List of practice Questions

Arun, Bashir and Joseph were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. They admitted Daksh as a new partner who acquired his share entirely from Arun. If Arun sacrificed \( \frac{1}{5} \)th from his share to Daksh, Daksh's share in the profits of the firm will be :

A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is : 

A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is : 

If \( 15 \cot A = 8 \), then \( \sin A = \, ? \)

If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature \(27^\circ\)C. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, \(R = \frac{100}{12} \text{ J mol}^{-1} \text{K}^{-1}\), and molecular mass of \(O_2 = 32 \text{ g/mol}\), 1 atm pressure = \(1.01 \times 10^5 \text{ N/m}^2\)]
Area of a sector of a circle with radius 4 cm and angle 30° is (use \( \pi = 3.14 \)):
Consider a three-firms oligopoly market with a linear demand function given by \( P = 25 - Q \), where \( P \) is the unit price and \( Q \) is the total quantity supplied. The total quantity \( Q = q_1 + q_2 + q_3 \), where \( q_i \) is the output from the \( i^{th} \) firm with \( i = 1,2,3 \). The total cost (TC) curve of firm \( i \) is given by \( TC_i = \alpha_i + 5q_i \), where \( \alpha_i \)'s are positive real numbers. Assuming a Cournot solution exists, the value of \( Q \) is:
Assertion (A): Cu cannot liberate \( H_2 \) on reaction with dilute mineral acids. Reason (R): Cu has positive electrode potential.

Derry in On the Face of it is a victim of self-pity. Analyse Derry’s behaviour in the light of the above statement.
 

"___ how little changes in the environment can have big repercussions" Tishani Doshi in Journey to the End of the Earth gives an awakening call for man. Analyse the theme of the lesson in the light of the above statement.

Select the correct option from those given in brackets, to fill in the blank: The incident made the speaker realize that the discrimination was ____ (dehumanizing / elevating).
Gandhi said, “The real relief for them is to be free from fear.” (Indigo) Roosevelt knew when he said, “All we have to fear is fear itself.” (Deep Water) Analyse the status of sharecroppers and plight of William Douglas in the light of the above statements.
Mr. Lamb: “____ you thought it has an empty house, but inside it’s full.” What do these words tell you about Mr. Lamb? (On the Face of It)
Sophie is an escapist and a dreamer. Franz loves to miss school. Analyse the result of both these characters as a result of their attitude towards life. (Going Places, The Last Lesson)
“Not at all,” Sadao said. “It is inconvenient to have you here any longer.” (The Enemy) What image do you form of Dr. Sadao based on the above remark?
Complete the following suitably: On the days when there was a ‘crowd-shooting’. By the phrase ‘crowd-shooting’, the author refers to _____ .
What is the significance of the third level? ( Third Level)
Given below are two statements:
Statement I: Fig fruit is a non-vegetarian fruit as it has enclosed fig wasps in it.
Statement II: Fig wasp and fig tree exhibit a mutual relationship as the fig wasp completes its life cycle in the fig fruit and the fig fruit gets pollinated by the fig wasp.
If assumed mean of a data is 47.5, \( \sum f_i d_i = 435 \) and \( \sum f_i = 30 \), then mean of that data is:
The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant \(K_1\) and \(K_2\) with thickness \(d/2\) and \(d/2\) respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If \(K_1 = 1.25 K_2\), the value of \(K_2\) is :
The radius of Martian orbit around the Sun is about 1.5 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?
Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the z direction. When filled with a liquid of surface tension \(S\) and density \( \rho \), the liquid surface makes angle \( \theta_0 \) (\( \theta_0 < < 1 \)) with the x-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is: (take \(g\) as the acceleration due to gravity) 

Match List I with List II
List IList II
A. PteridophyteIV. Salvinia
B. BryophyteIII. Polytrichum
C. AngiospermII. Ginkgo
D. GymnospermI. Salvia