List of practice Questions

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

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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

Consider the binary operation ∨ on the set {1,2,3,4,5} defined by a ∨b=min {a,b}. Write the operation table of the operation∨.

Determine whether or not each of the definition of given below gives a binary operation.
In the event that * is not a binary operation, give justification for this.
(i) On Z⁺, define * by a * b = a − b
(ii) On Z⁺, define * by a * b = ab
(iii) On R, define * by a * b = ab²
(iv) On Z⁺, define * by a * b = |a − b|
(v) On Z⁺, define * by a * b = a

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In one plant adventitious roots are modified for storage and in the other plant a lateral branch with short intemodes and each node bearing a rosette of leaves and a tuft of roots is found. They are

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