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In standard form, the number 829030000 is written as K × 10⁸ where K is equal to (a) 82903 (b) 829.03 (c) 82.903 (d) 8.2903

Answer: (d) 8.2903 Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of... View Article

(2/3)³ × (5/7)³ is equal to (a) ((2/3) × (5/7))⁹ (b) ((2/3) × (5/7))⁶ (c) ((2/3) × (5/7))³ (d) ((2/3) × (5/7))⁰

Answer: (c) ((2/3) × (5/7))3 For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n. am × bm =... View Article

Which of the following is not equal to 1 ? (a) (2³ × 3³)/(4 × 18) (b) [(-2)³ × (-2)⁴] ÷ (-2)⁷ (c) (3⁰ × 5³)/(5 × 25) (d) 2⁴/(7⁰ + 3⁰)³

Answer: (d) 24/(70 + 30)3 Consider the option (a) (23 × 33)/(4 × 18) = (2 × 2 × 2 × 3 × 3 × 3)/(4... View Article

Which of the following is not equal to (-5/4)⁴? (a) (-5)⁴/4⁴ (b) 5⁴/(-4)⁴ (c) –(5⁴/4⁴) (d) (-5/4) × (-5/4) × (-5/4) × (-5/4)

Answer: (c) –(54/44) (-5/4)4 = (-5)4/44 (-5/4)4 = 54/(-4)4 (-5/4)4 = (-5/4) × (-5/4) × (-5/4) × (-5/4) (-5/4)4≠... View Article

cube of (-1/4) is (a) -1/12 (b) 1/16 (c) -1/64 (d) 1/64

Answer: (c) -1/64 Cube of (-1/4) is = -13/43 = (-1 × -1 × -1)/(4 × 4 × 4) = -1/64 An exponent of a number represents... View Article

Square of (-2/3) is (a) -2/3 (b) 2/3 (c) -4/9 (d) 4/9

Answer: (d) 4/9 Square of (-2/3) is = -22/32 = (-2 × -2)/(3 × 3) = 4/9 An exponent of a number represents the number of times the... View Article

In standard form, the number 72105.4 is written as 7.21054 × 10ⁿ where n is equal to (a) 2 (b) 3 (c) 4 (d) 5

Answer: (c) 4 Any number can be expressed as a decimal number between 1.0 and 10.0 including 1.0 multiplied by a power of 10. Such a form of a... View Article

Which of the following is equal to 1? (a) 2⁰ + 3⁰ + 4⁰ (b) 2⁰ × 3⁰ × 4⁰ (c) (3⁰ – 2⁰) × 4⁰ (d) (3⁰ – 2⁰) × (3⁰ + 2⁰)

Answer: (b) 20 × 30 × 40 For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n, a0 = 1 So, 20 = 1... View Article

If 2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K2¹⁹⁹⁵, then the value of K is (a) 1 (b) 2 (c) 3 (d) 4

Answer: (c) 3 21998 - 21997 - 21996 + 21995 = K21995 By cross multiplication we get, (21998/21995) - (21997/21995) - (21996/21995) +... View Article

The standard form of the number 12345 is (a) 1234.5 × 10¹ (b) 123.45 × 10² (c) 12.345 × 10³ (d) 1.2345 × 10⁴

Answer: (d) 1.2345 × 104 Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10.... View Article

Value of (10²² + 10²⁰)/10²⁰ is (a) 10 (b) 10⁴² (c) 101 (d) 10²²

Answer: (c) 101 By splitting, (1022 + 1020)/1020 we get, (1022 + 1020)/1020 = (1022/1020) + (1020/1020) By using the rule am ÷ an =... View Article

(1⁰ + 2⁰ + 3⁰) is equal to (a) 0 (b) 1 (c) 3 (d) 6

Answer: (c) 3 For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n, a0 = 1 So, 10 = 1 20 = 1 3o = 1 Then,... View Article

a^m × aⁿ is equal to (a) (a²)^mn (b) a^m–n (c) a^m+n (d) a^mn

Answer: (c) am+n am × an is equal to am + n An exponent of a number represents the number of times the number is multiplied by itself.... View Article

For any two non-zero rational numbers x and y, x⁵ ÷ y⁵ is equal to (a) (x÷y)¹ (b) (x÷y)⁰ (c) (x÷y)⁵ (d) (x÷y)¹⁰

Answer: (c) (x÷y)5 For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n, am ÷ bm = (a/b)m x5... View Article

x is a non-zero rational number. Product of the square of x with the cube of x is equal to the (a) second power of x (b) third power of x (c) fifth power of x (d) sixth power of x

Answer: (c) fifth power of x From the question, it is given that, The square of x = x2 The cube of x = x3 As per the condition given in the... View Article

For a non-zero rational number x, x⁸ ÷ x² is equal to (a) x⁴ (b) x⁶ (c) x¹⁰ (d) x¹⁶

Answer: (b) x6 For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n, am ÷ an = am–n , m>n so,... View Article

[(-3)²]³ is equal to (a) (-3)⁸ (b) (-3)⁶ (c) (-3)⁵ (d) (-3)²³

Answer: (b) (-3)6 For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n, (am)n = amn [(-3)2]3 = -3(2 × 3)... View Article

State whether the statement given in question isTrue or False: Sum of two rational numbers is always a rational number.

Answer: The sum of two rational numbers is always a rational number. - True A rational number, in Mathematics, can be defined as any number... View Article

State whether the statement given in question isTrue or False: . If p/q is a rational number and m is a non-zero integer, then (p/q) = (p × m)/(q × m) is a rational number not equivalent to p/q.

Answer: If p/q is a rational number and m is a non-zero integer, then (p/q) = (p × m)/(q × m) is a rational number not equivalent to... View Article

State whether the statement given in question isTrue or False: In a rational number, denominator always has to be a non-zero integer.

Answer: In a rational number, the denominator always has to be a non-zero integer - True A number that can be expressed in the form p/q, where p... View Article