DPP - 02NCERT : Daily Practice Problems - MATHEMATICS - 27/09/2021

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Q1. Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2),
(3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive

Q2. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive

Q3. Show that if f : A → B and g : B → C are one-one, then gof : A → C is
also one-one.

Q4.  Show that if f : A → B and g : B → C are onto, then gof : A → C is
also onto

Q5. Let f : N → Y be a function defined as f(x) = 4x + 3, where,
Y = {y ∈ N: y = 4x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse.

Q6.  Find the value of cos (sec–1 x + cosec–1 x), | x | ≥ 1

Q7. Show that 2tan–1 (cos x) = tan–1 (2 cosec x)

Q8. sin–1 (1 – x) – 2 sin–1 x = π/2, then x is equal to.

Q9. If a matrix has 8 elements, what are the possible orders it can have?

Q10. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:?