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WorksheetsMTH-101 Key Questions
Total questions: 123
Worksheet time: 4hrs 6mins
Given that the universal set µ = {X E N:1≤ x ≤10}. If A = {x E N:4≤x≤8} and B = {5} are proper subsets of µ. find A' ∆ B'?
{2,4,6}
{4,6,7}
{3,4,6}
{4,7}
Given that the universal set µ = {1,2,……10}. If X = {2,3,5,7} and Y = {1,3,5,7,9} are proper subsets of µ. Find (X n Y)'?
{1,2,4,6,8,9,10}
{2,4,6,8,}
{1,3,5,7,9}
{2,3,5,7}
In a class of 100, all students study mathematics, chemistry or both, if 50 study mathematics and 60 study chemistry; find the number of students that study both mathematics and chemistry?
6
5
10
20
For all x, k E R, which of the following is true:
│x│< k ↔-k
│x│
│x│< k↔ k
│x│< k↔ -x
If A = {all prime factors of 30}, B = {all factors of 18} and C = {all positive even less than 10}. Find (A n B n C)?
{1}
{2}
{3}
{4}
Given that ∑nr=1 (2r + 1)(3r + 1) = ½ n(4n2 + 11n + 9), find Pk+1?
½(k+1)[4(k+1)2 + 11(k+1) + 9]
½ (k+1)[4(k+1) + 11(k+1)2 + 9]
½ (k+1)[4(k2+1) + 11(k+1) + 9]
½ (k+1)[4(k+1)2 + 11(k2 + 1) + 9]
What is the Pk+1 of (1x3) + (2x4) +…..+ n(n + 2) = ⅙n(n + 1)(2n + 7)?
⅙[2k2 + 15k3 + 31k2 + 18]
⅙[2k3 + 15k2 + 31k + 18]
⅙ [2k4 + 15k3 + 31k2 + 18]
⅙[2k5 + 15k3 + 31k2 + 18]
Find the sum of an AP: ⅔, ¾ and 7/12,…up to 19 terms.
22
10
3
0
Insert three arithmetic means between 1 and 13?
4,7 and 11
4,7 and 10
4,7 and 9
3,6 and 9
State the nature of the roots of a quadratic equation: k2 - 6k + 9=0.
Real and unequal
Real and equal
Real and imaginary
All of the above.
Evaluate: 1/α + 1/β.
3/5
-3/5
5/3
-5/3
Compute α2 + β2?
31/16
16/31
-16/31
-31/16
If (x + y) + i(x - y) = 8 + 2i.
5 and 3
3 and 5
-5 and -3
-3 and -5
Express Z in the form: a + bi?
1 + 3i
1 - 3i
1 - 2i
1 + 2i
Find the modulus of Z?
11
10
8
5
If the universal set is {a,b,c…..,j} and A = {a,b,c,d,e} and B = {c,f,h,i}. find AcBc?
{a,b,d,e,f,g,h,i}
{i,j}
{j,g}
{a,b,d,i,j}
In the department of mathematics, all the 50 students speak Nupe or English or both. If 35 speak Nupe and 18 speak English, find the number of students that speaks both languages?
2
3
33
5
Given that 1 + 3 + 5 +…+ (2n - 1) = n2 for all positive integers of n. Find Pk+1?
(k+1)2
(2k+2)2
(2k+1)2
(k-1)2
The following are examples of AP sequence except?
6,2,-2,-6,-10
2,4,8,16,32
3,6,9,12,15,18
x+y,x,x-y,x-2y
The 20th term of the sequence: 6,2,-2,-6,-10…… is?
-69
-70
70
82
Given the AP: 69,64,59,54,…… which of its term is 14?
n = 9
n = 10
n = 11
n = 12
What is the number of terms in an AP? Given that its first and last term are 6 and -50 respectively and its common difference is -4?
13
15
14
16
If α and β are roots of 3x2 + 5x + 7 = 0, find 1/α + 1/β.
-5/7
-5/3
7/3
7/5
Find the coefficient of x5 in the expansion of (x + 3)9?
