# COMBINE QUESTIONS FOR SCIENCES

1. The variability in errors in a set of measurement, which is usually estimated by least square

method is called

A. Personal error

B. Indeterminate error

C. Operative error

D. Relative error

Answer: B

2. Which of the types of errors is best described as the reproducibility of measurements?

A. Relative accuracy

B. Probable error

C. Precision

D. Average deviation

Answer: C

3. If 𝑍 = 𝐺

𝑌

⁄ , the maximum error in Z is best expressed as

A. 𝐸𝑧 = (

𝐸𝐺

𝐺

+

𝐸𝑌

𝑌

)

B. 𝐸𝑧 = 𝑍 (

𝐸𝐴

𝐴

+

𝐸𝐵

𝐵

)

C. 𝐸𝑧 = 𝑍 (

𝐸𝐴

𝐴

−

𝐸𝐵

𝐵

)

D. 𝐸𝑧 = 𝑍 (

𝐸𝐺

𝐺

+

𝐸𝑌

𝑌

)

Answer: D

4. Given the summation 𝑌 = 1.05(±0.02) + 4.10(±0.03) − 1.97(±0.05), the absolute error

and percentage relative error in the measurement is

A. 0.06 and 1.89%

B. 0.05 and 1.87%

C. 0.06 and 1.87%

D. 0.05 and 1.89%

Answer: A

5. A solution of 0.5moldm-3 NaOH was titrated against 0.2moldm-3 H2SO4 in the burette using

phenolphthalein as indicator. The results obtained are:

Initial Burette reading = 2.98 ±0.05𝑐𝑚3

Final Burette reading = 38.75 ±0.05𝑐𝑚3

where ±0.05 is the maximum errors

Determine the absolute error and relative error in ppt. of the measurements.

A. ±0.20, 2.8‰

B. ±0.20, 3.8‰

C. ±0.10, 4.8‰

D. ±0.10, 2.8‰

Answer: D

6. Which of the following is/are true? I. Numbers 1-9 are significant II. 0 digit is most times

III. Zeros before figures are not significant IV. Zeros after decimal are significantA. I, II, III

B. I, III, IV

C. I, IV

D. III, IV

Answer: B

7. Evaluate 𝑉 =

22.1𝑑𝑚3 𝑥 751.2𝑚𝑚𝐻𝑔

760𝑚𝑚𝐻𝑔

A. 76.20𝑑𝑚3

B. 76.2𝑑𝑚3

C. 76𝑑𝑚3

D. 76.2072𝑑𝑚3

Answer: B

8. The relationship between the substances undergoing chemical reactions is known as

A. Chemical Formula

B. Molecular formula

C. Stoichiometry

D. Mass Spectrometry

Answer: Stoichiometry

9. The general formula for balancing organic chemical reactions is written as:

A. 𝐶𝑥𝐻𝑦 + 𝑦𝑂2 → 𝑥𝐶𝑂2 +

𝑦

2

𝐻2𝑂

B. 𝐶𝑥𝐻𝑦 + (

𝑥+𝑦

4

)𝑂2 → 𝑥𝐶𝑂2 +

𝑦

2

𝐻2𝑂

C. 𝐶𝑥𝐻𝑦 + (𝑥 +

𝑦

4

)𝑂2 → 𝑥𝐶𝑂2 +

𝑦

2

𝐻2𝑂

D. 𝐶𝑥𝐻𝑦 + (

𝑥−𝑦

4

)𝑂2 → 𝑥𝐶𝑂2 +

𝑦

2

𝐻2𝑂

Answer: C

10. Empirical formula is best defined as

A. The simplest formula that shows the number of atoms of a compound

B. The simplest formula that shows the number of atoms of each element in one ion of a

compound

C. The simplest formula that shows the number of atoms of each element in one molecule

of a compound

D. The simplest formula that shows the actual composition of a molecule of a compound

Answer: C

11. Molecular formula is best defined as

A. The formula that shows the number of atoms of a compound

B. The formula that shows the number of atoms of each element in one ion of a compound

C. The formula that shows the number of atoms of each element in one molecule of a

compound

D. The formula that shows the actual composition of a molecule of a compound

Answer: D

12. 6g of metal M reacts completely with 23.66g of chlorine to form 29.66g of the metallic

chloride. Find the empirical formula of the metallic fluoride

A. 𝑀𝐶𝑙

B. 𝑀𝐶𝑙3

C. 𝑀𝐶𝑙4

D. 𝑀𝐶𝑙2

𝐴𝑛𝑠𝑤𝑒𝑟: B

13. The equivalence of 1mole of any gas at s.t.p. is

A. 22.4cm3

B. 22400dm3

C. 0.0224m3

D. 2.24m3

Answer: C

14. How many moles of atoms of oxygen are there in 0.3mole of SO2?

A. 0.3mole

B. 0.6mole

C. 0.9mole

D. 1.2mole

Answer: B

15. How many atoms of oxygen are there in 10g of H2SO4?

A. 2.47 x 1023

B. 2.46 x 1023

C. 2.45 x 1023

D. 2.44 x 1023

Answer: B

16. What is the number of copper atoms in a 1naira coin which weighs 7.39g, assume the

material from the coin is made is contains 86% copper

A. 6.02 x 1023

B. 6.02 x 1022

C. 6.02 x 1021

D. 6.2 x 1023

Answer: B

17. What is the mass of oxygen O2 needed to burn 4.6g of Na in the reaction below?

4𝑁𝑎 + 𝑂2 → 2𝑁𝑎2𝑂

A. 1.3g

B. 1.6g

C. 1.5g

D. 1.4g

Answer: B

18. How many moles of NH3 are there in 500cm3 of the gas?

A. 0.02mol

B. 0.2mol

C. 0.002mol

D. 2.00mol

Answer: A

19. What is the mass in grams of 1.45 x 1023 molecules of sucrose C12H22O11?

A. 82.11g

B. 82.09g

C. 82.08g

D. 82.12g

Answer: C

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20. What mass of CuSO4 will be obtained by starting with 10g of CuO from the following reaction

(Cu = 63.5g)?

A. 20.04g

B. 20.05g

C. 20.06g

D. 20.07g

Answer: C

21. Calculate the solubility of a solution containing 6g of NaCl {NaCl = 58.44} in 200cm3 of solution

A. 1.531

B. 0.153

C. 0.513

D. 1.153

Answer: C

22. Calculate the amount in moles and grams of KMnO4 present in 3dm3 of 0.250mol

A. 1.23mol & 54g

B. 0.75mol & 119g

C. 0.25mol & 233g

D. 0.135mol & 23g

Answer: B

23. A 0.6025g of sample of a chloride salt was dissolved in water and the chloride precipitated by adding

excess silver nitrate. The precipitate of silver nitrate was filtered, washed, dried and found to weight

0.7134g. Calculate the percentage chloride in the sample [Cl = 35.45, Ag = 107.87]

A. 22.95%

B. 95.22%

C. 29.25%

D. 25.29%

Answer: C

24. The smallest unit of matter than has the properties of an element is called

A. Atom

B. Molecule

C. Ion

D. Particles

Answer: A

25. The nucleus of an atom contributes to its .........while electrons contributes to its............

A. Mass/weight

B. Volume/Mass

C. Mass/volume

D. volume/volume

Answer: C

26. Given an atomic species: 𝑀𝑋

𝐷 , The atomic identity of X is determined by its

A. D

B. M

C. M-D

D. D-M

Answer: B

27. Isotopes are

A. Atoms of same element with different atomic numbers

B. Atoms of same element with differences in their number of neutrons

C. Atoms of different elements with same mass number

D. Atoms of different elements with the same atomic number

Answer: B

28. Isobars are

A. Atoms of same element with the same number of neutrons

B. Atoms of same element with differences in their number of neutrons

C. Atoms of different elements with same mass number

D. Atoms of different elements with the same atomic number

Answer: C

29. Isotones are

A. Atoms of same element with the same number of neutrons

B. Atoms of same element with differences in their number of neutrons

C. Atoms of different elements with same mass number

D. Atoms of different elements with the same atomic number

Answer: A

30. The father of atomic theory was

A. J.J. Thompson [1766 – 1823]

B. Ernest Rutherford [1911 – 1934]

C. John Dalton [1766 – 1844]

D. R.A. Millikan [1835-1927]

Answer: C

31. Atoms are .......

A. Indestructible and unchangeable

B. Indestructible and predictable

C. The smallest particle of an ion

D. All of the above

Answer: A

32. When elements combine, they do so in

A. Simple whole number fractions

B. Multiple whole number ratios

C. Simple whole number ratios

D. Multiple whole number fractions

Answer: C

33. Atom of the same two or more given elements can combine indifferent single whole numbers ratio to

form different compounds. This statement is best described as

A. Law of Mass Action

B. Law of Variable proportion

C. Law of Standard proportion

D. Law of Multiple proportion

Answer: D

34. The parameters that describe the distribution of electrons in an atom and their fundamental nature are

called

A. The Principal quantum numbers

B. The Azimuthal quantum numbers

C. The Magnetic quantum numbers

D. The Quantum numbers

Answer: D

35. Principal quantum number describes

A. Main energy distribution

B. Main energy shell

C. Main energy sub-level

D. Main energy orientation

Answer: B

36. Azimuthal quantum number describes

A. Main energy distribution

B. Main energy shell

C. Main energy sub-level

D. Main energy orientation

Answer: C

37. Azimuthal quantum number is otherwise known as

A. Subordinate quantum number

B. Proportional quantum number

C. Analytical quantum number

D. Subsidiary quantum number

Answer: D

38. The respective shapes of 𝑑, 𝑓, 𝑠 & 𝑝 −𝑜𝑟𝑏𝑖𝑡𝑎𝑙𝑠 are

A. Dumbbell, spherical, characteristic shape & double-dumbbell

B. Spherical, double-dumbbell, dumbbell & characteristic shape

C. Dumbbell, double-dumbbell, spherical & characteristic shape

D. Double-dumbbell, characteristic shape, spherical & dumbbell

Answer: D

39. The number of possible orientations in a 3-dimensional space for each type of orbital can best be

described as

A. Spin Quantum number

B. Magnetic Quantum number

C. Azimuthal quantum number

D. Principal quantum number

Answer: B

40. The number of possible orientations that an electron can have in the presence of a magnetic field or in

relation to another is best be described as

A. Spin Quantum number

B. Magnetic Quantum number

C. Azimuthal quantum number

D. Principal quantum number

Answer: A

41. f student took a reading for 20.44% instead of 20.34%. calculate the absolute error and the relative

error respectively

A. 0.10%, 0.05

B. 0.10%, 0.005

C. 1.0%, 0.005

D. 1.0%, 0.05

Answer: B

42. The molar concentration of a solution is determined by four separate titrations, the results being

0.2041, 0.2039. 0.2049 and 0.2043. calculate the mean & median of the data

A. 0.2042 & 0.2044

B. 0.2043 & 0.2042

C. 0.2043 & 0.2043

D. 0.2043 & 0.2041

Answer: B

43. Calculate the root mean square velocity (r.m.s.) of 1 mole of CO2 at 270C (mm = 44gmol-1

)

A. 4.12 x 102m/s

B. 12 x 102m/s

C. 5.2 x 102m/s

D. 1.2 x 102m/s

Answer: A

44. In a first order reaction, half of the reactant is decomposed in 300seconds. The time taken for 2

/3 of the

reactant to be decomposed is ……………..

A. 198.84sec

B. 475.49sec

C. 2.54 x 10-3

sec

D. 4.75 sec

Answer: B

45. The rate constant for the first order reaction at 500C is twice that at 300C. the activation energy (Ea) of

the reaction is ………………. (R = 8.314Jmol-1

)

A. 178KJ

B. 187KJ

C. 188KJ

D. 177KJ

Answer: C

46. Addition of catalyst to a reaction at a particular temperature ……….the rate of reaction by

…………….the activation energy

A. increase, lowering

B. decreasing, lowering

C. increase, increasing

D. decreasing, increasing

Answer: A

47. The electronic configuration of potassium with the atomic number 19 is ……………

A. 1s22s22p63s23p6

B. 1s22s22p63s23p64s1

C. 1s22s22p63d9

D. 1s22s22p63s23p43d1

Answer: B

48. ………….ions/molecules are always larger than the atoms from which they are formed

A. neutral

B. positive

C. negative

D. none

Answer: C

49. The value of m1 when l = 2 is

A. +2, +1, 0, -1, -2

B. +2, +1, 0

C. +2, +1, 0, -1

D. -2, -1, 0

Answer: A

50. ………….is a substance which accepts a lone pair of electrons in forming a co-ordinate bond

A. base

B. acid

C. salt

D. proton

Answer: B

51. ……….is an example of Lewis base

A. NH3

B. H+

C. SO3

D. He

Answer: B

52. ………… is an example of a monoprotic acid

A. CH3COOH

B. H2SO4

C. H2C2O4

D. H3PO4

Answer: A

53. Find the pOH of 0.1moldm- hydrochloric acid

A. 1

B. 12

C. 13

D. 8

Answer: 13

54. A 0.453g sample of a liquid consisting C, H and O was burned in pure oxygen and 1.039g of CO2 and

0.6369 of H2O were obtained. What is the empirical formula of this compound? [C = 12.01115,

H = 1.00797,O = 15.9994]

