List of practice Questions

For each binary operation * defined below, determine whether * is commutative or associative.
(i) On Z, define a * b=a−b
(ii) On Q, define a * b=ab+1
(iii) On Q, define a * b= $\frac {ab}{2}$.
(iv) On Z⁺, define a * b=2ab
(v) On Z⁺, define a * b=ab
(vi) On R−{−1},define a * b= $\frac {a}{b+1}$

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.

Find the value of $tan^{-1\sqrt3-sec^{-1}(-2)}$ is equal to

Find the value of if sin^-1$x=y$, then

What is the perpendicular distance of the point P(6, 7, 8) from xy-plane?

Pathogenecity of bacteria causing tuberculosis and leprosy is due to

Find the principal value of cosec^-1$(-\sqrt2)$

Find the principal value of cos^-1$\bigg(-\frac{1}{\sqrt2}\bigg)$

Find the principal value of sec^-1$(\frac{2}{\sqrt3})$

A disc of mass 2kg and diameter 2m is performing rotational motion. Find the work done, if the disc is rotating from 300rpm to 600rpm.

Find the principal value of tan^-1$(-1)$

Find the principal value of cos^-1$\bigg(-\frac{1}{2}\bigg)$

Find the principal value of tan^-1$\bigg(-\sqrt3\bigg)$

Find the principal value of cosec^-1$(2)$

Find the principal value of cos^-1$\bigg(\frac {\sqrt3} {2}\bigg)$

There is an air filled $1 \,pf$ parallel plate capacitor. When the plate separation is doubled and the space is filled with wax, the capacitance increases to $2\,pf$. The dielectric constant of wax is

Haemophilia disease in man is linked with

Find the principal value of sin^-1$\Big(\frac {-1}{2}\Big)$

Find which of the operations given above has identity.

Let * be a binary operation on the set Q of rational numbers as follows:
(i) a * b=a−b
(ii) a * b=a²+b²
(iii) a * b=a+ab
(iv) a * b= (a−b)²
(v) a * b= $\frac {ab} {4}$
(vi) a * b=ab²

Find which of the binary operations are commutative and which are associative.

Let * be the binary operation on N defined by a * b=H.C.F. of a and b. Is * commutative? Is * associative? Does there exist identity for this binary operation on N?

Is * defined on the set {1,2,3,4,5} by a*b=L.C.M. of a and b a binary operation? Justify your answer.

Let * be the binary operation on N given by a*b=L.C.M. of a and b. Find
(i) 5*7, 20*16
(ii) Is * commutative?
(iii) Is * associative?
(iv) Find the identity of * in N
(v) Which elements of N are invertible for the operation *?

Let*′ be the binary operation on the set {1,2,3,4,5} defined by a*′b=H.C.F. of a and b. Is the operation *′ same as the operation * defined in Exercise 4 above? Justify your answer.

Consider a binary operation * on the set {1,2,3,4,5} given by the following multiplication table.
(i) Compute (2 * 3)*4 and 2 *(3 * 4)
(ii)Is * commutative?
(iii)Compute (2 * 3)*(4 * 5).

(Hint: use the following table)

*	1	2	3	4	5
1	1	1	1	1	1
2	1	2	1	2	1
3	1	1	3	1	1
4	1	2	1	4	1
5	1	1	1	1	5