, $7 + 3 = 22$, then $8 + 4 = ?$

Find the effective resistance of the network of resistors between points A and F as shown in the figure.

In the given graph, the polynomial \(p(x)\) is shown. Number of zeroes of \(p(x)\) is