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The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is (a) Rs 4,000 (b) Rs 4,080 (c) Rs 4,280 (d) Rs 4,050

Answer: (b) Rs 4,080 Given P = Rs.50000 R = 4% T = 2 years Compound interest is the interest calculated on the principal and the interest... View Article

Suppose a certain sum doubles in 2 years at r % rate of simple interest per annum or at R% rate of interest per annum compounded annually. We have (a) r < R (b) R < r (c) R = r (d) can’t be decided

Answer: (b) R < r When the total amount received in two years is the same for both simple and compound interest on the same principal, the... View Article

Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities. (i) C > S (ii) C = S (iii) C < S Then: (a) only (i) is correct. (b) either (i) or (ii) is correct. (c) either (ii) or (iii) is correct. (d) only (iii) is correct.

Answer: (a) only (i) is correct. Let Principal (P) = Rs. 100 Rate = 10% Time = 2 year Simple interest (SI)= (P × R × T)/100 SI =... View Article

Factorised form of 18mn + 10mnp is ________.

Answer: Factorised form of 18mn + 10mnp is 2mn (9 + 5p) In Mathematics, factorization or factoring is defined as the breaking or decomposition of... View Article

Common factor of ax2 + bx is __________.

Answer: Common factor of ax2 + bx is x(ax + b) Common factors are defined as factors that are common to two or more numbers. In other words, a... View Article

The product of two polynomials is a ________.

Answer: The product of two polynomials is a polynomial. Polynomials are algebraic expressions that consist of variables and coefficients.... View Article

(x + a) (x + b) = x² + (a + b) x + ________.

Answer: (x + a) (x + b) = x2 + (a + b) x + ab (x + a) (x + b) ⇒ x × (x + b) + a × (x + b) ⇒ x2 + xb + xa + ab ⇒ x2 +... View Article

(a + b)² – 2ab = _ + __

Answer: (a + b)2 – 2ab = a2 + b2 (a + b)2 – 2ab = a2 + 2ab + b2 – 2ab (a + b)2 – 2ab = a2 + b2 Important standard... View Article

(a – b)² + ____________ = a² – b²

Answer: (a – b)2 + (2ab – 2b2) = a2 – b2 (a – b)2 + (2ab – 2b2) = a2 + b2 – 2ab + 2ab – 2b2 = a2... View Article

a² – b²= (a + b ) __________.

Answer: a2 – b2 = (a + b)(a – b) Important standard algebraic formula a2 – b2 = (a – b)(a + b) (a + b)2 = a2 + 2ab +... View Article

(a – b) _________ = a² – 2ab + b²

Answer: (a – b)(a - b) = a2 – 2ab + b2 (a – b) (a – b) = (a – b)2 = a2 – 2ab + b2 (a – b)(a –... View Article

a (b + c) = a × + a × _.

Answer: a (b + c) = a × b + a × c Distributive property explains that the operation performed on numbers, available in brackets... View Article

The product of two terms with unlike signs is a ____ term.

Answer: The product of two terms with unlike signs is a negative term. Let us assume two, unlike sign terms, are, – 5p and 2q = -5p... View Article

The product of two terms with like signs is a ____ term.

Answer: The product of two terms with like signs is a positive term. Example 1: Let us assume two terms with like sign are, 3p and 2q The... View Article

The value of (a + b)²– (a – b)² is (a) 4ab (b) – 4ab (c) 2a² + 2b² (d) 2a² – 2b²

Answer: (a) 4ab The value of (a + b)2 is (a + b)2 = (a2 + b2 + 2ab) The value of (a – b)2 is (a2 + b2 – 2ab) (a + b)2 – (a... View Article

The value of (a + b)² + (a – b)² is (a) 2a + 2b (b) 2a – 2b (c) 2a² + 2b² (d) 2a² – 2b²

Answer: (c) 2a2 + 2b2 We know that (a + b)2 = (a2 + b2 + 2ab) (a – b)2 = (a2 + b2 – 2ab) (a + b)2 + (a – b)2 = (a2 + b2 +... View Article

The value of (3x³ +9x² + 27x) ÷ 3x is (a) x² +9 + 27x (b) 3x³ +3x² + 27x (c) 3x³ +9x² + 9 (d) x² +3x + 9

Answer: (d) x2 +3x + 9 Takeout 3x as a common in (3x3 +9x2 + 27x) (3x3 +9x2 + 27x) = 3x (x2 + 3x + 9) The value of (3x3 +9x2 + 27x) ÷ 3x... View Article

The value of (2x² + 4) ÷ 2 is (a) 2x² + 2 (b) x² + 2 (c) x² + 4 (d) 2x² + 4

Answer: (b) x2 + 2 The value of (2x2 + 4) ÷ 2 (2x2 + 4) can be written as (2x2 + 4) = 2(x2 + 2) (2x2 + 4) ÷ 2 = [2(x2 + 2)]/2 (2x2... View Article

The value of (– 27x²y) ÷ (– 9xy) is (a) 3xy (b) – 3xy (c) – 3x (d) 3x

Answer: (d) 3x (– 27x2y) can be written as (– 27x2y) = (-27 × x × x × y) (– 9xy) can be written as (–... View Article

The factors of x² – 4 are (a) (x – 2), (x – 2) (b) (x + 2), (x – 2) (c) (x + 2), (x + 2) (d) (x – 4), (x – 4)

Answer: (b) (x + 2), (x – 2) When a number is said to be a factor of any other second number, then the first number must divide the second... View Article

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