List of practice Questions

\(96\cos\frac{π}{33}\cos \frac{2π}{33}\cos\frac{4π}{33}\cos\frac{8π}{33}\cos\frac{16π}{33}\) is equal to
Let a, b, c be three distinct positive real numbers such that (2a)logea = (bc)logeb and bloge2 = alogec. Then 6a + 5bc is equal to _____.
Let f : (-2, 2) → IR be defined by \(f(x) =   \begin{cases}     x[x]       & \quad -2<x<0\\     (x-1)[x],  & \quad 0\leq x<2   \end{cases}\)
Where [x] denotes the greatest integer function. If m and n respectively are the number of points in (-2, 2) at which y = |f(x)| is not continuous and not differentiable, then m + n is equal to ______.
Let y = p(x) be the parabola passing through the points (–1, 0), (0, 1) and (1, 0). If the area of the region \(\{x,y):(x+1)^2+(y-1)^2≤1,y≤p(x)\}\) is A, then 12(π-4A) is equal to__.
Let a common tangent to the curves y2 = 4x and (x – 4)2 + y2 = 16 touch the curves at the points P and Q. Then (PQ)2 is equal to ________.
The distance between two plates of a capacitor is \(d\) and its capacitance is \(C_1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac {2d}{3}\) and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C_2\). The ratio \(\frac {C_2}{C_1}\) is
A gas is compressed adiabatically, which one of the follwing statement is NOT true.
Given below are two statement:
statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g).
statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.
In the light of the above statements , choose the correct answer from the options given below
The time period of a satellite revolving above earth's surface at a height equal to R will be
(given: \(g= \pi^2 \ m/s^2\), R= radius of earth)
Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is :
A rectangular block of mass 5 kg attached to an horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14s. The maximum force exerted by spring on block is _____N.
Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm2. The area of cross section at the oulet is 10 mm2. If the piston is pushed at a speed of 4 cm s-1, the speed of outgoing fluid is ______ cm s-1.
Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm2.
A force of \(-P\hat k \) acts on the origin of the coordinate system. The torque about the point \((2, -3)\) is \(P(a\hat i+b\hat j)\), The ratio of \(\frac ab\) is \(\frac x2\). The value of x is -
If the maximum load carried by an elevator is 1400 kg (600 kg - Passengers + 800 kg- elevator), which is moving up with a uniform speed of 3 ms-1 and the frictional force acting on it is 2000 N, then the maximum power used by the motor is ____ kW. (g=10 m/s2)
An electron revolves around an infinite cylindrical wire having uniform linear charge density \(2×10^{–8}\ Cm^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ____ \(\times 10^6 ms^{-1}\). Given mass of electron = \(9\times10^{-31}\) kg.
an infinite cylindrical wire having uniform linear charge density
If 917 Å be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be _____ Å.
A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses L1 and L2 with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens L1 as shown in the figure. The distance between the object and the image formed by the system of two lenses is _____ cm.
two thin symmetrical coaxial convex lenses L1 and L2 with focal length
A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries as sinusoidally varying current of amplitude 2.5 A and angular frequency 700 rad s–1. The central axes of the loop and selenoid coincide. The amplitude of the emf induced in the loop is x×10–4 V . The value of x is ______ . (Take, \(\pi\) = 22/7)
A straight wire carrying of 14 A is bent into a semi-circular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc is ____ × 10–4 T.
A straight wire carrying of 14 A is bent into a semi-circular arc of radius 2.2 cm
A rectangular parallelopiped is measured as 1 cm × 1 cm × 100 cm. If its specific resistance is 3 × 10-7 Ωm, then the resistance between its two opposite rectangular faces will be _____ ×10-7 Ω.
Match List I with List II:

List I

List II

A16 g of CH4 (g)IWeight 28g
B1 g of H2 (g)II60.2 × 1023 electrons
C1 mole of N2 (g)IIIWeighs 32 g
D0.5 mol of SO2 (g)IV Occupies 11.4 L volume at STP
Choose the correct answer from the options given below:
The correct relationships between unit cell edge length ‘a’ and radius of sphere ‘r’ for face-centred and body-centred cubic structures respectively are:
Ferric chloride is applied to stop bleeding because-
The correct order of metallic character is:
Gibbs energy vs T plot for the formation of oxides is given below.
Gibbs energy vs T plot for the formation of oxides

For the given diagram, the correct statement is -