Find the values of the constants a and b if the straight lines

1. ax + 5y = 3, and 4x + by = 1 intersect at the point (2, -1)

ANSWER: a = 4, b = 7

[2a – 5 = 3, 2a = 8, a = 4, 8 – b = 1, b = 7]

2. 3x + ay = 4, and bx – 5y = 6 intersect at the point (2, -2)

ANSWER: a = 1, b = -2

[6 – 2a = 4, 2a = 2, a = 1, 2b + 10 = 6, 2b = -4, b = –2]

3. ax + 2y = -3, and 2x + by = 6   meet at the point (1, 2)

ANSWER: a = -7, b = 2

[a + 4 = -3, a = -7, 2 + 2b = 6, 2b = 4, b = 2]

1. Factorize completely a4 + 4a3b + 6a2b2 + 4ab3 + b4

ANSWER: (a + b)4

2. In how many ways can 5 persons be seated in a row of 5 seats.


[5! = 5 x 4 x 3 x 2 x 1 = 20 x 6 = 120]

3. Find the coordinates of the point of inflexion of the curve y = x3 – 6x2 + 16x.

ANSWER: (2, 16)

[dy/dx = 3x2 – 12x + 16, d2y/dx2 = 6x – 12 = 0, x = 2, y = 8 – 24 + 32 = 16, (2, 16)]

PREAMBLE: Which species in each pair is a better-reducing agent under standard state conditions?

  1. Na or Li

answer: Li

  1. H2 or I2

answer: H2

  1. Fe2+or Ag

answer: Fe2+

PREAMBLE: Convert each of the following temperatures to the indicated scales.

  1. 50 to Fahrenheit degree :

Answer: 122 0F

  1. 40 to Kelvin

Answer: 313.15K

  1. 60 to Kelvin

Answer: 288.71K

PREAMBLE: Identify the classes the following organisms belong to in phylum Platyhelminthes: Turbellaria, Trematoda, and Cestoda

  1. Taenia Solium

Answer: Cestoda

  1. Echinococcus

Answer: Cestoda

  1. Fasciola

Answer: Trematoda

  1. A box of mass 1.0kg is attached to a spring of length 50 cm, if the spring stretches by 2.0 cm. The box is pulled down until the length of the spring becomes 60cm. What is the elastic energy stored in the spring in this condition, if g = 10 m/s2

Answer: 2.5J

  1. A spring constant of 800 N/m has an extension of 5.00cm. Calculate the work done in extending it from 5.00cm to 15.0 cm.

Answer: 8.00J

  1. When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, find the increase in the stored energy

Answer: 300 J

PREAMBLE: One mole of copper (II) oxide reacts with one mole of sulphuric acid producing one mole of CuSO4 and one mole of water. [ Cu = 63.5, S= 32.0, O= 16.0, H= 1.0]

  1. What mass of CuSO4 could be obtained by starting with 15.0g of CuO?

Answer: 30.0g

  1. What mass of pure sulphuric acid would be needed to react with 10 tonnes of copper (II) oxide?

Answer: 12.2g

  1. What mass of water could be obtained by starting with 15.0g of CuO?

Answer: 3.75g

PREAMBLE: Determine the respective number of sigma bond(s) and pi bond(s) in each of the following chemical substances.

  1. Benzene

Answer: 12 and 3

  1. Toluene

Answer: 15 and 3

  1. Phenol

Answer: 13 and 3

PREABLE: The human brain is divided into lobes. These lopes are areas made up of nerve fibres and neurons that are known to perform certain specific functions. Identify the particular lobe that performs the following functions:

  1. Sensation, Language, Perception, Body awareness, Attention

Answer: Parietal lobe

  1. Vision and Perception

Answer: Occipital lobe

  1. Movement, Problem-solving, Concentrating or thinking, Behavior (personality, mood)

Answer: Frontal lobe

  1. Who was/were the first to propose that cell membranes are phospholipid bilayers?

Answer: E. Gorter and F. Grendel

  1. Who proposed that membranes are a phospholipid bilayer between two layers of hydrophilic proteins?

Answer: H. Davson and J. Danielli

  1. Who proposed that the membrane is a mosaic of protein molecules bobbing in a fluid bilayer of phospholipids?

Answer: S. Singer and G. Nicolson

  1. The specific heat capacity of 18.0Kg of silver is 0.359KJ/KgK. Find the energy needed to change the temperature of 18.0Kg of silver by 20.0 o

Answer: 129 kJ

  1. The specific heat capacity of 28.0Kg of gold is 0.235KJ/KgK. Find the energy needed to raise the temperature of 28.0Kg of gold by 12K

Answer: 79 kJ

  1. The specific heat capacity of 12.0Kg of brass is 0.127KJ/KgK. Find the energy needed to raise the temperature of 12.0Kg of brass by 10.0 0

Answer: 15.2 Kj

PREAMBLE: Determine whether the following points will lie on the given curve.

