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1
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A function f:R+ →R where R, is the set of all nonnegative real numbers) defined by f(x) = 4x + 3 is:
- one-one but not onto
- onto but not one-one
- both one-one and onto
- neither one-one nor onto
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2
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Assertion(A): The domain of the function sec-1 2x is
（-∞, _ 1/2] U [1/2∞）
Reason(R): sec-1 (-2) = - π/4
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A)
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A)
- Assertion (A) is true and Reason (R) is false
- Assertion (A) is false and Reason (R) is true
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3
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Let f: R - {4/3} → R be a function defined as f (x) = 4x/ 3x + 4, Show that f is a one-one function. Also, check whether f is an onto function or not.
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4
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Let A = (x €Z: 0 ≤ x ≤ 12}. Show that R = {(a, b) : a, b, €, A, la - bl is divisible by 4} is an equivalence relation.
Find the set of all elements related to 1. Also write the equivalence class [2].
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5
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Evaluate: sin-1 (sin 3π/4) + cos-1 (cos 3π/4) + tan-1 (1)
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6
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A relation Ron set A = {1, 2, 3, 4, 5) is defined as R = f(x, y) : X2- Y2) < 8} . Check whether the relation R is reflexive, symmetric and transitive.
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7
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Find the value of : tan-1 (- 1/√3) + Cot-1 (1/√3)+ tan-1 [Sin -(π/4)].
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8.
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Find the domain of the function f(x) = sin-1 x2 - 4).
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9.
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Let N be the set of natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc
for all a, b, c, d e N. Show that Ris an equivalence relation.
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10.
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Read the following passage and answer the following questions.
Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin's sister Raji observed and noted the possible outcomes of the throw every time belonging to the set (1,2,3,4,5,6). Let A be the set of players while B be the set of all.
(i) Raji wants to know the number of functions from A to B. Find the number of all possible functions.
(ii) Raji wants to know the number of relations possible from A to B. Find the number of possible relations.
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