A. CHO

B. C4H12O

C. C2H6O2

D. C2H6O2

Answer: B

55. A reducing agent does

A. accepts electrons

B. donates a lone pair of electrons

C. donates electrons

D. donates and accepts at the same time

Answer: C

56. How many moles of oxygen atom are combined with 4.20moles of Cl atoms in Cl2O7?

A. 4.20

B. 42.00

C. 17.40

D. 14.70

Answer: D

57. What is the pH of a solution that is 0.5mol/dm3

in acetic acid (CH3COOH) adn2.5mol/dm3

in sodium

acetate (CH3COONa), Ka of acetic acid is 1.75 x 10-3

A. 5.23

B. 4.12

C. 5.44

D. 3.50

Answer: D

58. Kp = Kc when and only when Δn is

A. < 1

B. > 1

C. Zero

D. > 1

Answer: C

59. The oxidation number of ‘B’ in the compound E2BK3 is ……. [E = +1; K = -2]

A. +3

B. +2

C. +4

D. -2

Answer: C

60. The following principles are applicable to writing electronic configurations except

A. Hundi’s principle

B. Aufbau principle

C. Pauli’s principle

D. Hund’s principle

Answer: A

61. The process of building atoms from the ground level, placing the first electron at the lowest potential

energy is known as

A. Hundi’s principle

B. Aufbau principle

C. Pauli’s principle

D. Hund’s principle

Answer: B

62. The electronic configuration of oxygen is

A. 1𝑠

2 2𝑠

2 2𝑝𝑥

2

2𝑝𝑦

1

2𝑝𝑧

1

B. 1𝑠

2 2𝑠

2 2𝑝

2 4𝑑

2

C. 1𝑠

2 2𝑠

2 3𝑝

2 4𝑑

2

D. 1𝑠

2 2𝑠

2 2𝑝𝑥

1

2𝑝𝑦

1

2𝑝𝑧

1

Answer: A

63. The idea of arranging electrons into generated orbitals one by one before pairing is known as

A. Hundi’s principle

B. Aufbau principle

C. Pauli’s principle

D. Hund’s principle

Answer: D

64. The statement “Electrons to the opposite spin can occupy the same orbital” is best described as

A. Hundi’s principle

B. Aufbau principle

C. Pauli’s principle

D. Hund’s principle

Answer: C

65. The state of equilibrium is limited to chemical reactions in

A. An open system

B. A reversible system

C. A closed system

D. A dynamic system

Answer: C

66. The Law of Mass Action states that:

A. 𝑅𝑎𝑡𝑒 ∝ 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛

B. 𝑅𝑎𝑡𝑒 ∝ 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡?

C. 𝑅𝑎𝑡𝑒 ∝ 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛

D. 𝑅𝑎𝑡𝑒 ∝ 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠

Answer: D

67. Consider a hypothetical reaction: 𝑎𝐴 + 𝑏𝐵 → 𝑐𝐶 + 𝑦𝑌

Which of the following statements is correct?

A. 𝑘𝑓

[𝐶]

𝑐

[𝑌]

𝑦 = 𝑘𝑟

[𝐴]

𝑎[𝐵]

𝑏

B. 𝑘𝑓

[𝐴]

𝑎[𝐵]

𝑏 = 𝑘𝑟

[𝐶]

𝑐

[𝐷]

𝑑

C. 𝑘𝑓

[𝐴]

𝑎[𝐵]

𝑏 = 𝑘𝑟

[𝐶]

𝑐

[𝑌]

𝑦

D. 𝑘𝑟

[𝐶]

𝑐

[𝑌]

𝑦 = 𝑘𝑓

[𝐴]

𝑎[𝐵]

𝑏

Answer: C

68. For the reaction: 𝑁2 + 3𝐻2 ↔ 2𝑁𝐻3

, the value of 𝑘𝑝 is

A. 𝑃𝑁𝐻3

2

𝑃𝑁2

𝑃𝐻2

3

B.

𝑃𝑁𝐻3

2

𝑃𝑁 𝑃𝐻2

3

C. 𝑃𝑁𝐻3

3

𝑃𝑁2

𝑃𝐻2

2

D. 𝑃𝑁𝐻3

𝑃𝑁2

𝑃𝐻2

3

Answer: A

69. The relationship between 𝑘𝑝 and 𝑘𝑐

is

A. 𝑘𝑝 = 𝑘𝑝. (𝑅𝑇)

B. 𝑘𝑝 = 𝑘𝑐

. (𝑅𝑇)

∆𝑛

C. 𝑘𝑐 = 𝑘𝑝. (𝑅𝑇)

∆𝑛

D. 𝑘𝑝 = 𝑘𝑐

. (𝑅𝑇)

Answer: B

70. When ∆𝑛 is positive, the value of 𝑘𝑝 is

A. Greater than 𝑘𝑐

B. Less than 𝑘𝑐

C. Equal to 𝑘𝑐

D. Less than 𝑘𝑐 by 1

Answer: A

71. When ∆𝑛 is negative, the value of 𝑘𝑝 is

A. Greater than 𝑘𝑐

B. Less than 𝑘𝑐

C. Equal to 𝑘𝑐

D. Less than 𝑘𝑐 by 1

Answer: B

72. When ∆𝑛 is zero, the value of 𝑘𝑝 is

A. Greater than 𝑘𝑐

B. Less than 𝑘𝑐

C. Equal to 𝑘𝑐

D. Less than 𝑘𝑐 by 1

Answer: C

73. For the reaction: 𝑁2 + 𝑂2 ↔ 2𝑁𝑂, the value of 𝑘𝑐

is

A. 4𝑥

2

[𝑎−𝑥][𝑏−𝑥]

B. 4𝑥

2

[𝑎−𝑥][𝑏+𝑥]

C. 2𝑥

2

[𝑎−𝑥][𝑏−𝑥]

D. 4𝑥

2

[𝑎+𝑥][𝑏+𝑥]

