Q1.

If The ratio of the roots of the equations 4x2 - 6x + p is 1 : 2, then the value of p will be. 

  • 2

  • 1

  • -3

  • -4

Solution:

NA

Q2.

Find the positive value of k for which the equations

x2 + kx + 64 = 0 and x2 - 8x + k = 0will have real roots

  • 12

  • 16

  • 18

  • 22

Solution:

NA

Q3.

The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right angled triangle is formed. The side of the equilateral triangle is

  • 17 units

  • 16 units

  • 15 units

  • 13 units

Solution:

NA

Q4.

A man rowing at the rate of 5 km in an hour in still water takes thrice as much time in going 40 km up the river as in going 40 km down . Find the rate at which the river flows : 

  • 9 km/hr 

  • 2.5 km/hr 

  • 12 km/hr 

  • None 

Solution:

NA

Q5.

If area and perimeter of a rectangle is 6,000 cm2 and 340 cm respectively, then the lenght rectangle is :  

  • 140

  • 120

  • 170

  • 200

Solution:

NA

Q6.

If the lenght of  a rectangle is 5 cm more than the breadth and if the perimeter of the rectangle is 40 cm , then the length & breadth of the rectangle will be :

  • 7.5 cm , 2.5 cm 

  • 10 cm, 5 cm

  • 12.5 cm , 7.5 cm

  • 15.5 cm, 10.5 cm 

Solution:

NA

Q7.

Roots of the equation 3x2 - 14x + k  = 0 will be reciprocal of each other if : 

  • k = -3 

  • k = 0

  • k = 3

  • k = 14 

Solution:

NA

Q8.

If the ratio of the roots of the Equation 4x2 - 6x + p = 0 is 1 : 2 then the value of p is 

  • 1

  • 2

  • -2

  • -1

Solution:

NA

Q9.

Roots of equation 2x2 + 3x + 7 = 0 are a and b . The value of

ab-1  + ba-1 is  

  • 2

  • 3/7

  • 7/2

  • -19/14

Solution:

NA 

Q10.

If a and b are the roots of the equation x2 + 7x + 12 = 0 , then the equation whose roots (a + b)2   and (a - b)2 will be :

  • x2 - 14x + 49  = 0

  • x2 - 24x + 144 = 0 

  • x2 - 50x + 49 = 0 

  • x2 - 19x + 144 = 0 

Solution:

NA

Q11.

If a and b be the roots of the quadratic equation 2x2 - 4x = 1 , the value of  (a2/b) + (b2/a) is __________ . 

  • -11

  • 22

  • -22

  • 11

Solution:

NA

Q12.

If   ax2 + bx + c = 0 ,   has equal roots, then find the value of c.

  • \( {b^2 \over 4a}\)

  • 2b

  • \({-b \over 2a}\)

  • 4b

Solution:

NA

Q13.

If one root of a equation is 2 + \( {\sqrt{5}\ }\)

then find the quadratic equation.

  • x2 + 4x - 1 = 0

  • x2 - 4x - 1 = 0

  • x2 - 6x - 4 = 0

  • x2 + 3x + 2 = 0

Solution:

NA

Q14.

If difference between the roots of the equation x2 - kx + 8 = 0 is 4, then the value of k is ________.

  • \(x = {\pm 4\sqrt{3} \ }\)

  • 5

  • -4

  • \(x = {\pm 5\sqrt{6} \ }\)

Solution:

NA

Q15.

If one root of the equation 4x2 - 2x + (k - 4) = 0, be the reciprocal of the other, then find k.

  • -5

  • 9

  • 8

  • -6

Solution:

NA

Q16.

If one root of the equation ax2 + bx + c = 0 is three times the other, then find ac : b2 

  • 7 : 16

  • 16 : 3

  • 2 : 1

  • 3 : 16

Solution:

NA

Q17.

A two-digit number if four times the sum and three times the product of its digits, find the number.

  • 24

  • 45

  • 51

  • 60

Solution:

NA

Q18.

The condition if one root is twice the other in quadratic equation ax2 + bx + c =0 is 

  • b = 2ac

  • 2b2 = 9ac

  • b2 = 4ac

  • b = ac

Solution:

NA