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

(c) not symmetric

(d) transitive

Answer (c) 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

(c) 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

(c) 0, -1

(d) -1, 1

Answer (c) 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

(c) 360

(d) 240

Answer (c) 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

(c) 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

(c) 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)

(c) 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)

(c) (-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)

(c) (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)

(c) (2, 3)

(d) (1, 3)

Answer (a) (0, 1)

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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

(c) not symmetric

(d) transitive

Answer (c) 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

(c) 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

(c) 0, -1

(d) -1, 1

Answer (c) 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

(c) 360

(d) 240

Answer (c) 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

(c) 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

(c) 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)

(c) 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)

(c) (-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)

(c) (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)

(c) (2, 3)

(d) (1, 3)

Answer (a) (0, 1)

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