Answer: A

74. Phosphorus pentachloride dissociates on heating according to the equation 𝑃𝐶𝑙5 ↔ 𝑃𝐶𝑙3 + 𝐶𝑙2

. If the

𝑘𝑐

for the reaction is 0.0326 𝑚𝑜𝑙𝑑𝑚−3

, calculate the value of 𝑘𝑝 in Pascal at 1910𝐶 and R =

8.314J/molK is

A. 152.67

B. 125.69

C. 125.76

D. 127.56

Answer: C

75. Factors affecting reactions in equilibrium are

A. Catalyst, Light, Concentration, Pressure

B. Catalyst, Temperature, Concentration, Pressure

C. Catalyst, Light, Concentration, Surface Area

D. Catalyst, Surface Area, Concentration, Pressure

Answer: B

76. The shifting of the equilibrium position to annul the effect of changes to re-establish equilibrium is

termed

A. Pauli’s Exclusion Principle

B. Le-Chatelier Principle

C. Aufbau Principle

D. Exclusion Principle

Answer: B

77. In an equilibrium reaction, pressure increase will favour the side with

A. Lower Volume

B. Equivalent Volume

C. Higher Volume

D. Volume

Answer: A

78. In the reaction: 𝐻2 + 𝐼2 ↔ 2𝐻𝐼,

A. Pressure has no effect

B. Increase in pressure will cause equilibrium to shift to the right

C. decrease in pressure will cause equilibrium to shift to the right

D. decrease in pressure will cause equilibrium to shift to the left

Answer: A

79. In the reaction: 𝑃𝐶𝑙5 ↔ 𝑃𝐶𝑙3 + 𝐶𝑙2

,

A. Pressure has no effect

B. Increase in pressure will cause equilibrium to shift to the right

C. decrease in pressure will cause equilibrium to shift to the left

D. No Answer

Answer: D

80. Increase in the concentration of products in a reaction will cause the equilibrium position to

A. Shift to the left

B. Shift to the right

C. Will have no effect

D. Shift to both right and left

Answer: A

81. What is the effect of increase in concentration on the equilibrium constant of a reaction?

A. The value of equilibrium constant increases

B. The value of equilibrium constant decreases

C. The value of equilibrium constant remains constant

D. The value of equilibrium constant first increases, and later decreases

Answer: C

82. Increase in temperature will

A. Favour the forward reaction of an exothermic reaction

B. Favour the reverse reaction of an exothermic reaction

C. Favour both forward and reverse reaction of an exothermic reaction

D. Have no effect

Answer: B

83. Does temperature changes affect the equilibrium constant of a reaction?

A. No, it doesn’t

B. Yes it does

C. Yes, it doesn’t

D. No, it does

E. Answer: B

84. Catalyst speeds up the rate of

A. Forward reaction

B. Reverse reaction

C. Both forward and reverse reaction

D. All reactions

Answer: C

85. Catalyst speeds up the rate of

A. Forward reaction

B. Reverse reaction

C. Both forward and reverse reaction

D. All reactions

Answer: C

86. Catalyst ................... the rate of reaction by ................... the activation energy

A. decreases/raising

B. decreases/lowering

C. increases/raising

D. increases/lowering

Answer: D

87. Calculate the solubility in gdm-3 at 298K of calcium fluoride (CaF2) in a 0.1M NaF solution.

[𝐾𝑠𝑝 = 3.9 𝑥 1014𝑚𝑜𝑙3𝑑𝑚−9

, 𝐶𝑎 = 40, 𝐹 = 19𝑔]

A. 3.04 𝑥 10−9𝑔𝑑𝑚−3

B. 3.04 𝑥 10−10𝑔𝑑𝑚−3

C. 3.04 𝑥 10−8𝑔𝑑𝑚−3

D. 3.04 𝑥 10−7𝑔𝑑𝑚−3

Answer: A

88. The reducing and oxidizing agents respectively in the reaction 𝐹𝑒2𝑂3 +3𝐶𝑂 → 2𝐹𝑒 + 3𝐶𝑂2 are

A. 𝐹𝑒2𝑂3 and 𝐶𝑂

B. 𝐹𝑒 and 𝐶𝑂

C. 𝐶𝑂 𝑎𝑛𝑑 𝐹𝑒2𝑂3

D. 𝐶𝑂2 and 𝑁𝐻3

Answer: C

89. The oxidation numbers of hydrogen and oxygen are respectively +1 and -2 except in

A. Peroxides and Halogens

B. Peroxides and Metallic Halides

C. Metallic hydrides and peroxides

D. Peroxides

Answer:

C

90. In the reaction 𝑀𝑛𝑂4

− +𝐹𝑒2+ + 𝐻

+ → 𝑀𝑛2+ + 𝐹𝑒3+, the oxidation number of manganese changes

from

A. +5 to +2

B. +7 to +2

C. +2 to +3

D. +6 to +2

Answer: B

91. To balance a redox reaction in basic medium, 𝐻2𝑂 is added to the side with

A. Lesser number of oxygen atoms

B. Lesser number of hydrogen atoms

C. More oxygen atoms

D. Equivalent number of oxygen atoms

Answer: C

92. The values of w, x and g in the redox reaction: 𝐼𝑂3

− + 𝑤𝐶𝑟3+ + 𝑥𝑂𝐻− → 𝑧𝐼− + 2𝐶𝑟𝑂4

2− + 5𝐻2𝑂

is

A. 2,10, 1

B. 2,1,10

C. 10,1,2

D. 10,2,1

Answer: A

93. A reaction in which the same substance on the reactant side is being oxidized and reduced

simultaneously is known as

A. Combustion reaction

B. Addition reaction

C. Dispropornation reaction

D. Substitution reaction

Answer: C

94. Substances that dissolve in water to release hydroxonium ion is known as

A. Base

B. Salt

C. Lewis Base

D. Acid

Answer: D

95. A substance that ionizes in solution to produce hydroxyl ion is

A. Base

B. Salt

C. Acid

D. Lewis Acid

Answer: A

96. The definitions of Arrhenius emphasizes ..........and.......... in water

A. 𝐼𝑂3

− & 𝐻

2+

B. 𝑂𝐻− & 𝐻

+

C. 𝐻

2+ & 2𝑂𝐻−

D. 𝐼𝑂3

3− & 𝐻

3+

Answer: B

97. The Arrhenius acid and base respectively in the reaction 𝑁𝐻3 +𝐻2𝑂 ↔ 𝑁𝐻4

+ +𝑂𝐻−

A. 𝐻2𝑂 𝑎𝑛𝑑 𝑁𝐻3

B. 𝑁𝐻3 𝑎𝑛𝑑 𝐻2𝑂

C. 𝑂𝐻− 𝑎𝑛𝑑 𝐻2𝑂

D. 𝑁𝐻4

+

𝑎𝑛𝑑 𝑁𝐻3

𝐴𝑛𝑠𝑤𝑒𝑟: 𝐴

98. The conjugate base and acid respectively in question 97 above are

A. 𝐻2𝑂 𝑎𝑛𝑑 𝑁𝐻3

B. 𝑁𝐻3 𝑎𝑛𝑑 𝐻2𝑂

C. 𝑂𝐻− 𝑎𝑛𝑑 𝐻2𝑂

D. 𝑁𝐻4

+

𝑎𝑛𝑑 𝑁𝐻3

𝐴𝑛𝑠𝑤𝑒𝑟: 𝐴

99. Water is best described as

A. Acid

B. Base

C. Amphiprotic

D. Ampiteric

Answer: C

100.In the dissociation of water: 𝐻2𝑂 ↔ 𝐻

+ + 𝑂𝐻−, the value of 𝑘𝑤 is

A. 𝑘𝑤 =

[𝑂𝐻−][𝐻

+]

[𝐻3𝑂]

B. 𝑘𝑤 =

[𝑂𝐻−][𝐻

+]

[𝐻2𝑂]

C. 𝑘𝑤 =

[𝐻2𝑂]

[𝑂𝐻−][𝐻+]

D. 𝑘𝑤 =

[𝐻3𝑂]

[𝑂𝐻−][𝐻+]

Answer: B

101.The hydrogen ion concentration of pure water is

A. 1 𝑥 1014

B. 1 𝑥 10−14

C. 1 𝑥 10−7

D. 1 𝑥 107

Answer: C

102.The pH of pure water is

A. 14

B. -14

C. -7

D. 7

Answer: D

103.What is the pH of a neutral solution at 250C?

