Paper II Mathematics

  1. If is a solution of the equation ax2 – 6x + b = 0 where a and b are real numbers, then the value of a + b is equal to
    (A) 10
    (B) 22
    (C) 30
    (D) 29
    (E) 31
  2. If the roots of the equation x2 – bx + c = 0 are two consecutive integers, then b2 – 4c is
    (A) –1
    (B) 0
    (C) 1
    (D) 2
    (E) 3

  3. If and are the roots of the equation ax2 + bx + c = 0, (c ≠ 0), then the equation whose roots are and is
    (A) acx2 – bx + 1 = 0
    (B) x2 – acx + bc + 1 = 0
    (C) acx2 + bx – 1 = 0
    (D) x2 + acx – bc + 11 = 0
    (E)  acx2 – bx – 11 = 0

  4. If a and b are the roots of the equation x2 + ax + b = 0, a≠0, b≠0, then the values of a and b are respectively
    (A) 2 and –2
    (B) 2 and –1
    (C) 1 and –2
    (D) 1 and 2
    (E) –1 and 2

  5. If x2 + px + q = 0, has the roots and , then the value of is equal to
    (A) p2 – 4q
    (B) (p2 – 4q)2
    (C) p2 + 4q
    (D) (p2 + 4q)2
    (E) q2 – 4p

  6. If the sum to first n terms of the A.P. 2, 4, 6, ... is 240, then the value of n is
    (A) 14
    (B) 15
    (C) 16
    (D) 17
    (E) 18

  7. The value of

    is equal to
    (A) –10
    (B) 11
    (C) 14
    (D) 13
    (E) –8

  8. An A.P. consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is
    (A) 6
    (B) 5
    (C) 4
    (D) 3
    (E) 2

  9. If a1, a2 , a3 , ..., an are in A.P. with common difference 5 and if ai aj ≠ –1 for i,j = 1,2,...,n, then
    is equal to

    (A) 
    (B) 
    (C) 
    (D) 
    (E) 

  10. The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 is equal to
    (A) 715
    (B) 702
    (C) 615
    (D) 602
    (E) 589

 

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