19683
10206
12006
12600
In a certain class of 100 students, all the students take physics or chemistry subject. If 97 students take physics and 64 take chemistry. The number of students taking only chemistry is?
3
4
5
6
Which of the following is not an irrational number?
2
3
4
5
Given that 1 + 2 + 22 + 23 + ? + 2(n-1) = 2n-1, then by the principle of mathematical induction Pk+1 is?
2k+2 -1
2k+1 -1
2k -1
2k-1 -1
Find the cube roots of the complex number (Z) =-8.
1 - i3 , -2, 1 + i3
1 + 3 , -2, 1 - i3
-2, 1 - i3 , 1 + i3
1 - i3, 1+i3, -2
Given that 1 + x2 + …. xn = xn+1-
Find the cube roots of the complex number (Z) =-8.
1 - i3
-2
1 + i3
1 - i3, 1+i3, -2
Given that 1 + x2 + …. xn = xn+1-1/x-1 for all n>1. Using mathematical induction to show that if P(k) is true then P(k+1) is:
xk+1-1/x-1
x(k+1)-1-1/x-1
xk+2-1/x-1
x2k-1/x-1
Given the sequence: 3.75, 3.5, 3.25, 3,…. Then the 16th term is?
-1
0
1
2
An AP is given by p,2p/3,p/3,0….. find its sixth term?
-P/3
P/3
-2P/3
2P/3
Find the sum of 19 terms in the series: ¾ + 2/3 + 7/12 +….?
2
1
0
-1
The 4th and the 11th terms of an AP are respectively 11 and 32. Then the first and the common difference are:
2 and 3
3 and 2
2 and 4
4 and 2
The three geometric means between 1 and 16 are:
2,4,6
2,4,8
2,4,10
2,4,12
In the series 1 + 3/7 + 9/49 + 27/343 +…. The sum to infinity is?
5/7
7/5
4/7
7/4
The solution to the quadratics equation: x2 - 2(p+2)x + 8p = 0
4p, 2
4p, 2p
4, 2p
4, 2
The cardinality of an empty set is?
2
1
0
Φ
The coefficient of x3y2 in the expansion of (x + y)5 is?
6
24
10
36
Represent the complex number z = 3 + 3i in polar form?
32 (cos π/4 + I sin π/4)
23 (cos π/4 + i sin π/4)
32 (cos 2π + i sin 2π)
23 (cos 2π + i sin 2π)
If α and β are roots of 3x2 + 4x - 1 = 0, find the value of α2 + β2?
22/3
22/9
16/9
20/3
One root of the equation: 27x2 + bx + 8 = 0 is known to be the square of the other. Find the value of b?
-30
30
20
15
If 3 and b are roots of a quadratic equation; find the equation?
x2 + bx + 3b = 0
x2 - (3 + b)x + 3b = 0
x2 + (3 + b)x + 3 = 0
x2 + (3 + b)x + 6 = 0
For any x,y E N one and only one of the following is true: x>y, x+y or y>x. This is known as:
The law of equality
The law of inequality
The law of trichotomy
None of the above
Suppose that A and B are subsets of universal set: U = {x:x E N, 1≤X≤10}, Given that A = {3,4,6} and B = {3,5,7,9}. Find Ac n Bc?
{2,4,6}
Φ
{3,4,6}
{1,2,8,10}
List the elements in the following set: {x:x E R, x2 + 5x - 6}
{2,3}
{-3, -2}
{-2,3}
{-3,2}
Express 1/1+5i in the form of a + bi?
1/26 + 26i/5
-1/26 - 5i/26
1/26 - 5i/26
1/26 + 5i/26
Evaluate α/β = /α ? if α + β are roots of the equation: x2 -12x + 7 = 0.
144/7
7/130
144/130
130/7
(3 + 4i)2 - 3(x - iy) -1 = x + iy; for real gases. Find x and y?
x = -7 and y = 24
x =3 and y = -12
x = -2 and y = -12
x = -24 and y = -7
Find the value of n, if the sums of the following arithmetic progressions are equal: 1, 5, 9, 13, 17 …. nth term 19, 17, 15, 13 …… nth term.