A. 14

B. 3

C. 7

D. 1

Answer: C

104. What is the pH of a basic solution whose hydroxyl ion concentration is 0.00001M?

A. 9

B. 5

C. 1

D. 4

Answer: A

105. The pH of a 0.25M solution of acetic acid [HC2H3O2] is found to be 2.68. What is the Ka for this

solution and what percentage of the acid ionized?

A. 1.76 x 10-5M and 0.74%

B. 1.76 x 10-5M and 0.84%

C. 6.17 x 10-5M and 0.64%

D. 6.71 x 10-5M and 0.54%

Answer: B

106. The change in the concentration of reactant or product per unit time is known as

A. Rate Law

B. Order of a reaction

C. Rate of a reaction

D. Molecularity of a reaction

Answer: C

107.In a hypothetical reaction 𝐴 → 𝐵, the rate of the reaction is expressed as:

A. 𝑑[𝐴]

𝑑𝑡

=

+𝑑[𝐵]

𝑑𝑡

B. −𝑑[𝐴]

𝑑𝑡

=

−𝑑[𝐵]

𝑑𝑡

C. ±𝑑[𝐴]

𝑑𝑡

=

+𝑑[𝐵]

𝑑𝑡

D. −𝑑[𝐴]

𝑑𝑡

=

+𝑑[𝐵]

𝑑𝑡

Answer: D

108. Rate of a reaction is measured in

A. 𝑚𝑜𝑙 𝑙𝑖𝑡−1𝑚𝑖𝑛−1

B. 𝑚𝑜𝑙 𝑐𝑚−1

𝑠𝑒𝑐−3

C. 𝑚𝑜𝑙 𝑐𝑚−3

𝑠𝑒𝑐−1

D. 𝑚𝑜𝑙 𝑐𝑚−1ℎ𝑟

−1

𝐴𝑛𝑠𝑤𝑒𝑟: 𝐴

109.The rate of a reaction is directly proportional to the concentration of reactants. This is referred to as

A. Order of a Reaction

B. Rate of a Reaction

C. Overall order of a Reaction

D. Molecularity of a Reaction

Answer: B

110.The correct expression for the rate of the reaction: 𝐴 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 is

A. 𝑅𝑎𝑡𝑒 = [𝐴]

𝑛

B. 𝑅𝑎𝑡𝑒 = [𝐵]

𝑛

C. 𝑅𝑎𝑡𝑒 = 𝑘[𝐴]

𝑛

D. 𝑅𝑎𝑡𝑒 ∝ 𝑘[𝐴]

𝑛

Answer: C

111.The correct expression for the rate of the reaction: 2𝐴 + 𝐵 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 is

A. 𝑅𝑎𝑡𝑒 = 𝑘[𝐴]

2𝑥

[𝐵]

𝑦

B. 𝑅𝑎𝑡𝑒 = [𝐴]

𝑥

[𝐵]

𝑦

C. 𝑅𝑎𝑡𝑒 ∝ [𝐴]

𝑥

[𝐵]

𝑦

D. 𝑅𝑎𝑡𝑒 ∝ [𝐴]

2𝑥

[𝐵]

𝑦

Answer: C

112.An expression which shows how a reaction is related to concentration is termed

A. Order of reaction

B. Molecularity of reaction

C. Equilibrium Law

D. Rate Equation

Answer: D

113.The powers to which the concentration of each reactant is raised to give a correct dependence of rate on

concentration is termed

A. Order of reaction

B. Molecularity of reaction

C. Equilibrium Law

D. Rate Equation

Answer: D

114.For a given reaction whose rate expression is given as: 𝑅𝑎𝑡𝑒 = 𝑘[𝐴]𝑚[𝐵]

𝑛

, the order of reaction is

A. m, n

B. m+n

C. m-n

D. n-m

Answer: A

115.The sum of all exponents of the reactants as contained in the experimentally determined rate law is

known as

A. Overall rate law

B. Overall molecularity of reaction

C. Overall order of reaction

D. Overall equilibrium law

Answer: C

116. Order of a given reaction can only be determined

A. Experimentally

B. From the Rate Equation

C. From the Molecuarity of reaction

D. From the chemical reaction

Answer: A

117.The number of molecules/ions of the reactants present in the balanced stoichiometric equation is

referred to as:

A. Order of reaction

B. Molecularity of reaction

C. Equilibrium Law

D. Rate Equation

Answer: B

118.For a second order reaction 𝐴 +𝐵 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡, the rate constant expression is

A. 𝑘2 =

2.303

𝑡

log10

𝑏(𝑎−𝑥)

𝑎(𝑏−𝑥)

B. 𝑘2 =

2.303

𝑡

log10 (

𝑎

𝑎−𝑥

)

C. 𝑘2 =

1

𝑡

log10

𝑥

𝑎−𝑥

D. 𝑘2 =

𝑥

𝑡

𝐴𝑛𝑠𝑤𝑒𝑟: A

119.For a zero order reaction 𝐴 +𝐵 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡, the rate constant expression is

A. 𝑘0 =

2.303

𝑡

log10

𝑏(𝑎−𝑥)

𝑎(𝑏−𝑥)

B. 𝑘0 =

2.303

𝑡

log10 (

𝑎

𝑎−𝑥

)

C. 𝑘0 =

1

𝑡

log10

𝑥

𝑎−𝑥

D. 𝑘0 =

𝑥

𝑡

Answer: D

120.For a first order reaction 𝐴 + 𝐵 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡, the rate constant expression is

A. 𝑘0 =

2.303

𝑡

log10

𝑏(𝑎−𝑥)

𝑎(𝑏−𝑥)

B. 𝑘0 =

2.303

𝑡

log10 (

𝑎

𝑎−𝑥

)

C. 𝑘0 =

1

𝑡

log10

𝑥

𝑎−𝑥

D. 𝑘0 =

𝑥

𝑡

Answer: B

121.The half-life of a first order reaction depends on

A. Initial concentration of the reactions

B. Concentration of the reactant left

C. Concentration of product

D. Rate constant

Answer: D

122.The half-life of a first order reaction depends on

A. Initial concentration of the reactants

B. Concentration of the reactant left

C. Concentration of product

D. Rate constant

Answer: A

123.The unit of rate constant, K, in a first order reaction is

A. 𝑚𝑜𝑙𝑙𝑖𝑡𝑟𝑒−1

𝑠𝑒𝑐−1

B. 𝑠𝑒𝑐−1

C. 𝑙𝑖𝑡𝑟𝑒𝑚𝑜𝑙−1

𝑠𝑒𝑐−1

D. 𝑠𝑒𝑐𝑙𝑖𝑡𝑟𝑒−1𝑚𝑜𝑙−1

Answer: B

124.Photolytic reactions take place in the presence of

A. Pressure

B. Light

C. Catalyst

D. Heat

Answer: B

125.The unit of rate constant, K, in a first order reaction is

A. 𝑚𝑜𝑙𝑙𝑖𝑡𝑟𝑒−1

𝑠𝑒𝑐−1

B. 𝑠𝑒𝑐−1

C. 𝑙𝑖𝑡𝑟𝑒𝑚𝑜𝑙−1

𝑠𝑒𝑐−1

D. 𝑠𝑒𝑐𝑙𝑖𝑡𝑟𝑒−1𝑚𝑜𝑙−1

Answer: A

OBJECTIVE CBT QUESTIONS ON SET THEORY

(MTH 101)

