List of practice Questions

Read the following statements:

A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

B. Two bodies P and Q having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by P and Q are in the ratio 1 : 1.15.

C. A carnot Engine working between 100 K and 400 K has an efficiency of 75%.

D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below

Two identical positive charges Q each are fixed at a distance of 2a apart from each other. Another point charge q0 with mass m is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q0 executes SHM. The time period of oscillation of charge q0 will be
A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given \(\pi\) = 3.14)

Let 
\(\stackrel{→}{a} = \hat{i} + \hat{j} + \hat{2k}, \stackrel{→}{b} = \hat{2i} - \hat{3j} + \hat{k}\)
and 
\(\stackrel{→}{c}= \hat{i} - \hat{j} + \hat{k}\)
be three given vectors.
Let \(\stackrel{→}{v}\) be a vector in the plane of \(\stackrel{→}{a}\) and \(\stackrel{→}{b}\) whose projection on \(\stackrel{→}{c}\) is \(\frac{2}{\sqrt3}\).
If \(\stackrel{→}{v}.\hat{j}\) = 7 , then \(\stackrel{→}{v}.(\hat{i}+\hat{k})\) is equal to :

The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be:
(Radius of earth = 6400 km)
As per the given figure, two blocks each of mass \(250\ g\) are connected to a spring of spring constant \(2\ Nm^{–1}\). If both are given velocity v in opposite directions, then maximum elongation of the spring is:
Two projectiles thrown at 30° and 45° with the horizontal, respectively, reach the maximum height in same time. The ratio of their initial velocities is :
A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale.]
A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s2 and then climbs up with an acceleration of 5 m/s2. Choose the correct option (g = 10 m/s2).
Match List-I with List-II
List-I (Compound)List-II (Shape)
(A) \(BrF_5\)(I) bent
(B) \([CrF_6]^{3–}\)(II) square pyramidal
(C) \(O_3\)(III) trigonal bipyramidal
(D) \(PCI_5\)(IV) octahedral
Choose the correct answer from the options given below :
Given two statements below:
Statement I : In \(Cl_2\) molecule the covalent radius is double of the atomic radius of chlorine.
Statement II : Radius of anionic species is always greater than their parent atomic radius.
Choose the most appropriate answer from options given below:
The boolean expression (~(p ∧q)) ∨q is equivalent to:
The value of \(cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})\) is equal to:
Let the equation of two diameters of a circle x2 + y2 – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x2 – y2 = 3 passing through the center of the circle is equal to _______.
Refining using the liquation method is the most suitable for metals with:
Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:
Which of the following can be used to prevent the decomposition of \(H_2O_2\)?
Five numbers, \(x_1, x_2, x_3, x_4, x_5\) are randomly selected from the numbers \(1, 2, 3\),….., \(18\) and are arranged in the increasing order \((x_1<x_2<x_3<x_4<x_5)\). The probability that \(x_2 = 7\) and \(x_4 = 11\) is:
Borazine, also known as inorganic benzene, can be prepared by the reaction of 3-equivalents of “X” with 6-equivalents of “Y”. “X” and “Y”, respectively are:
Which of the given reactions is not an example of a disproportionation reaction?
An expression for a dimensionless quantity P is given by \(P=\frac{α}{β} log_e(\frac{kt}{βx})\); where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be
The dark purple colour of \(KMnO_4\) disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the reaction is :
\(\dot Cl + CH_4 → A + B\)
A and B in the above atmospheric reaction step are:
Which technique among the following, is most appropriate in separation of a mixture of 100 mg of p-nitrophenol and picric acid?
Which of the following compounds is not aromatic?