1000 is a perfect square.
Question: 1000 is a perfect square. Solution: False 1000 = 2 x 2 x 2 x 5 x 5 x 5 = 22x 52x 2 x 5 Clearly, it is not a perfect square, because it has two unpaired factors 2 and 5....
Read More →The sum of first n odd natural
Question: The sum of first n odd natural numbers is n2. Solution: True. The sum of odd numbers = (2n 1) = (2 n (n + 1))/2 n = n2+ n n = n2...
Read More →There are 200 natural numbers
Question: There are 200 natural numbers between 1002and 1012. Solution: True Natural numbers between $100^{2}$ and $101^{2}$ $=10 t^{2}-100^{2}-1 \quad[\because$ natural numbers between $a$ and $b=b-a-1]$ $=(101+100)(101-100)-1=201-1=200$...
Read More →There are five perfect cubes
Question: There are five perfect cubes between 1 and 100. Solution: False There are eight perfect cubes between 1 and 100, i.e. 8,27,64,125,216,343,512 and 729...
Read More →The cube root of 8000 is 200.
Question: The cube root of 8000 is 200. Solution: Flase We have, $\sqrt[3]{8000}=\sqrt[3]{(2 \times 2 \times 2) \times(2 \times 2 \times 2) \times(5 \times 5 \times 5)}$...
Read More →Solve this
Question: $\sqrt{4 i}$ Solution: Let, $(a+i b)^{2}=0+4 i$ Now using, $(a+b)^{2}=a^{2}+b^{2}+2 a b$ $\Rightarrow a^{2}+(b i)^{2}+2 a b i=0+4 i$ Since $i^{2}=-1$ $\Rightarrow a^{2}-b^{2}+2 a b i=0+4 i$ Now, separating real and complex parts, we get $\Rightarrow a^{2}-b^{2}=0$ ..eq.1 $\Rightarrow 2 \mathrm{ab}=4$ .. eq.2 $\Rightarrow a=\frac{2}{b}$ Now, using the value of a in eq.1, we get $\Rightarrow\left(\frac{2}{b}\right)^{2}-\mathrm{b}^{2}=0$ $\Rightarrow 4-\mathrm{b}^{4}=0$ $\Rightarrow b^{4}...
Read More →The square of every natural number is
Question: The square of every natural number is always greater than the number itself. Solution: False 1 is a natural number and square of 1 is not greater than 1....
Read More →The square root of 0.9 is 0.3.
Question: The square root of 0.9 is 0.3. Solution: False As, the square of 0.3 = (0.3)2= 0.3 x 0.3 =0.09...
Read More →The cube of 0.4 is 0.064.
Question: The cube of 0.4 is 0.064. Solution: True Cube of 0.4 = (0.4)2= 0.4 x 0.4 x 0.4 = 0.064...
Read More →The square of 2.8 is 78.4.
Question: The square of 2.8 is 78.4. Solution: False The square of 2.8 = (2.8)2= 2.82.8 = 7.84...
Read More →Each prime factor appears 3 times
Question: Each prime factor appears 3 times in its cube. Solution: True If a3 is the cube and m is one of the prime factors of a. Then, m appears three times in a3....
Read More →The square root of 1521 is 31.
Question: The square root of 1521 is 31. Solution: Falsie % As, the square of 31 = (31)2= 31 x 31 = 961...
Read More →There is no square number
Question: There is no square number between 50 and 60. Solution: True Numbers between 50 and 60 are 51,52, 53, 54, 55, 56, 57, 58 and 59. We observed that there is no square number between 50 and 60....
Read More →The equation representing the y-axis is
Question: The equation representing they-axis is (a)x= 0 (b)y= 0 (c)x=a (d)y=a Solution: (a)x = 0...
Read More →Solve this
Question: $\sqrt{i}$ Solution: Let, $(a+i b)^{2}=0+i$ Now using, $(a+b)^{2}=a^{2}+b^{2}+2 a b$ $\Rightarrow a^{2}+(b i)^{2}+2 a b i=0+i$ Since $i^{2}=-1$ $\Rightarrow a^{2}-b^{2}+2 a b i=0+i$ Now, separating real and complex parts, we get $\Rightarrow a^{2}-b^{2}=0$ ..eq.1 $\Rightarrow 2 \mathrm{ab}=1$ .. eq.2 $\Rightarrow \mathrm{a}=\frac{1}{2 b}$ Now, using the value of a in eq.1, we get $\Rightarrow\left(\frac{1}{2 b}\right)^{2}-b^{2}=0$ $\Rightarrow 1-4 b^{4}=0$ $\Rightarrow 4 b^{2}=1$ Simpl...
Read More →The product of twtfperfect squares
Question: The product of twtfperfect squares is a perfect square. Solution: True e.g. If 4 and 25 are the perfect square, then 4 x 25 = 100 is also a perfect square. Clearly, the product of two perfect squares is a perfect square....
Read More →In which of the following quadrants does the point (–7, –1) lie?
Question: In which of the following quadrants does the point (7, 1) lie? (a) thex-axis (b) they-axis (c) a line parallel to they-axis (d) a line parallel to thex-axis Solution: (d) a line parallel to thex-axis...
Read More →The sum of two perfect squares
Question: The sum of two perfect squares is a perfect square. Solution: False e.g. 16 and 25 are the perfect squares, but 16 + 25 = 41 is not a perfect square....
Read More →The abscissa of a point is its distance from the
Question: The abscissa of a point is its distance from the (a) origin (b)x-axis (c)y-axis (d) none of these Solution: (c)y-axis...
Read More →The square of 86 will have 6 at
Question: The square of 86 will have 6 at the units place. Solution: True We know that, the units digit of the square of a number having digit at units place as 4 or 6 is 6....
Read More →In which of the following quadrants does the point Q (–4, 1) lie?
Question: In which of the following quadrants does the pointQ(4, 1) lie? (a) I (b) II (c) III (d) IV Solution: (b) II...
Read More →Cube of a number ending in 7
Question: Cube of a number ending in 7 will end in the digit________ Solution: 3 We know that, the cubes of the numbers ending in digits 3 or 7 ends in digits 7 or 3, respectively. i.e 7 x 7 x 7 = 343 Hence, the cube of a number ending in 7 will end in the digit 3....
Read More →In which of the following quadrants does the point A (2, –3) lie?
Question: In which of the following quadrants does the pointA(2, 3) lie? (a) I (b) II (c) III (d) IV Solution: (d) IV...
Read More →The least number by which 72 be divided
Question: The least number by which 72 be divided to make it a perfect cube, is________ Solution: 9 Resolving 72 into prime factors, we get 72=2 x 2 x 2 x 3 x 3 Grouping the factors in triplets of equal factors, we get 72 = (2 x 2 x 2) x 3 x 3 Clearly, if we divide 72 by 3 x 3, the quotient would be 2 x 2 x 2, which is a perfect cube. Hence, the least number by which 72 be divided to make it, a perfect cube, is 9....
Read More →In which of the following quadrants does the point (–7, –1) lie?
Question: In which of the following quadrants does the point (7, 1) lie? (a) I (b) II (c) III (d) IV Solution: (C) III...
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