The digit at the one’s place
Question: The digit at the ones place of 572 is________ Solution: 2 We know that, the unit's digit of the square of a number having digit at unit's place as 3 or 7 is 9 . The digit at one's place of $57^{2}=9$ $[\because 7 \times 7=49]$...
Read More →The sum of first six odd natural
Question: The sum of first six odd natural numbers is________ Solution: We know that, sum of first $n$ odd natural numbers $=n^{2}$ $\therefore$ Sum of first six odd natral numbers $=(6)^{2}=36$...
Read More →The square of 0.7
Question: The square of 0.7 is________ Solution: 0.49 Square of 0.7 = (0.7)2= 07 x 07 = 0.49...
Read More →Solve this
Question: $\sqrt{5+12 i}$ Solution: Let, $(a+i b)^{2}=5+12 i$ Now using, $(a+b)^{2}=a^{2}+b^{2}+2 a b$ $\Rightarrow a^{2}+(b i)^{2}+2 a b i=5+12 i$ Since $i^{2}=-1$ $\Rightarrow a^{2}-b^{2}+2 a b i=5+12 i$ Now, separating real and complex parts, we get $\Rightarrow a^{2}-b^{2}=5 \ldots \ldots \ldots \ldots \ldots$ eq. 1 $\Rightarrow 2 \mathrm{ab}=12 \ldots \ldots . . \mathrm{q} .2$ $\Rightarrow \mathrm{a}=\frac{6}{b}$ Now, using the value of a in eq.1, we get $\Rightarrow\left(\frac{6}{b}\right)...
Read More →One’s digit in the cube
Question: Ones digit in the cube of 38 is________ Solution: 2 We know that, the cube of a number having 8 at one's place $\therefore$ One's digit in cube of $38=2$...
Read More →1m3 =________ cm3.
Question: 1m3=________ cm3. Solution: $1000000 \mathrm{~cm}^{3}$ $1 \mathrm{~m}^{3}=(100 \mathrm{~cm})^{3}$ $[\because 1 \mathrm{~m}=100 \mathrm{~cm}]$ $=(100 \times 100 \times 100) \mathrm{cm}^{3}$ $=1000000 \mathrm{~cm}^{3}$...
Read More →The histogram given below shows the number of literate females in the age group of 10 to 40 years.
Question: The histogram given below shows the number of literate females in the age group of 10 to 40 years. Study the histogram carefully and answer the question that follow: (i) Write the classes, assuming that all the classes are of equal width. (ii) What is the class width? (iii) In which age group are the literate females the least? (iv) In which age group is the number of literate females the highest? Hint. Number of class intervals of equal width $=6$ (given), class width $=\frac{(40-10)}...
Read More →1m2 =________ cm2.
Question: 1m2=________ cm2. Solution: $10000 \mathrm{~cm}^{2}$ $1 \mathrm{~m}^{2}=(100 \mathrm{~cm})^{2}$ $[\because 1 \mathrm{~m}=100 \mathrm{~cm}]$ $=10000 \mathrm{~cm}^{2}$...
Read More →Solve this
Question: $2 x^{2}+3 i x+2=0$ Solution: Given $2 x^{2}+3 i x+2=0$ $\Rightarrow 2 x^{2}+4 i x-i x+2=0$ $\Rightarrow 2 x(x+2 i)-i\left(x-\frac{2}{i}\right)=0$ $\Rightarrow 2 x(x+2 i)-i\left(x-\frac{2 \times i}{i \times i}\right)=0$ $\Rightarrow 2 x(x+2 i)-i\left(x-\frac{2 \times i}{-1}\right)=0$ $\Rightarrow 2 x(x+2 i)-i(x+2 i)=0$ $\Rightarrow(x+2 i)(2 x-i)=0$ $\Rightarrow x+2 i=0 \ 2 x-i=0$ $\Rightarrow \mathrm{x}=-2 \mathrm{i} \^{x=\frac{i}{2}}$ Ans: $\mathrm{x}=-2 \mathrm{i}$ and $^{x}=\frac{i}...
Read More →The cube of 100 will havfe
Question: The cube of 100 will havfe________zeroes. Solution: 6 Cubeof100 = 1003 = 100x100x100 = 1000000...
Read More →Look at the histogram given below and answer the question that follow:
Question: Look at the histogram given below and answer the question that follow: (i) What information is being given by the histogram? (ii) How many teachers are of age less than 45 years? (iii) How many teachers are of age 40 years or more but less than 55 years? Solution: (i) The given histogram tells about the number of teachers in a school from the age group $25-30$ to $55-60$. (ii) Number of teachers with age less than 45 years $=3+5+7+6=21$ (iii) Number of teachers with age more than 40 ye...
Read More →The square root of 5.3 x 5.3
Question: The square root of 5.3 x 5.3 is________ Solution: $5.3$ Square root of $5.3 \times 5.3=\sqrt{(5.3)^{2}}$ $=(5.3)^{2 / 2}=5.3$...
