1. Which quadratic equation has a root (−1 + √−5) ?
a. x2 + 2 x + 6 = 0
b. x2 − 2 x + 6 = 0
c. x2 + 2 x − 6 = 0
d. x2 − 2 x − 6 = 0
2. The sum of the roots of the equation (x + α)(x − β) + ( x − β)(x+ γ) + ( x + γ)(x+ α) = 0, ifa. α + β + γ
b. α = β + γ
c. β = α + γ
d. γ = α + β
3. For what values of k, roots of (k − 1)x2 − (k + 2)x + 4 = 0 will be real and equal?
a. 2,10
b. 12,10
c. 2, 1
d. None
4. Find the value of x4 − 4x3 + 6x2 − 4x + 5; if x = 2 + i.
a. 0
b. 12
c. 5
d. 7
5. The height, in fect, to which a golf ball rises when it is short upward from ground level is described by
h(t) = −16t2 + 48t. Where, t is the time elapsed in seconds. Use the discriminant to determine whether
the golf ball can reach a height of 32 feet or not, and if it can then how many times it reaches that height.
a. Not possible
b. Possible to reach the height 2 times
c. Possible only once
d. None of these
n
n
6. Let n be a positive integer. Then the value of ∑k=0 (−1)k ( ) isk
a. −1
b. 0
c. 1
d. None of them
1
1
1
7. The value of √− + √− + √− +
2
2
2
1±i
a.
2
⋯
∞ is-
b. ±(1+i)
c. ±(1−i)
d. ± ( 1 + i)
2
8. Find the square root of 2i.
a. ±(1−i)
b. ±√2i
c. ±i
d. ±(1+i)
9. Find the condition that one root of the quadratic equation px2 − qx + p = 0 is 1 more than the other.
a. p2 − 4q 2 = 0
b. q 2 − 5p2 = 0
c. q 2 − 4p2 = 0
d. p2 − 5q 2 = 0
10. A company produces 2 types of product. It uses 3 plants for the production. The 1st product requires one
nd
hour in plant 1 and 3 hours in plant 3 for producing item. The 2
product requires 2 hours each in plant 2
and 3 for one production. Total available hours in plants 1,2 and 3 in a week are 4, 12 and 18 respectively.
Profit for each item of product 1 is 3 thousand, and for product 2 is 5 thousand. The possible maximum
weekly profit for the company isa. 18 thousand
b. 33 thousand
c. 36 thousand
d. 3
11. If i2 = −1, then √(8 + 6i) = ?
a. (3+i)
b. −(3+i)
c. ±(3+i)
d. (3−i)
−1
1
12. In the expansion of (1 + x ) , when − 1 < x < 1, the coefficient of x7 isa. 1
b. −1
c.
1
2
1
2
13. Alal and Dulal shopped at the same store. Alal bought 5 kg of apples and 2 kg of bananas and paid
altogether BDT22. Dulal bought 4 kg of apples and 6 kg of bananas and paid together BDT 33. Find the
cost of 1 kg of bananas.
d. −
a. BDT 3.5
b. BDT 3
c. BDT 2.5
d. BDT 4.5
14. (2 − i) is a solution of x2 − 4x + k = 0. Find the value of k.
a. 5 + 8 i
b. 8
c. 8 + 5 i
d. 5
15. For what value of r, the co-efficient of the terms (r + 1)th and (r + 2)th will be equal in the expansion of
3 19
(2x2 + x) ?
a. 11
b. 13
c. 14
d. 10
16. If two consecutive coefficients in the expansion of (1 + x)24 are in the ratio of 4 : 1 then the terms area. 5, 6
b. 4, 5
c. 20,21
d. a & c
17. The coefficient of xn in the expansion of
a. 4n+1 − 1
x
is(1−4x)(1−5x)
b. 4n + 5n
c. 5n − 4n
d. 5n+1 − 1
18. x2 + ax + 8 = 0 -এর একিট ম ূল 4 এবং x2 + a x + b = 0 এর ম ূলদয় সমান হেল b এর মান কত?
a. 4
b. 8
c. 9
d. 12
e. 32
4
19. The value of √−81 is3
a. ± (1 ± i)
√2
3
b. ± (1 ± 2i)
√2
3
c. ± (2 ± i)
√2
3
d. ± (1 ± i)
√2
e. a,d
3 2 16
20. Find the term independent of x in the expansion of ( x − ) .
2
3x
3
a.
11
5
b.
12
7
c.
11
7
d.
12
1 2
4 7
1 a
21. If A = [
],B=[
] and AB−1 = [
] , then a = ?
3 4
3 5
3 5
a.
1
b.
c.
d.
−
1
C
a
N
n
o
n
n
o
e
t
o
f
b
e
t
h
f
e
o
s
u
e
n
d
22. Which one is correct for the inequality 3 ≤ −6 − 5x < 12.
a. 12 ≤ x ≤ −6
b. 1.6 ≤ x ≤ −8.8
c. −3.6 ≤ x ≤ −1.8
d. 1.8 ≤ x ≤ −3.6
23. What is the total number of terms of (x + 3y + 5z)20 ?
a. 231
b. 250
c. 501
d. 102
24. For what values of a, roots of ax2 + 3x + 4 = 0 will be complex?
9
a. a =
16
9
b. a <
16
9
c. a >
16
9
d. a ≥
16
25. The value of √i isa. ±(1+i)
b. ± ( 1 + i)
2
1
c. ± (1+i)
√2
d. ±√2(1+i)
26. If i2 = −1, then the value of
3
a. − + i
2
3
b. + i
2
3
c. − − i
2
d. None of these
2−3i
=?
2i
0
