Relations and Functions Book Back One Mark Online Test

Relations and Functions Book Back One Mark Online Test (10th Standard Mathematics)

Pick how many questions you want and set a time limit, then start. You'll get your score at the end with the correct answer and an explanation for every question. Free, in Tamil and English — 15 questions available.

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If \(n(A \\times B) = 6\) and \(A = \\{1, 3\\}\) then \(n(B)\) is

A.1 B.2 C.3 D.6

If \(A = \\{a, b, p\\}\), \(B = \\{2, 3\\}\), \(C = \\{p, q, r, s\\}\) then \(n((A \\cup C) \\times B)\) is

A.8 B.20 C.12 D.16

If \(A = \\{1, 2\\}\), \(B = \\{1, 2, 3, 4\\}\), \(C = \\{5, 6\\}\) and \(D = \\{5, 6, 7, 8\\}\) then state which of the following statement is true.

A.\((A \\times C) \\subset (B \\times D)\) B.\((B \\times D) \\subset (A \\times C)\) C.\((A \\times B) \\subset (A \\times D)\) D.\((D \\times A) \\subset (B \\times A)\)

If there are 1024 relations from a set \(A = \\{1, 2, 3, 4, 5\\}\) to a set \(B\), then the number of elements in \(B\) is

A.3 B.2 C.4 D.8

The range of the relation \(R = \\{(x, x^2) \\mid x \\text{ is a prime number less than } 13\\}\) is

A.\(\\{2, 3, 5, 7\\}\) B.\(\\{2, 3, 5, 7, 11\\}\) C.\(\\{4, 9, 25, 49, 121\\}\) D.\(\\{1, 4, 9, 25, 49, 121\\}\)

If the ordered pairs \((a+2, 4)\) and \((5, 2a+b)\) are equal then \((a, b)\) is

A.(2, -2) B.(5, 1) C.(2, 3) D.(3, -2)

Let \(n(A) = m\) and \(n(B) = n\) then the total number of non-empty relations that can be defined from \(A\) to \(B\) is

A.\(mn\) B.\(n^m\) C.\(2^{mn} - 1\) D.\(2^{mn}\)

If \(\\{(a, 8), (6, b)\\}\) represents an identity function, then the value of \(a\) and \(b\) are respectively

A.(8, 6) B.(8, 8) C.(6, 8) D.(6, 6)

Let \(A = \\{1, 2, 3, 4\\}\) and \(B = \\{4, 8, 9, 10\\}\). A function \(f: A \\to B\) given by \(f = \\{(1, 4), (2, 8), (3, 9), (4, 10)\\}\) is a

A.Many-one function B.Identity function C.One-to-one function D.Into function

Q10

If \(f(x) = 2x^2\) and \(g(x) = \\frac{1}{3x}\), then \(f \\circ g\) is

A.\(\\frac{3}{2x^2}\) B.\(\\frac{2}{3x^2}\) C.\(\\frac{2}{9x^2}\) D.\(\\frac{1}{6x^2}\)

Q11

If \(f: A \\to B\) is a bijective function and if \(n(B) = 7\), then \(n(A)\) is equal to

A.7 B.49 C.1 D.14

Q12

Let \(f\) and \(g\) be two functions given by \(f = \\{(0, 1), (2, 0), (3, -4), (4, 2), (5, 7)\\}\) and \(g = \\{(0, 2), (1, 0), (2, 4), (-4, 2), (7, 0)\\}\), then the range of \(f \\circ g\) is

A.\(\\{0, 2, 3, 4, 5\\}\) B.\(\\{-4, 1, 0, 2, 7\\}\) C.\(\\{1, 2, 3, 4, 5\\}\) D.\(\\{0, 1, 2\\}\)

Q13

Let \(f(x) = \\sqrt{1+x^2}\) then

A.\(f(xy) = f(x) \\cdot f(y)\) B.\(f(xy) \\ge f(x) \\cdot f(y)\) C.\(f(xy) \\le f(x) \\cdot f(y)\) D.None of these

Q14

If \(g = \\{(1, 1), (2, 3), (3, 5), (4, 7)\\}\) is a function given by \(g(x) = \\alpha x + \\beta\) then the values of \(\\alpha\) and \(\\beta\) are

A.(-1, 2) B.(2, -1) C.(-1, -2) D.(1, 2)

Q15

Let \(f(x) = (x+1)^3 - (x-1)^3\) represents a function which is

A.linear B.cubic C.reciprocal D.quadratic

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About this Relations and Functions test

This free online practice test covers Relations and Functions from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

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