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For the standard form of the parabola y² = -4ax, the equation of the directrix is

Solution: Given y2 = -4ax Here focus is (-a, 0). Equation of directrix is x = a => x - a = 0 The required equation of the directrix is x... View Article

Factorise x⁶– 729.

Solution: Use formula a3 - b3 = (a - b)(a2 + ab + b2) x6 - 729 = (x2)3 - (32)3 = (x2 - 32)(x4 + 9x2 + 92) = (x2 - 9)(x4 + 9x2 + 81) = (x -... View Article

The daily expenditure of 100 families are given below. Calculate f₁ and f₂ if the mean daily expenditure is Rs.188.

Expenditure in Rs. 140-160 160-180 180-200 200-220 220-240 No. of families 5 25 f1... View Article

Look at this series: 80, 10, 70, 15, 60, . . . What number should come next?

Solution: This is an alternating addition and subtraction series. Observe the first pattern. 80, 70, 60. 10 is subtracted from each number to... View Article

Fill in the blanks. The matter is made up of tiny particles called

Solution: The matter is made up of tiny particles called atoms.... View Article

50 circular plates each of diameter 14 cm and thickness 0.5 cm are placed one above the other to form a right circular cylinder. Find its total surface area.

Given, 50 circular plates each with diameter 14 cm Radius of circular plates = 7 cm Thickness of plates = 0.5 cm As these plates are one... View Article

Twenty four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find each part

Let us assume the first part as x and second part be (24 - x) Now, as per the given condition, 7x + 5 (24 - x) = 146 On further calculation,... View Article

What is the next number in the series 2, 12, 36, 80, 150, ? (A) 263 (B) 251 (C) 284 (D) 252

Given series is 2, 12, 36, 80, 150 Step 1: Difference between the first and second term in the series 12 - 2 = 10 36 - 12 = 24 80 - 36 = 44... View Article

Looking at a portrait of a man, Harsh said, “His mother is the wife of my father’s son. Brothers and sisters I have none’. At whose portrait was Harsh looking? (A) His son (B) His cousin (C) His uncle (D) His nephew (E) None of these

His son Since Harsh has no brother or sister. Hence, he is only his father's son. Now, wife of my father's son means Harsh wife. His mother is... View Article

The Indian Partnership Act came into force on __________ (A) 1933 (B) 1932 (C) 1956 (D) 1934

1932 Most of the businesses in India adopt a partnership business, so to monitor and govern such partnership The Indian Partnership Act was... View Article

To the captain of a ship A, which is travelling with velocity vA = (3i + 4j)km/hr, a second ship B appears to have a velocity of (5i + 12j) km/hr. What is the true velocity of the ship B?

Given The true velocity of a ship A is And ship B appears to have a velocity of The relative velocity of ship B with respect to ship A is... View Article

Optimum speed for turning on a banked road is (A) √(Rgtanθ) (B) √(Rgcotθ) (C) √(Rgsinθ) (D) √(Rgsecθ)

Optimum speed is the speed with which one can take turns on banked roads without wear and tear. The proper velocity or optimum v on a road... View Article

Ventilators are provided at the top of room (A) To bring oxygen for breathing (B) So that sunlight may enter the room (C) To maintain convectional currents to keep the air fresh in the room (D) To provide an outlet for carbon dioxide

To maintain convectional currents to keep the air fresh in the room In a room containing a mixture of hot and cold air, the hot air being less... View Article

Monocotyledonous seeds possess a single cotyledon which is represented by (A) Tegman (B) Endosperm (C) Scutellum (D) Aleurone

Scutellum A monocotyledonous seed has embryos that possess only one large cotyledon called scutellum. Generally, the scutellum is shaped like a... View Article

In glycolysis, glucose molecule is converted into which substance? (A) Lactic acid (B) Ethanol (C) Pyruvate (D) Amino acid

Pyruvate Glycolysis is the process in which glucose is broken down to produce energy. It produces two molecules of pyruvate, ATP, NADH and water.... View Article

What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

Given, The amount deposited in the bank is Rs 500. At the end of first year, amount = Rs 500(1 + 1/10) = Rs 500 (1.1) At the end of 2nd year,... View Article

What is serum?

The serum is the liquid or undiluted part of the blood, which lacks clotting factors. Hence, it is formed after blood coagulation. The serum... View Article

15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries will each box contain?

Given that, Number of pastries = 15 Number of biscuit packets = 12 So, the required number of boxes which will contain equal number of both... View Article

Contamination of water with sewage is indicated by cysts of (A) Escherichia (B) Entamoeba (C) Pseudomonas (D) Leishmania

Entamoeba Contamination of water with sewage is indicated by cysts of Entamoeba histolytica. E. histolytica causes infection by ingestion of... View Article

Fill in the blank with a suitable adverb: She often comes _________ for the lectures. (A) Lately (B) Late (C) Lateness (D) Lateful

Late It is an adverb that denotes the way she comes and the time when she arrives for the lecture. Hence, among the given options 'late' is the... View Article