1. If A is a subset of a universal set U, the compliment of set A is given as:

A. U

B. U - A

C. U + B

D. U - B

Answer: B

2. The set statement (𝐴 ∪ 𝐵) ∩ 𝐶 = 𝐴 ∪ (𝐵 ∩)𝐶 is relevant to

A. Associative Law

B. Cummulative lowa

C. Distributibe Law

D. Closure

Answer: A

3. If U = (Integers < 20); D = {multiples of 4}; E = {multiples of 3}, the element of D/ ∩ E are

A. {1,2}

B. {3,6,9,15,18}

C. {4,8,16,20}

D. {3,6,9,.12,15,18}

Answer: B

4. The notation 𝐴 − 𝐵 is equivalent to

A. 𝐴 ∪ 𝐵

𝑐

B. 𝐴 ∪ 𝐵

C. 𝐴 ∩ 𝐵

D. 𝐴 ∩ 𝐵

𝑐

𝐴𝑛𝑠𝑤𝑒𝑟:𝐷

5. The notation (𝐴 ∪ 𝐵)

/

is equivalent to

A. 𝐴

𝑐 ∩ 𝐵

𝑐

B. 𝐴

𝑐 − 𝐵

𝑐

C. 𝐴 ∪ 𝐵

D. 𝐴 ∩ 𝐵

𝑐

𝐴𝑛𝑠𝑤𝑒𝑟: 𝐴

6. The number of distinct elements found in a given set is called

A. Power set of a set

B. Order of a set

C. Power of a cardinality

D. Cardinality of a power set

Answer: B

7. If two sets A and B are subsets of a universal set, then the notation 𝑛(𝐴 ∪ 𝐵) is equal to

A. 𝑛(𝐴) +𝑛(𝐵)

B. 𝑛(𝐴) +𝑛(𝐶)−𝑛(𝐴 ∪ 𝐵)

C. 𝑛(𝐴) +𝑛(𝐵) + 𝑛(𝐴 ∪ 𝐵)

D. 𝑛(𝐴) +𝑛(𝐵) − 𝑛(𝐴 ∩ 𝐵)

Answer: D

In a survey of 60 students, 60 study botany, 50 zoology and 48 biology. If 38 students study botany,

zoology and biology,

Use the information above to answer questions 8 & 9

8. How many study only zoology?

A. 12

B. 10

C. 0

D. 5

Answer: C

9. How many study non of the three courses?

A. 12

B. 10

C. 0

D. 5

Answer: C

10. How many study the Zoology and Botany?

A. 12

B. 10

C. 0

D. 5

Answer: A

**Recommended**:how-to-answer-english-comprehension

In a particular group of students during a school’s sports competition, 15 play lawn tennis, 11 swim, 9

play lawn tennis and swim and 3 none of the sport activities

11. How many students swim only?

A. 6

B. 2

C. 9

D. 20

Answer: B

12. How many students play lawn tennis only?

A. 6

B. 2

C. 9

D. 20

Answer: A

13. How many students are in the group?

A. 6

B. 2

C. 9

D. 20

Answer: D

14. In a group of 40students, 22 study Maths, 18 study physics, 14 study statistics, 9 study both Maths and

Physics, 7 study both Maths and Statistics, 5 study both Physics and Statistics and 2 study all the

subjects. How many study none of the subjects?

A. 4

B. 5

C. 6

D. 7

Answer: B

15. Simplify 1

2−√3

+

5

√3 + 2

−

1

√3− √2

A. 12 − 5√3− √2

B. 12 − 5√3+ √2

C. 12 + 5√3+ √2

D. 12 + 5√3− √2

Answer: D

16. Find the square root of 7 −√13

A. 0.8424

B. 1.8424

C. 1.8244

D. 0.8244

Answer: B

17. Find the roots of the equation: 𝑥

3 + 5𝑥

2 − 2𝑥 − 24

A. -4,3,2

B. -4,-3,-2

C. -4,-3,2

D. 4,3,-2

Answer: C

18. Find the roots of the equation 2𝑥

3 + 11𝑥

2 − 17𝑥 − 6

A. d

B. d

C. d

D. d

Answer:

19. Solve the equation 2𝑥

2 −5𝑥 + 7 = 0

A. 5±√31

4

B. 5±𝑖√31

4

C. 5±𝑖√31

2

D. 5±√31

2

Answer: B

20. In the expression 2

𝑦2+2𝑦+1

=

1

𝑦2+2𝑦−2

+

3

𝑦2+2𝑦+3

, determine the value of 𝑦

2 + 2𝑦 +1

A. 5±√71

4

B. 5±𝑖√−71

2

C. 5±𝑖√71

4

D. 5±𝑖√71

2

Answer: C

21. The value of k in √𝑘 − 1+ 5√𝑘 − 9 = 4√𝑘 − 6 is

A. 9

B. 10

C. 11

D. 12

Answer: B

22. If 5𝑔

4 + 9𝑔

3 −12𝑔

2 −9𝑔 +5 = 0, find the value of 𝑅 where 𝑅 is a positive integer and 𝑅 = 𝑔 −

1

𝑔

A. 2

B. 1

C. 1/5

D. -2

Answer: C

23. The values of 𝑥, 𝑦 in the equations 𝑥 + 2𝑦 = 3 & 𝑥

2 + 2𝑦

2 = 6 are

A. 1 +√2 ,

2−√2

2

B. 1 +√2 ,

2+√2

2

C. 1 −√2 ,

2−√2

2

D. 1 −√2 ,

2+√2

2

𝐴𝑛𝑠𝑤𝑒𝑟: A

24. a, b & c respectively in the equations 2𝑎𝑏 = 𝑎 + 𝑏, 5𝑎𝑐 = 6𝑐 − 2𝑎 & 3𝑏𝑐 = 3𝑏 +4𝑐 are

A. 3

2

,

1

2

,−1

B. 1

2

,

3

2

,−1

C. −

1

2

,−

3

2

,−1

D. 1

2

,

3

2

, 1

𝐴𝑛𝑠𝑤𝑒𝑟: 𝐵

25. Solve for x in the equation 163𝑥 =

1

4

(32)

𝑥−1

A. 1

B. 2

C. -2

D. -1

Answer: D

26. Simplify (216)^−1 /3× (0.16)^-1/2

A. 12/17

B. 5/13

C. 12/15

D. 5/12

Answer: D

27. Given that 𝑦 = 3𝑥, 𝑎𝑛𝑑 3

𝑥−𝑦 =

1

81

, find 𝑥

A. 2

B. 3

C. 4

D. 5

Answer: A

28. If 8

𝑥/2 = 2

3/8 × 4

3/4

, find the value of 4𝑥

A. 4

B. 5

C. 6

D. 7

Answer: 5

29. Solve for x in 3

2𝑥+1 − 18(3

𝑥

)− 81 = 0

A. -1

B. 3

C. -3

D. 2

Answer: D

30. Solve for x in 26(5

𝑥−1

) = 5

2𝑥 + 1

A. -1,-2

B. -1,1

C. -1,2

D. 2,-2

Answer: B

31. Evaluate 𝑙𝑜𝑔𝑎256 = 4

A. 2

B. 3

C. 4

D. 5

Answer: 4

32. Given that 𝑙𝑜𝑔264 = 𝑘, find 4𝑘𝑙𝑜𝑔1632

A. 60

B. 50

C. 40

D. 30

Answer: D

33. The value of x in 𝑙𝑜𝑔3𝑥 −3𝑙𝑜𝑔𝑥3 = 2 is

A. -1/3

B. -27

C. 27

D. 3

Answer: C

34. What is the positive value of y in 3𝑙𝑜𝑔8𝑦 = 𝑙𝑜𝑔4(𝑦 + 4)?

A. -2,3

B. -2,-3

C. 2,-3

D. 2,3

Answer: A

35. If 25𝑥+1 = 64 (

5

2

)

6

, 𝑓𝑖𝑛𝑑 𝑥

A. -1

B. 1

C. -2

D. 2

Answer: D

36. Simplify (

8

27)

1/3

− (

4

9

)

1/2

A. 0

B. 1

C. 2

D. 3

Answer: A

37. Simplify 6

2𝑛+2 × 9

𝑛 × 4

2𝑛−1

18𝑛+1 × 2

𝑛−1 × 122𝑛+1

A. 6

B. 12

C. 1/6

D. 1/12

Answer: D

38. If |𝑥| < 𝑝, 𝑡ℎ𝑒𝑛

A. 𝑝 < 𝑥 < −𝑝

B. −𝑝 < 𝑥 < 𝑝

C. – 𝑝 > 𝑥 < 𝑝

D. – 𝑝 < 𝑥 > 𝑝

Answer: B

39. The value of x in 5𝑥−1

3

−

1−2𝑥

5

< 8 +𝑥

A. 𝑥 < 8

B. 𝑥 < −8

C. 𝑥 > 8

D. 𝑥 > −8

Answer: A

40. Find the range of x for which 12 + 𝑥 − 𝑥

2 < 0

A. 𝑥 < 3 𝑜𝑟 𝑥 < −4

B. 𝑥 < −3 𝑜𝑟 𝑥 < 4

C. −3 < 𝑥 < 4

D. 3 < 𝑥 < −4

Answer: C

41. The equivalent of (𝑎 + 𝑏) (

1

𝑎

+

1

𝑏

) (

𝑎

2

𝑏

2 +

𝑏

2

𝑎2

) is

A. 16√𝑎𝑏

B. 16

C. 8√𝑎𝑏

D. 8

Answer: D

42. The equivalent of (𝑎 + 𝑏) (

1

𝑎2 +

1

𝑏

2

) (

𝑎

4

𝑏

2 +

𝑏

4

𝑎2

)

A. 16√𝑎𝑏

B. 16

C. 8√𝑎𝑏

D. 8

Answer: C

43. If 𝑥

(𝑥−1)

2(𝑥+3)

=

𝑃

16(𝑥−1)

+

𝐺

4(𝑥−1)

2 +

𝐻

16(𝑥+3)

, the value of P + G + H is

A. 3

B. 1

C. 7

D. 10

Answer: B

44. The first 3 terms of the sequence given by 𝑇𝑛 =

𝑛+1

3𝑛+2

respectively are

A. 3/8, 4/11, 5/14

B. 4/11, 5/14, 6/17

C. 2/5, 3/8, 4/11

D. 3/8, 4/11, 6/17

Answer: C

45. Given the nth term of a sequence 𝑙𝑜𝑔16(𝑛 + 3), what is the difference between the 13th and first

terms?

A. ½

B. 2

C. 1

D. -1

Answer: A

46. The sum of the terms of a sequence is known as

A. Series

B. Arithmetic sequence

C. Geometric sequence

D. Sequence

Answer: A

47. The type of sequence in which the next term differs from the preceding term by a difference is termed

A. Arithmetic Sequence

B. Geometric sequence

C. Geometric Infinity

D. Infinite series

Answer: A

48. The correct expression for the common difference in an A.P. is

A. 𝑇 − 𝑇𝑛

B. 𝑇𝑛 − 𝑇𝑛+1

C. 𝑇𝑛 − 𝑇𝑛−1

D. 𝑇𝑛 − 𝑇𝑛+2

𝐴𝑛𝑠𝑤𝑒𝑟: 𝐶

49. The common difference in the series 𝐾, 𝐾 + 3, 𝐾 + 6, … .. is

A. 2

B. 3

C. 4

D. -4

Answer: B

50. If the first 3 terms of an A.P. are 𝑦, 3𝑦 + 1, 7𝑦 − 4, find the 10th term of the sequence

A. 66

B. 55

C. 44

D. 33

Answer: A

51. The 6th and 13th term of an A.P. are 0 and 14 respectively, find the 20th term

A. 18

B. -18

C. 28

D. -28

Answer C

52. If P = {prime factors of 84} and Q = {prime factors of 315}, the elements of P U Q & P ∩ Q are

respectively

A. {3,4,5,7,9 & {3,7}

B. {3,4,5,7} & {5,7}

C. {2,3,5,7} & {3,7}

D. {2,3,5,7} & {2,7}

Answer: C

53. In a class of 100 students, 40 students study botany, 32 study microbiology while 44 study zoology.

The number of students that study botany and microbiology is 24, botany and zoology is 24, while 20

study microbiology and zoology. If 20 students study all the three subjects, how many study none of

the three courses

A. 32

B. 42

C. 68

D. 24

Answer: A

54. The union of the set A and B denoted by A U B denoted by A U B, is the set of elements which belong

to

A. either A nor B nor both

B. either A or B or both

C. neither A nor B or both

D. neither A or B nor both

Answer: B

55. The word “Infinity” is

A. a real number

B. a complex number

C. an integer number

D. constant

Answer: C

56. In a class, 220 students offer Mathematics or Chemistry or both. 125 offer Mathematics and 110 offer

Chemistry. How many offer Chemistry but not Mathematics? (a) 80 (b) 110 (c) 125 (d) 95

A. 80

B. 110

C. 125

D. 95

Answer: D

57. The universal set U contains only elements of the sets A, B, C where A = {3,q,r}, B = {a,2,c} and

C = {1,3,4,b}. what are the elements in [(A - B) ∩ {C – (A ∩ C)’}]

A. {3,q,r}

B. {q,r}

C. {3}

D. {3,1}

Answer: C

58. If R = {x: x

2 = 16, x > 5}, then R is equal to

A. 0

B. {0}

C. ø

D. {ø}

Answer: C

59. In a certain class, 22 pupils take one or more of Chemistry, Economics and Government. 12 take

Economics €, 8 take Government (G) and 7 take Chemistry (C). Nobody takes Economics and

Chemistry and 4 pupils take Economics and Government. How many pupils take both Chemistry and

Government?