6
7
8
9
Evaluate i1000?
i
-1
-i
1
If Z = -2 + 2i, Compute Z6?
512i
-512i
1 + 512i
1 - 512i
Compute the real and imaginary part of: Z = i-4/2i-3?
Real(z) = 14/13, Im(z) = 5/13
Real(z) = 5/13, Im(z) = 14/13
Real(z) = -14/13, Im(z) = -5/13
Real(z) = -5/13, Im(z) = -14/13
If Z1 = 2 + 2i and Z2 is conjugate of Z1, then Z1 + Z2 is?
4 + 4i
4 + 2i
4
4i
Find α2 + β2, if α and β are roots of the equation: x2 - (1 + n2)x + ½ (1 + n2 + n4) = 0.
1 + n2
1 - n2
n2
n4
Find A U B, if A = {x:x E Z and x < 5}, B = {y:y is a prime number < 10}
{1,2,3,4,5,6,7}
{1,2,3,4,5,7}
{2,3,5}
{2,3,5,7}
Find the power set of P = {x:x is even prime number}
2
1
3
Φ
Let A = {1,2,3,4,5} and B = {a,b,c,d,e}. which of the following statements are correct? (i) A is equal to B (ii) Cardinality of B is equal to cardinality of A (iii) A is equivalent to B (iv) A and B are disjoint Set.
I, ii and iii
ii, iii and iv
All of the above
None of the above
At a breakfast buffet, 93 people choose coffee and 47 people choose juice; 25 people choose both coffee and juice. If each person chose at least one of the beverages. Find the number of people that chose coffee only?
68
118
22
72
How many people visited the buffet?
72
115
118
22
For what value of n, are nth terms of two APS 63, 65, 67, …… and 3, 10, 17,…… are equal?
7
13
14
2
Find the sum of first 20 terms of the sequence: 2,5,8,11,……?
510
410
610
310
The following are AP sequences except?
i) 3,9,15
ii) 2,4,8
iii) -2,0,2
iv) 8,4,2
Which of the following is/are true about conjugate complex numbers? Sum of a complex number and its conjugate is 2 Re(z). Product of a complex number and its conjugate is Re(z) squared plus Im(z) squared. Difference of a complex number with its conjugate is im(z) squared. All of the above (B) i and ii (C) ii and iii (D) None of the above.
All of the above
i and ii
ii and iii
None of the above
If the first three terms of the expansion of (1 + kx)n in ascending powers of x are 1 + 18x + 135x2, find
If the first three terms of the expansion of (1 + kx)n in ascending powers of x are 1 + 18x + 135x2, find n and k?
5 and 3
3 and 6
6 and 3
3 and 5
Find the term independent of x in the expansion (x - 1/x)8?
70
-70
140
-140
Find the 15th term of a GP sequence if the first term is 5 and the common ratio is 2?
16,384
81,920
32,768
40,960
If a and b are roots of the equation: px2 + qx + r = 0, p is not equal to 0. Then evaluate a2b + ab2?
qr/p2
-qr/p2
pr/q2
-pr/q2
If (x + y) + i(x - y) = 7 + 2i, find the values of x and y respectively?
5/2 and 7/2
9/2 and 5/2
-5/2 and -7/2
-9/2 and -5/2
Insert three arithmetic means between 2 to 14?
5,8,11
6,9,12
7,10,13
8,11,14
Find the nth term of the geometric sequence: pq3, p2q5, p3q7,……?
pnq3n+1
pnq2n
p2n+1qn
pnq2n+1
The term of a sequence: a1, a2, a3, …… an where an - an-1 is constant for all integers greater than 1 is called?
Geometric Progression
Geometric Mean
Arithmetic Mean
Arithmetic Progression
Find the two possible values of a and r if the 3rd and 6th terms of a G.P are 1 and 1/8 respectively?
4 and 1/8
4 and ½
4 and -1/2
4 and -1/8
Write 3-i/1+i in the form of a + ib?
1 + 2i
2 + i
1 - 2i
2 - 4i
Find the values of x and y if x + iy = 5 + 4i?
4 and 5
3 and 5
5 and 4
5 and 3
Find b if the three consecutive terms of a GP are: (b - 4), b, (b + 5)?
30
24
20
22
Find the sum to infinity of the series: 1 + 3/7 + 9/49 + 27/343 + 81/2401 +….. ?
7/3
3/7
4/7
7/4
Find the number of people that speak Yoruba only?
40 + x
40 - x
39 + x
39 - x
Find the number of people that speak Igbo only?
18 + x
2(10 - x)
18 - x
2(10 + x)
Find the 20th term of the sequence: p + q, p, p - q, p - 2q?
p - 18q
p + 18q
18p - q
18p + q
If the sum of three consecutive terms of an AP is 15 and their product is 80. Find the first and the common difference respectively?
2 and 4
2 and 3
2 and 5
2 and 6
Find the difference between the complex number (Z) = 4 + 5i and its conjugate.
8 + 10i
8 + 0i
4 + 10i
0 + 10i
State the nature of the roots of the quadratic equation: x2 - 6x + 9 = 0.
Real and equal
Real and unequal
Real and complex
Real and irrational
Find the quadratic equation whose roots are: 3 + 3 and 3 - 5 ?
x2 - 3x + 5 = 0
x2 - 6x + 4 = 0
x2 - 35x + 4
x2 + 35x + 4 = 0
Write the complex number: 3 + -9 in standard form?
3 + 9i
3 - 9i
3 + 3i
3 - 3i
Find the modulus of the complex number?
7
25
-25
5
Find the argument of the complex number?
53.10
-53.10
233.10
-233.10
Find the polar form of the complex number?
-25(cos 53.10 + isin 53.10)
5(cos 53.10 + isin 53.10)
25(cos 53.10 + isin 53.10)
7(cos 53.10 + isin 53.10)
Which of the following is/are true for proving a given result by principle of mathematical induction?
I, ii, and iii
I, ii and iv
I, iii and iv
all of the above
In the quadratic formula, the expression b2 - 4ac is called?
Determinant
Discriminant
Factorization formula
Denominator
Use Pascal's triangle to state the coefficient of the binomial expression (x + y)7?
1, 7, 22, 35, 35, 22, 7, 1
1, 7, 20, 36, 36, 20, 7, 1
1, 7, 21, 35, 35, 21, 7, 1
1, 7, 21, 37, 37, 21, 7, 1
Given that 13 + 23 +….+ n3 = ¼ n2(n + 1)2 ; What is p(k+1)?
¼ (k + 1)2(k + 2)2
¼ (k + 1)2(k + 1)2
¼ (k + 1)2(k + 3)2
¼ (k + 2)2(k + 1)2
If the constant term in the (x - q/x2)10 is 405, find the value of q?
45
3
405
10
Express (1 - 2i)3 in the form of a + ib?
-11 - 2i
11 + 2i
11 - 2i
-11 + 2i
If A and B are two sets, n(A)=10, n(B)=18 and n(A U B)=23. Then n(A n B) is equal to?
28
10
5
18
If A={x:x is natural number less than 15 divisible by 2} and B={x: 0 < x < 8}. Find (A n B)?
{1,2,3,4,6,8}
{2,4,8}
{2,4,5}
{2,4,6}
The representation of {x:x E Z and x2 + 3x + 2 = 0} is?
{-1, 2}
{2, 1}
{-2, 1}
{-2, -1}
In a group of 72 students, 47 have background in electronics, 59 have background in mathematics while 42 have background in both subjects. How many students do not have background in any of the subjects?
8
9
10
11
If 50 study MATHS, 35 study CHEM, 38 study PHY, 10 study MATHS and CHEM, 9 study PHY and MATHS, 4 study CHEM and PHY and all students study at least one of the three subjects, find the number of student that study only CHEM?
5 - x
5 + x
21 + x
21 - x
If A = {1,2,3,4,5}, then the power set of A has?
