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Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?

Let us there are two AP’s with first terms a and A Let their common differences be d and D respectively Suppose n... View Article

For the AP: -3, -7, -11, …, can we find directly a₃₀ – a₂₀ without actually finding a₃₀ and a₂₀? Give reasons for your answer.

Solution The given statement is True As per the given details First term, a = – 3 Common difference, d... View Article

Justify whether it is true to say that -1, -3/2, -2, 5/2,… forms an AP as a₂ – a₁ = a₃ – a₂

Solution The given statement is False Given that a1 = -1 a2 = -3/2 a3 = -2 a4 = 5/2 Common difference can be calculated... View Article

Which of the following form an AP? Justify your answer. (i) -1, -1, -1, -1,… (ii) 0, 2, 0, 2,… (iii) 1, 1, 2, 2, 3, 3… (iv) 11, 22, 33… (v) 1/2,1/3,1/4, … (vi) 2, 22, 23, 24, … (vii) √3, √12, √27, √48, …

Solution (i) –1, –1, –1, –1,… Answer According to the given data we get to know that a a1 = –... View Article

If the common difference of an AP is 5, then what is a₁₈ – a₁₃? (A) 5 (B) 20 (C) 25 (D) 30

Answer The correct answer is (C) 25 Solution We know that the nth term of an AP is given by... View Article

Which term of the AP: 21, 42, 63, 84… is 210? (A) 9th (B) 10th (C) 11th (D) 12th

Answer The correct answer is (B) 10th Solution We know that the nth term of an AP is given by... View Article

If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term? (A) 30 (B) 33 (C) 37 (D) 38

Answer The correct answer is (B) 33 Solution We know that the nth term of an AP is given by... View Article

The 21st term of the AP whose first two terms are -3 and 4 is (A) 17 (B) 137 (C) 143 (D) -143

Answer The correct answer is (B) 137 Solution We know that the nth term of an AP is given by the... View Article

The first four terms of an AP, whose first term is -2 and the common difference is -2, are (A) – 2, 0, 2, 4 (B) – 2, 4, – 8, 16 (C) – 2, – 4, – 6, – 8 (D) – 2, – 4, – 8, -16

Answer The correct answer is (C) – 2, – 4, – 6, – 8 Solution We know that the nth... View Article

The 11th term of the AP: -5, (-5/2), 0, 5/2, …is (A) -20 (B) 20 (C) -30 (D) 30

Answer The correct answer is (B) 20 Solution We know that the nth term of an AP is given by the... View Article

The list of numbers – 10, – 6, – 2, 2,… is (A) an AP with d = – 16 (B) an AP with d = 4 (C) an AP with d = – 4 (D) not an AP

Answer The correct answer is (B) an AP with d = 4 Solution We know that nth term of an AP... View Article

In an AP, if a = 3.5, d = 0, n = 101, then an will be (A) 0 (B) 3.5 (C) 103.5 (D) 104.5

Answer The correct answer is(B) 3.5 Solution We know that nth term of an AP is given by the formula... View Article

In an AP, if d = -4, n = 7, a_n = 4, then a is (A) 6 (B) 7 (C) 20 (D) 28

Answer The correct answer is (D) 28 Solution We know that nth term of an AP is given by the... View Article

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?

Solution Let Zeba’s age = A According to the given details (A -5)²=11+5A A ²+25-10A =11+5A A ²-15A +14=0 A... View Article

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.

Given The train travels at a uniform speed of 360 km. It would have taken 48 minutes less to travel... View Article

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

Given A natural number, when increased by 12, equals 160 times its reciprocal Find out We have to determine the... View Article

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

Given A natural number’s square diminished by 84 is equal to thrice of 8 more than the given number. Find... View Article

Find the roots of the quadratic equations by using the quadratic formula in each of the following: i) 2 x² – 3x – 5 = 0 ii) 5x² + 13x + 8 = 0 iii) -3x² + 5x + 12 = 0 iv) -x² + 7x – 10 = 0 v) x² + 2 √2x – 6 = 0 vi) x² – 3 √5x + 10 = 0 vii) (½)x²– √11x + 1 = 0

The quadratic formula for finding the roots of the quadratic equation ax2 + bx + c = 0, a ≠ 0... View Article

A quadratic equation with integral coefficient has integral roots. Justify your answer.

Answer No, a quadratic equation with integral coefficients may or may not have integral roots. Justification Consider the equation, 8x2 – 2x... View Article

Write whether the following statements are true or false. Justify your answers. i) Every quadratic equation has exactly one root. ii) Every quadratic equation has at least one real root. iii) Every quadratic equation has at least two roots. iv) Every quadratic equations has at most two roots. v) If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots. vi) If the coefficient of x² and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Solution: (i) The given statement is False. Let us consider an example, a quadratic equation x2 – 25 = 0 has two... View Article

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