A. 1

B. 2

C. 3

D. 4

Answer: A

60. The universal set U has subsets M and N such that 𝑀 ⊆ 𝑁. The set of 𝑀 ∩ (𝑀 ∩ 𝑁)

/

is

A. M

B. ∅

C. N

D. U

Answer: B

61. Given the universal set U = {2,3,4,5,6,7,8,9} and subsets P = {2,4,6,8} and Q = {x: 𝑥

2 < 50,

𝑥 𝑖𝑠 𝑜𝑑𝑑}, find (𝑃 ∩ 𝑄)

/

A. {9}

B. {0}

C. ∅

D. U

Answer: U

62. Simplify √(729𝑦

−6)

1⁄2

3

A. 1

3𝑦

B. 3𝑦

C. 𝑦

3

D. 3

𝑦

Answer: D

63. Evaluate √

0.0024 𝑥 35000

0.0105

3

, leaving your answer in standard form

A.2 𝑥 101

B. 2 𝑥 102

C.1 𝑥 102

D.1 𝑥 101

Answer: A

64. The square root of 3 −√2 is

A. 1−√2

2

B. 2−√2

2

C. 1+2√2

4

D. 1−2√2

2

Answer: D

65. If a & b are positive numbers, evaluate

4

4

2

4

2 2

1 1 4

a

b

b

a

a b

a b

A. 32

B. 32√𝑎𝑏

C. 16

D. 16√𝑎𝑏

Answer: B

66. In the equation 5x4 + 9x3 – 12x2 – 9x + 5 = 0, find the value of x –

1

/x

A. -1

/5, 2

B. 1

/2, 5

C. 1

/5, -2

D. 5, 2

Answer: C

67. Determine the square of the remainder when 3x4 – 2x3 – 10x – 5 is divided by x – 4

A. 595

B. 475

C. 354025

D. 225625

Answer: C

68. In resolving

1

1

2

x x

into partial fraction, what are the values of the constants A, B & C?

A. -2, 1

/2,

1

/2,

B. -1, 1

/2,

½

C. -1, 1

/2, -1

1

/2

Answer: B

69. Find the range of the validity of x in the equation

1

2 1

x

x

A. x <1 or x > 0

B. x < 0 or x < 1

C. x < 0 or x < 1

D. x > 0 or x > 1

Answer: D

70. What is the remainder when x

3 + 3x2 – 13x – 10 is divided by (x – 3)?

A. 4

B. 4

1

/4

C. 6

D. 5

Answer: D

71. Given that -2 = A(x – 1)2 + B(x – 1) (x – 2) + C(x – 2), find the value of C

A. 2

B. -2

C. 1

D. -1

Answer: A

72. Resolve into partial fraction

2

3 2

1 2

5 15

x x

x x x

& give the values of A, B, C respectively

A. 2,3,4

B. 2,3,0

C. 2,0,3

D. 2, -2, 3

Answer: D

73. Determine the range of values of x for which

2

1

4

2

2

2

x

x x

A. x > -4 or x > 2

B. x < -4 or x < 2

C. x < 4 or x > 2

D. x < -4 or x > 2

Answer: A

74. In the equation 5x4 – x

3 + 9x2 – x + 5 = 0, find the value of

x

x

1

A. 1∓√21

10

B. 1±√21

5

C. 1±√21

15

D. 1±√21

10

Answer: D

75. Determine the values of p & q if (x – 1) & (x + 2) are factors of 2x3 + px2 – x + q

A. p = -5, q = -6

B. p = 5, q = 6

C. p = 5, q = -6

D. p = -6, q = -5

Answer: C

76. Find the value of the constant k if 4x3 + kx2 + 7x – 23 has a remainder 7 when divided by 2x – 5

A. 8

B. -16

C. -8

D. 16

Answer: C

77. Expresses

2

2

1

3 1

x x

x x

in partial fractions and find the value of A + B – C

A. -3

B. 2

C. 6

D. 7

Answer: C

78. Solve the inequality

1 4

4

y

y

A. -4 < y < 0

B. 4 < y < 0

C. 0 > y > -4

D. 0 < y < 4

Answer: A

79. The sum of the square of three positive numbers in arithmetic progression is 165. If the sum of the

number is 21, find the sum of cubes of each of the numbers?

A. 4

B. 1400

C. 1407

D. 104

Answer: C

80. The sum of the first n terms of an AP whose difference is not zero equals half the sum of its subsequent

n members. Find the ratio of the sum of the first 3n terms and the sum of the first …terms

A. 6

B. 4

C. 8

D. 3

Answer: A

81. Given the following series: ln 𝑥 , ln 𝑥

2

, ln 𝑥

4

, ln 𝑥

8

, find the 21st term

A. 20 ln ?

B. 2

20 ln 𝑥

C. 202

ln 𝑥

D. 20 ln 𝑥

2

𝐴𝑛𝑠𝑤𝑒𝑟: 𝐵

82. Find the 8th term and the sum of the first 8 terms of the GP sequence: 1

2

,−1, 2,−4, … . . ?

A. −64,−42.5

B. -64, 42.5

C. 64, 42.5

D. -64, 45.4

Answer: A

83. The sum of the first eight terms of the AP: ln 𝑥 , 𝑙𝑛𝑥

2

, ln 𝑥

3 … .. is

A. ln 𝑥

8

B. ln 𝑥

9

C. ln 𝑥

36

D. ln 𝑥

72

Answer: C

84. Don Mike places a sum of money on a savings account in the bank. On each succeeding birthday, he

deposits two times more than on the previous birthday. His total sum of the first eleven deposits is

N20,480. How much was his first deposit?

A. N20

B. N25

C. N10

D. N12.50

Answer: C

85. The fourth term and the seventh term of an AP are in the ratio 5:8. Find the ratio of the 3rd and 6th term.

A. 4:5

B. 6:5

C. 4:6

D. 4:7

Answer: D

86. The second term of an AP is four times the first term, the last term is 13 times the first term and the

sum of the series is 70. Find the first three terms of the progression

A. 2,4,6

B. 2,8,14

C. 2,4,8

D. 8,12,14

Answer: B

87. A polygon has 25sides, the length of which starting from the smallest side are in AP. If the perimeter of

the polygon is 1100cm, and the length of the largest side is ten times that of the smallest, find the

length of the smallest side

A. 5cm

B. 6cm

C. 7cm

D. 8cm

Answer: D

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