List of practice Questions

The number of ways of distributing $50$ identical things among $8$ persons in such a way that three of them get $8$ things each, two of them get $7$ things each, and remaining $3$ get $4$ things each, is equal to
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
The number of ways in which $8$ different flowers can be strung to form a garland so that $4$ particular flowers are never separated is
The number of ways in which a mixed doubles game in tennis can be arranged from 5 married couples, if no husband and wife play in the same game, is
The number of ways in which the six faces of a cube be painted with six different colours is
The number of vectors of unit length perpendicular to the vectors $\vec{a} = 2\hat{i} +\hat{j } +2\hat{k}$ and $\vec{b} = \hat{j} + \hat{k}$ is
The number of ways in which 4 men and 3 ladies sit at a round table so that no two ladies sit together is
The number of unpaired electrons in gaseous species of $Mn^{3+}$, $Cr^{3+}$ and $V^{3+}$ respectively are_____and the most stable species is_____.
The number of vacant orbitals in the valence shell of phosphorus is
The number of terms in the expansion of$ [(a + 4b)^3 (a - 4b)^3]^2$ are
The number of the proper subset of {a, b, c} is:
The number of triangles whose vertices are at the vertices of an octagon but none of whose side happen to come from the sides of the octagon is
The number of $sp^2-s$ sigma bonds in benzene are
The number of structural isomers of $C_3H_9N$ are
The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects ?
The number of real roots of the equation $|2-|1-|x|||=1$ is
The number of real roots of $(x - 1) (x - 2) (x - 3) (x - 4) = 3$ is
The number of rectangles which we can form on a chess board is
The number of six digit numbers, whose all digits are odd (i.e., $1 , 3 , 5 , 7 , 9 )$, is
The number of plant species recorded from India, is
The number of points in $[-2\pi,2\pi]$ , the tangents at which to the curve $y = \sin x$ are perpendicular to the $y-axis$ is
The number of positive integral solutions of $ \frac {x^2 (3x-4)^3 (x-2)^4} {(x-5)^5 (2x-7)^6 }\leq 0$ is .
The number of radial nodes and angular nodes for d-orbital can be represented as
The number of pairs of consecutive odd natural numbers both of which are larger than 10, such that their sum is less than 40, is
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines: