List of practice Questions

The two equal sides of an isosceles triangle with fixed base \(b\) are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base?
Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is

A short bar magnet placed with its axis at 30º with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to             4.5 × 10-2 J. What is the magnitude of magnetic moment of the magnet?

one million electrons are added to a glass rod. The total charge on the rod is

The resultant capacitance between A and B in the following figure is equal to

Find:
(i) 0.2 × 6
(ii) 8 × 4.6
(iii) 2.71 × 5
(iv) 20.1 × 4
(v) 0.05 × 7
(vi) 211.02 × 4
(vii) 2 × 0.86
In a pond of water, a flame is held 2 m above the surface of water. A fish is at depth of 4 m from water surface. Refractive index of water is 43. The apparent height of the flame from the eyes of fish is:
The sum of n terms of two arithmetic series are in the ratio $2n + 3 : 6n + 5$, then the ratio of their 13th terms is
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
A student read common difference of an A.P. as - 3 instead of 3 and obtained the sum of first 10 terms as - 30. Then the actual sum of first 10 terms is equal to
Describe the changing relationship between the author and his grandmother. Did their feelings for each other change?
The story is divided into pre-War and post-War times. What hardships do you think the girl underwent during these times?

Write the function in the simplest form: \(\tan ^{-1}(\frac{3a^2x-x^3}{a^3-3ax^2}),a>0;\frac {-a}{\sqrt3} \leq x\leq\frac{ a}{\sqrt3}\)

$\frac{x + 4}{x -3} < 2 $ is satisfied when $x$ satisfies
Give two examples of each.
1. Kharif crop
2. Rabi crop
4 cells each of emf2 V and internal resistance of $ 1 O $ are connected in parallel to a load resistor of $ 2 O $ . Then the current through the load resistor is
How does the poet speak to the wind — in anger or with humour? You must also have seen or heard of the wind “crumbling lives”. What is your response to this? Is it like the poet’s?
Why are the classification systems changing every now and then?
From an elevated point $P$, a stone is projected vertically upwards. When the stone reaches a distance $h$ below $P$, its velocity is double of its velocity at a height $h$ above $P$. The greatest height attained by the stone from the point of projection $P$ is
Find the equivalent resistance between terminal A and B for the given network.
the equivalent resistance between terminal A and B

Name the oxometal anions of the first series of the transition metals in which the metal exhibits the oxidation state equal to its group number.

Find RL of R?
RL of P [BM = 200.000
PointStaff Readings
Back side		Staff Readings
Fore side		Remarks
P-2.050 -200.000
Q1.0500.95Change Point
R --1.655 -
There is a critical activity is going to have a cost of Rs. 30,000. If this activity is getting completed in 15 days and this work will done in 12 days there will be a cost of Rs. 54,000? Statement I: This crashing is advisable economical if indirect cost is Rs. 8,500 per day. Statement II: This crashing is advisable economical if indirect cost is Rs. 10,000 per day.
What will be the relative density? 
M = 0.5 percentage of air voids 
γmin = 1.3 gm/cc 
γmax = 1.8 gm/cc
What will the angle of the failure plane from horizontal for sand be? 
σ3=300 
σ1=300+100=400