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# Maths Online Questions with Answers - 6

Mathematics Entrance Test

Free Maths Online Questions with Answers for the preparation of Engineering Entrance Test like AIEEE, IIT-JEE, CET etc.

Test 3

(1) Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

(a) a function

(b) reflexive

© not symmetric

(d) transitive

Answer © not symmetric

(2) Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

(a) x2 + 18x + 16 = 0

(b) x2 - 18x - 16 = 0

© x2 + 18x - 16 = 0

(d) x2 - 18x + 16 = 0

Here x2 read as x Square

Answer (d) x2 - 18x + 16 = 0

(3) If (1 – p) is a root of quadratic equation x2 + px + (1-p) = 0 , then its roots are

(a) 0, 1

(b) -1, 2

© 0, -1

(d) -1, 1

Answer © 0, -1

(4) How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

(a) 120

(b) 480

© 360

(d) 240

Answer © 360

(5) If one root of the equation x2 + px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, then the value of ‘q’ is

(a) ^{49}⁄_{4}

(b) 4

© 3

(d) 12

Answer (a) ^{49}⁄_{4}

(6) A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is and when he retires 40 meter away from the tree the angle of elevation becomes . The breadth of the river is

(a) 20 m

(b) 30 m

© 40 m

(d) 60 m

Answer (a) 20 m

(7) The graph of the function y = f(x) is symmetrical about the line x = 2, then

(a) f(x + 2)= f(x – 2)

(b) f(2 + x) = f(2 – x)

© f(x) = f(-x)

(d) f(x) = - f(-x)

Answer (b) f(2 + x) = f(2 – x)

(8) A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is

(a) (2, 4)

(b) (2, -4)

© (-^{9}⁄_{8}, ^{9}⁄_{2})

(d) (^{9}⁄_{8}, ^{9}⁄_{2})

Answer (d) (^{9}⁄_{8}, ^{9}⁄_{2})

(9) The normal to the curve x = a(1 + cosq), y = asinq at ‘q’ always passes through the fixed point

(a) (a, 0)

(b) (0, a)

© (0, 0)

(d) (a, a)

Answer (a) (a, 0)

(10) If 2a + 3b + 6c =0, then at least one root of the equation ax2 + bx + c lies in the interval

(a) (0, 1)

(b) (1, 2)

© (2, 3)

(d) (1, 3)

Answer (a) (0, 1)

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