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Find the HCF of the following numbers 34, 102.

Solution: Highest common factor (HCF) is the greatest factor present in between given two or more numbers. Using prime factorisation, we... View Article

Silk and woollen clothes are often damaged by:

(A) Flies (B) Insects (C) Bacteria (D) Animals Solution: Silk and wool are animal fibres. Silk and woollen clothes are often damaged by... View Article

If 1 + sin²θ = 3 sin θ cos θ, then prove that tan θ = 1 or 1/2.

Solution: Given 1 + sin2 θ = 3 sin θ cos θ …(i) Put sin2 θ + cos2 θ = 1 in (i) sin2 θ + cos2... View Article

Evaluate 1 + 2x + 3x² + 4x³+ … upto infinity, where ∣x∣<1.

Solution: Let S = 1 + 2x + 3x2 + 4x3+...(i) Multiply both sides by x xS = x + 2x2 + 3x3 + 4x4 + ..(ii) Subtract (ii) from (i) (i) - (ii)... View Article

Factorise 3x³ – x² – 3x + 1.

Answer: 3x3 - x2 - 3x + 1 = 3x3 - 3x - x2 + 1 = 3x(x2 - 1) - (x2 - 1) = (3x - 1)(x2 - 1) = (x - 1)(x + 1)(3x - 1) Hence the factors of the... View Article

Find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.

Answer: Let ABCD be a rectangle with AB = 35 cm and BC = 12 cm. Diagonal is AC. In a rectangle, all the angles are 900. So by Pythagoras... View Article

Find the square of (2a + b).

Solution: Use identity (a+b)2 = a2 + 2ab + b2 (2a + b)2 = 4a2 + 4ab + b2... View Article

The sex chromosomes of both male and female are respectively

(A) YY, XX (B) YX, XY (C) XY, XX (D) All of the above Answer: The sex chromosomes of both male and female are respectively XY and XX. The Y... View Article

Find the sum to n terms of the series: 5 + 11 + 19 + 29 + 41…

Solution: 5 + 11 + 19 + 29 + 41… = (1 + 22) + (2 + 32) + (3 + 42) + (4 + 52) + … tn = n + (n + 1)2 = n + n2 + 2n + 1 = n2 + 3n... View Article

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