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Welcome to ICOME Quiz Corner

Q1. Is 194 a term of sequence 3,8,13,-------- .

(a) Yes (b) No (c) Can't say

Solution.
(b) No
Tn = 194
a + (n - 1)d = 194
3 + (n - 1)5 = 194
3 + 5n - 5 = 194
5n - 2 = 194
5n = 196
n =
196 / 5

n = 39.2
n is not a natural number so 194 is not a term of the given sequence
Solution

Q2. Sum of three consecutive terms of an A.P is 60, find middle term.

(a) 40 (b) 5 (c) 10 (d) 20

Solution.
Three consecutive terms of an A.P a - d, a , a + d

a - d + a + a + d = 60

3a = 60

a = 20
Solution

Q3. Two AP's have the same difference . The difference between their 10th term is 1122. What is the difference between their 93rd term .

(a) 93 (b) 20 (c) 122 (d) 1122

Solution.
(d) 1122

Let the two A.P's be a1,a2 --------an and b1,b2, b3---------bn, d is common difference an = a1 + (n - 1)d
an - bn = a1 - b1 (independent of n).
Solution

Q4. How many numbers of two digits are divisible by 7?

(a) 11 (b) 13 (c) 15 (d) 14

Solution.
Sequence will be 14, 21, 28--------98. 98 is the last number of two digits that is divisible by 7,

Tn = 98

14 + (n-1)d = 98

14 + 7n - 7 = 98

n = 13
Solution

Q5. If the Tn of an A.P is 2n+3, find the sum of first n terms of an A.P.

(a) n(n + 4) (b) n(n - 4) (c) (n + 4) (d) n

Solution.
Tn = 2n + 3

T1 = 5

Sn = n/2(a + l)

= n/2 (5 + 2n + 3)

= n/2(8 + 2n)
n(4 + n)
Solution

Q6. The first term of an A.P is P and its common difference is s, find its 10th term.

(a) 2PS (b) 9S (c) P- 9S (d) P + 9S

Solution.
Tn = a + (n - 1)d

T10 = P + 9S.
Solution

Q7. Which number is added both side to solve a equation x2 + (b/a)x + c/a = 0 by completing the square.

(a) b/2a (b) b/2c (c) (2a/c)2 (d) (b/2a)2

Solution.
(d) (b/2a)2
Solution

Q8. Curve of the quadratic equation 2x2 + 4x + 1 opens __________.

(a) upwards (b) downward (c) can't say

Solution.
(a) upwards
Solution

Q9. For which value of k equation ky2 - 5y + k = 0 has real and equal roots.

(a) ∓ 2/3 (b) ∓ 3/5 (c) ∓ 5/2 (d) ∓ 2/3

Solution.
(c) ∓ 5/2
Solution

Q10. For which value of C the equation ax2 + 2bx + C = 0 has real and equal roots.

(a) b/a (b) b2/a (c) a/b (d) a2/b

Solution.
b2 - 4ac = 0

4b2 - 4ac = 0

b2 = 4ac

C = b2/a
Solution