5 subset
20 subset
32 subset
25 subset
Solve /2x - 3/ = 7?
x = 2, 5
x = 5, -2
x = -5, 2
x = -2, 5
Let R, Z, C, Q, N represent the sets of real numbers, integers, complex, rational and natural numbers respectively. The following are not chain of relation EXCEPT?
N
N
N
N
In the trichotomy law for all x, y E Z one and only one of the following holds: (i) x2 > y (ii) x > y (iii) x2 = y (iv) y > x (v) y2 > x (vi) x = y
ii, iv, vi
ii, v, vi
I, ii, iii
i, v, vi
The smallest set A such that: A U {4,5} = {3,4,5,6,7}?
{3,4,7}
{3,4,5}
{3,6,7}
{4,5,6}
Given that: ∑r2 = ⅙n (n + 1)(2n + 7) for all positive integers n. find Pk+1?
⅙ (k + 1)[(k + 1) + 1][2(k + 1) + 7]
⅙(k + 1)[(k + 1) + 2][2(k + 1) + 8]
⅙ (k + 1)[k + 1][2(k + 2) + 7]
⅙ k[(k + 1) + 1][2(k + 1) + 7]
Find the sum of the nth term of the series: 15 + 11 + 7 + 3 +……
n2(17 - 2n)
n(17 - 2n)
n(17 + 2n)
n(34 - 2n)
What is the number of terms in an AP, given that its first term and last term are 4 and -228 respectively and the common difference is -4?
-57
57
-59
59
The third term of an AP is 20 and the seventh term is 44, find first term and the common difference?
a = -8, d = 6
a = 8, r = 6
a = -8, r = -6
a = 8, d = -6
Insert five arithmetic means between 3 and 51?
3,11,19,27,35
19,27,35,43,51
8,16,24,32,40
11,19,27,35,43
If the three consecutive terms of an AP are: x + 3, 3x + 5, 12. The value of x is?
-1
1
2
-2
If the 5th and 9th of a GP are 2048 and 8 respectively, find the possible value of a and r?
a = 524288, r = ¼
a = -524288, r = ¼
a = 524288, r = -¼
a = -524288, r = -¼
A GP sequence is given by: p, 1, 1/p, 1/p2,…… find the nth term?
p2+n
p-2+n
p-2-n
p2-n
Insert four geometric means between 1 and 1024?
4,16,64,256
16,64,256,1024
4,16,64,1024
1,4,16,64
Find the sum of nth term of GP sequence: xy3, x2y5, x3y7 where x and y > 1.
(xn+1 y2n+3 + xy3)/(xy2 + 1)
(xn+1y2n+3 - xy3)/(xy2 - 1)
(xn-1y2n-3 - xy3)/(xy2 + 1)
(xn+1y2n+3 - xy3)/(xy2 + 1)
The sum to infinity of the series: 1 + ½ + ¼ + 1/8 +….. is?
0
1
2
3
Find the equation whose roots are: 5 + 3 and 5 - 3?
x2 + 10x + 22
x2 - 10x - 22
x2 + 10x - 22
x2 - 10x + 22
If α and β are roots of an equation such that α - β = 1 and αβ = 6, find α andβ.
α = 2, -3 and β= -3, -2
α = -2, 3 and β= -3, 2
α = -3, 2 and β= -2, 3
α = 2, 3 and β= 3, 2
The following are the properties of binomial expansion EXCEPT …….?
There are (n + 1) terms.
The power of the first term is in ascending order and that of the second term is in descending order.
The sum of the powers of the terms is equal to the power of the binomial expansion.
The power of the first term is in descending order and that of the second term is in ascending order.
Expand (2x + 1/x)4?
16x4 - 32x2 + 24 - 8/x2 + 1/x4
16x4 - 32x2 - 24 - 8/x2 - 1/x4
16x4 + 32x2 + 24 + 8/x2 + 1/x4
16x4 + 32x2 - 24 + 8/x2 - 1/x4
The differences of any given complex number z and its conjugate is?
2Re (z)
Re (z)
2Im (z)
Im (z)
Given (2 + iy) (4 - 3i) = 5 + 4i, find the values of y?
y = 1, 5/2
y = 1, -5/2
-1, 5/2
-1, -5/2
