List of practice Questions

If $U= \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$, $A = \{2, 4, 7\}$, $B = \{3, 5, 7, 9, 11\}$ and $C = \{7, 8, 9, 10, 11\}$, compute $(A \cap U) \cap (B \cup C)$.

If two circular arcs of the same length subtend angles of $60^{\circ}$ and $80^{\circ}$ at their respective centres, then the ratio of their radii is

If two coins are tossed 5 times, the chance that there will be 5 heads and 5 tails is

If two events are independent, then

If two identical bar magnets, each of length I , pole strength m and magnetic momen M are placed perpendicular to each other with their unlike poles in contact, the magnetic moment of the combination is

If $\theta =\cot^{-1}7+\cot ^{-1}8+\cot^{-1}18$, then $\cot\,\theta $ is equal to

If three particles of masses 2kg, 1kg and 3 kg are placed at comers of an equilateral triangle of perimeter 6m then the distance of center of mass which is at origin of particles from 1kg mass is (approximately) (Assume 2kg on x-axis )

If travelling at same speeds, which of the following matter waves have the shortest wavelength?

If the work done in stretching a wire by $1 \,mm$ is $2 J$, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by $1 \,mm$ is

If there were a smaller gravitational effect which of the following forces do you think would alter in some respect?

If $\theta$ and $\phi$ are acute angles, $\sin \, \theta = \frac{1}{2} , \cos \, \phi = \frac{1}{3},$ then the value of $\theta + \phi $ lies in

If $\theta$ and $\phi$ are the roots of the equation $8x^2 + 22x + 5 = 0$ , then

If the velocity of an electron in Bohr?? first orbit is $2.19 \times 10^6\, m\, s^{-1}$, what will be the de Broglie wavelength associated with it?

If the wavelength of first member of Balmer series of hydrogen spectrum is 6564 A$^\circ$, the wavelength of second member of Balmer series will be:

If the wavelength of the first line of the Balmer series of hydrogen is $6561 \, ?$, the wavelength of the second line of the series should be

If the time of flight of a projectile is doubled, what happens To the maximum height attained

If the value of $1 + 2 + 3 + ..........+n $ is $55,$ then the value of $1^3 + 2^3 + 3^3 + ..........+ n^3$ is

If the value of force is $100 \,N$ and value of acceleration is $0.001 \,ms^{-2}\, s$, what is the value of mass in this system of units ?

If the temperature of hot black body is raised by $5\%$, rate of heat energy radiated would be increased by how much percentage ?

If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is

If the three planes x = 5, 2x - 5ay + 3z - 2 = 0 and 3bx + y - 3z = 0 contain a common line, then (a, b) is equal to

If the standard electrode potential of $Cu^{2+}/ Cu$ electrode is 0.34 V, what is the electrode potential of 0.01 M concentration of $Cu^{2+}$?(T = 298 K)

If the sum of the roots of the equation $(m + 1) x^2 + 2mx + 3 = 0 $ is $1$, then the value of $m$ is

If the set $A$ contains $5$ elements and the set $B$ contains $6$ elements, then the number of one-one and onto mappings from $A$ to $B$ is

If the set A has p elements, B has q elements, then the number of elements in $A \times B$ is