Read More →Solve this
Question: $x^{2}+3 i x+10=0$ Solution: Given: $x^{2}+3 i x+10=0$ $\Rightarrow \mathrm{x}^{2}+5 \mathrm{ix}-2 \mathrm{i} \mathrm{x}+10=0$ $\Rightarrow x(x+5 i)-2 i\left(x-\frac{10}{2 i}\right)=0$ $\Rightarrow x(x+5 i)-2 i\left(x-\frac{5 \times i}{i \times i}\right)=0$ $\Rightarrow^{x(x+5 i)-2 i\left(x-\frac{5 \times i}{-1}\right)}=0$ $\Rightarrow x(x+5 i)-2 i(x+5 i)=0$ $\Rightarrow(x+5 i)(x-2 i)=0$ $\Rightarrow \mathrm{x}+5 \mathrm{i}=0 \ \mathrm{x}-2 \mathrm{i}=0$ $\Rightarrow \mathrm{x}=-5 \mat...
Read More →Look at the histogram given below and answer the question that follow:
Question: Look at the histogram given below and answer the question that follow: (i) How many students have height more than or equal to 135 cm but less than 150 cm? (ii) Which class interval has the least number of students? (iii) What is the class size? (iv) How many students have height less than 140 cm? Solution: (i) Number of students $=14+18+10=42$ (ii) Class interval with least number of students $=150-155$ (iii) Class size $=130-125=5$ (iv) Number of students with height less than $140=1...
Read More →The square of 5.5 is
Question: The square of 5.5 is________ Solution: 30.25 Square of 5.5= (5.5)2= 55 x 5.5= 30.25...
Read More →The square root of 24025 will have
Question: The square root of 24025 will have________digits. Solution: 3 Given number is 24025 . Here, number of digits, $n=5$ (odd) $\therefore$ Number of digits in the square root of $24025=\frac{n+1}{2}=\frac{5+1}{2}=3$...
Read More →The weights (in kg) of 30 students of a class are
Question: The weights (in kg) of 30 students of a class are 39, 43, 32, 37, 29, 26, 31, 45, 46, 31, 37, 38, 30, 39, 36, 41, 35, 34, 41, 46, 39, 38, 36, 38, 40, 42, 33, 43, 44, 33. Prepare a frequency distribution table using one class interval as 3035, in which 30 is included and 35 excluded. Using the above data. draw a histogram. Solution: Frequency distriubution table...
Read More →Solve this
Question: $x^{2}+13=4 x$ Solution: Given: $x^{2}+13=4 x$ $\Rightarrow x^{2}-4 x+13=0$ Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by: $x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$ $\Rightarrow x=\frac{-(-4) \pm \sqrt{(-4)^{2}-(4 \times 1 \times 13)}}{2 \times 1}$ $\Rightarrow x=\frac{4 \pm \sqrt{16-52}}{2}$ $\Rightarrow x=\frac{4 \pm \sqrt{-36}}{2}$ $\Rightarrow x=\frac{4 \pm 6 i}{2}$ $\Rightarrow x=\frac{4}{2} \pm \frac{6}{2} i$ $\Rightarrow x=2 \pm 3 i$ Ans: $x...
Read More →The marks obtained (out of 20) by 30 students of a class in a test are given below:
Question: The marks obtained (out of 20) by 30 students of a class in a test are given below: 7, 10, 8, 16, 13, 14, 15, 11, 18, 11, 15, 10, 7, 14, 20, 19, 15, 16, 14, 20, 10, 11, 14, 17, 13, 12, 15, 14, 16, 17. Prepare a frequency distribution table for the above data using class intervals of equal width in which one class interval in 38(including 2 and excluding 8). From the frequency distribution table so obtained, draw a histogram. Solution: Frequency distribution table...
Read More →There are natural numbers between
Question: There are natural numbers between n2and (n + l)2 Solution: $2 n$ Natural numbers between $n^{2}$ and $(n+1)^{2}=\left[(n+1)^{2}-n^{2}\right]-1$ $=\left[n^{2}+2 n+1-n^{2}\right]-1$ $=2 n+1-1=2 n$...
Read More →The square of 500 will have zeroes.
Question: The square of 500 will have zeroes. Solution: four The square of 500 = (500)2 = 500 x 500 = 250000 Hence, the square of 500 will have four zeroes....
Read More →Solve this
Question: 18. $21 x^{2}-28 x+10=0$ Solution: Given: $21 x^{2}-28 x+10=0$ Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by: $x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$ $\Rightarrow x=\frac{-(-28) \pm \sqrt{(-28)^{2}-(4 \times 21 \times 10)}}{2 \times 21}$ $\Rightarrow x=\frac{28 \pm \sqrt{784-840}}{42}$ $\Rightarrow x=\frac{28 \pm \sqrt{-56}}{42}$ $\Rightarrow x=\frac{28 \pm 2 \sqrt{14} i}{42}$ $\Rightarrow x=\frac{28}{42} \pm \frac{2 \sqrt{14}}{42} i$ Ans: $x=\fr...
Read More →The following table shows the number of illiterate persons in the age group (10–58 years) in a town.
Question: The following table shows the number of illiterate persons in the age group (1058 years) in a town. Represent the given data by means of a histogram. Hint.Take 1 small division = 5 persons. Solution:...
Read More →The unit’s digit in the square
Question: The units digit in the square of 1294 is________ Solution: 6 We know that, the units digit of the square of a number having digit .at units place as 4 or 6 is 6. Hence, the units digit in the square of 1294 is 6 as 4 x 4 = 16....
Read More →There are________ perfect cubes
Question: There are________ perfect cubes between 1 and 1000. Solution: 8 There are 8 perfect cubes between 1 and 1000, i.e. 8, 27,64,125, 216, 343 and 729....
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