  1. y = 3x -5, (-1, -8)

Answer: Yes, it will lie on the curve

  1. 5x -2y +7 = 0, (1, -1)

Answer: No

  1. y = x3, ( -4, 64)

Answer: No

  1. A mass m attached to a spring oscillates every 4 seconds. If the mass is increased by 4 kg, the period increases by 1 second. Find the initial mass m.

Ans: 7.1 kg

  1. A 300g object attached to the end of a spring oscillates with an amplitude of 5cm and a frequency of 7 Hz. What is its speed when it is 40cm from its equilibrium position?

Ans: 132× 10-2ms-1 = 1.32ms-1.

  1. A student is provided with 500mL of 600ppm solution of sucrose. What volume of this solution in millilitre contains 0.15kg of sucrose?

ANS: 250m L       [ 0.15kg/600ppm = 0.25L.   0.25x 1000mL]

  1. What is the charge on the copper ion in the mineral azurite, Cu3(CO3)2(OH)2?

Answer: +2

  1. How many hydrogen bonds can a molecule of water form?

Answer: 4

  1. 20 g of NaOH is dissolved in 800g of water. What is the molal concentration of this solution?

Answer: 0.2 mol/kg

  1. What is the name given to the hormone secreted by the pineal gland in humans?

Answer: Melatonin

  1. During transpiration, the stomata open when guard cells gain entry of which ions?

Answer: Potassium ions (K+ ions)

  1. Name the two plant hormones that act antagonistically to regulate seed dormancy

Answer: Gibberellins (Gibberellic acid) and Abscisic acid.

PREAMBLE A body of mass 50g vibrates at the end of a spring with amplitude of 12 cm and a period of 1.70s calculates

  1. Maximum acceleration of the mass.

Answer: 1.6m/s2

  1. Spring constant

Answer: 0.68N/m

  1. Maximum speed of mass

Answer: 0.44m/s

PREAMBLE: Give two techniques for separating the constituents of a mixture based on the following:

  1. Basis of separation: Size

Answer: Filtration, Dialysis, Size-exclusion chromatography.

  1. Basis of separation: Density

Answer: Liquid-liquid extraction, centrifugation

  1. Basis of separation: Change in physical state

Answer: Distillation, Sublimation, Recrystallization s

PREABLEM: Cerebrospinal fluid is located inside the ventricles of brain, the central canal of the spinal cord, and in the subarachnoid space around the brain and spinal cord. Give one function of the cerebrospinal fluid:


  • Provide shock-absorbing medium
  • Provide buoyancy to the brain
  • Carries harmful metabolic wastes, drugs, and other substances from the brain to the blood
  • Carries hormones to different parts of the brain

  1. 0 g of KCl were dissolved in 80.0 g of distilled water at 30oC. Calculate the solubility of the solute in moldm-3. Take the molar mass of KCl = 74.5 g/mol

Answer: 4.2 moldm-3

  1. Water was added to 50.0 g of sodium chloride to produce 100 cm3 of a saturated solution at 25oC. If the solubility of the salt at this temperature is 7.0 moldm-3, calculate the number of moles of undissolved salt.

Answer:  0.15 mol.

  1. The solubility of Pb (NO3)2 is 1500 g per 1000 g of water at 40 o Calculate the mass of Pb(NO3)2 that will crystallize out of the solution if 120 g of the saturated solution at 85oC is cooled to 40 oC.

Answer: 48 g

PREAMBLE: Distinguish between Cartilaginous fishes and Bony fishes with respect to the


  1. Position of mouth

Answer: Cartilaginous fishes – Ventrally placed while Bony fish mouth is terminal

  1. Main nitrogenous waste

Answer: Cartilaginous fishes – Urea while Bony fishes – Ammonia

  1. Type of Caudal fin

Answer: Cartilaginous fishes are heterocercal while Bony fishes are homocercal

Preamble: A and B are events in a sample space S.

  1. Find P(AUB) given that P(A) = 0.6, P(B) = 0.8 and A and B are independent.

Answer:  0.92

  1. Find P(A∩B) given P(A) = 0.4 and P(B) = 0.5, and A and B are disjoint.

Answer: 0

  1. Find P(A) given P(B) = 0.5, P(AUB)= 0.8 and P(A∩B) = 0.4

Answer: 0.7

  1. Which of the following organisms is described as having a Tube-within-Tube body plan?

Answer: Flatworms, sponges, cnidarians, roundworms, coelenterates

  1. Which phase in Prophase I synapsis occurs during cell division?

Answer: Zygotene phase

  1. What is Apiculture?

Answer: Rearing, management, and care of honey bees for obtaining honey and bee-wax


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