Find the area of a square field,
Question: Find the area of a square field, if its perimeter is 96 m. Solution: Given, perimeter of square field $=96 \mathrm{~m}$ $\because$ Perimeter of square $=4 \times$ Side $\Rightarrow 4 \times($ Side $)=96$ $\Rightarrow \quad$ Side $=24 \mathrm{~m}$ $\therefore$ Area of square field $=(\text { Side })^{2}=(24)^{2}=576 \mathrm{~m}^{2}$...
Read More →Plot a line graph for the variables x and y , where y = 2x + 1.
Question: Plot a line graph for the variablesxandy, wherey= 2x+ 1. Using the graph, find the value of (i)y, whenx= 5 and (ii)x, when y = 13. Solution: We have the following table for y = 2x+1...
Read More →The dimensions of a rectangular
Question: The dimensions of a rectangular field are 80m and 18m. Find the length of its diagonal. Solution: From the question it is given that, Length of rectangular field = 80 m Breadth of rectangular field = 18 m Then, Length of diagonal = (length2+ breadth2) = (802+ 182) = (6400 + 324) = 6724 = 82 m The Length of diagonal is 82 m....
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{3}{x-2}2, x \in R$ Solution: Given: $\frac{3}{x-2}2, x \in R$ Subtracting 2 from both the sides in the above equation $\frac{3}{x-2}-22-2$ $\frac{3-2(x-2)}{x-2}0$ $\frac{3-2 x+4}{x-2}0$ $\frac{7-2 x}{x-2}0$ Signs of $7-2 x$ : $7-2 x=0 \rightarrow x=\frac{7}{2}$ (Subtracting by 7 on both the sides, then multiplying by -1 on both the sides and then dividing both the sides by 2) $7-2 x0 \rig...
Read More →Plot a line graph for the variables p and q, where p is four times q, i.e., the equation is p = 4q.
Question: Plot a line graph for the variablespandq, wherepis four timesq, i.e., the equation isp= 4q. Using the graph, find the value of (i)p, whenq= 6 and (ii)q, whenp= 20. Solution: We have $p=4 q$ (i) When $q=6$ then $p=4 \times 4=16$ (ii) when $p=20$ then, $20=4 \mathrm{q}$ $5=\mathrm{q}$ And the graph of p = 4q is given by...
Read More →If one side of a cube is 15m in Length,
Question: If one side of a cube is 15m in Length, then find its volume. Solution: Given, one side of a cube $=15 \mathrm{~m}$ $\therefore$ Volume of cube $=(\text { Side })^{3}=(15)^{3}=3375 \mathrm{~m}^{3}$ Hence, the volume of cube is $3375 \mathrm{~m}^{3}$....
Read More →What will be the number of unit squares
Question: What will be the number of unit squares on each side of a square graph paper, if the total number of unit squares is 256? Solution: Let the numbor $5 e x$. Then, number of unit squares $=x \times x=x^{2}$ But total number of unit squares $=256$ $\therefore$ $x^{2}=256$ $\Rightarrow$ $x=\sqrt{256}=\sqrt{16 \times 16}=16$ Hence, the required number of squares is 16 ....
Read More →Study the table given below and draw a line graph for it.
Question: Study the table given below and draw a line graph for it. Is the graph drawn, a linear graph? Solution: No, the drawn graph is not linear....
Read More →Study the table given below and draw a line graph for it.
Question: Study the table given below and draw a line graph for it. Is the graph drawn, a linear graph? Solution: Yes, we can see that the drawn graph is linear....
Read More →A farmer wants to plough his square
Question: A farmer wants to plough his square field of side 150m. How much area will he have to plough? Solution: Given, side of square field $=150 \mathrm{~m}$ $\therefore \quad$ Area of square field $=$ Side $\times$ Side $=150 \times 150=22500 \mathrm{~m}^{2}$...
Read More →The following table gives the distances travelled by a car at various time-intervals.
Question: The following table gives the distances travelled by a car at various time-intervals. Study the table and draw a linear graph for the same. From your graph, answer the questions given below:(i) How much distance did the car cover during the period from 7.30 a.m. to 8 a.m.(ii)What was the time when the car had covered a distance of 100 km, since its start?(iii)How much distance had the car covered by 8.30 a.m.? Solution: (i) The car covers 20 km during the period from 7.30 a.m. to 8 a.m...
Read More →Find the decimal fraction,
Question: Find the decimal fraction, which when multiplied by itself, gives 84.64. Solution: Let the decimal fraction be $\boldsymbol{x}$. When a decimal fraction is multiplied by itself, then product $=x \times x=x^{2}$ But product $=84.64$ [given] $\therefore \quad x^{2}=84.64$ $\Rightarrow \quad x=\sqrt{84.64}$ Now, piace the bar over the numbers, then square root is given below. $\therefore \quad x=\sqrt{84.64}=9.2 .$ Hence, the required decimal is $9.2$....
Read More →The following line graph shows the journey made by two cyclists,
Question: The following line graph shows the journey made by two cyclists, cyclist I and cyclist II, one from town B to town A and the other from town A to town B.Study the above graph carefully and answer the questions given below: (i) At what time did cyclist II rest? For how long did the cyclist rest?(ii) Was cyclist II cycling faster or slower after the rest?(iii) At what time did the two cyclists meet?(iv) How far had cyclist II travelled when he met cyclist I?(v) When cyclist II reached to...
Read More →Solve each of the following in equations and represent the solution
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{x-7}{x-2} \geq 0, x \in R$ Solution: Given: $\frac{x-7}{x-2} \geq 0, x \in R$ $\frac{x-7}{x-2} \geq 0$ Signs of $x-7$ : $x-7=0 \rightarrow x=7$ (Adding 7 on both the sides) $x-70 \rightarrow x7$ (Adding 7 on both the sides) $x-70 \rightarrow x7$ (Adding 7 on both the sides) Signs of $x-2$ : $x-2=0 \rightarrow x=2$ (Adding 2 on both the sides) $x-20 \rightarrow x2$ (Adding 2 on both the si...
Read More →A decimal number is multiplied by itself.
Question: A decimal number is multiplied by itself. If the product is 51.84, then find the number. Solution: Let the number be $x$. Then, product $=x \times x=x^{2}$ But product $=51.84$ [given] $\therefore \quad x^{2}=51.84$ $\Rightarrow \quad x=\sqrt{51.84}$ Now, place the bar over the numbers, then square root is given below. $\therefore \quad x=\sqrt{51.84}=7.2$ Hence, the required number is $7.2$....
Read More →The following distance-time graph is for a car travelling to certain places.
Question: The following distance-time graph is for a car travelling to certain places.Study the above graph carefully and answer the questions given below: (i) How far does the car travel in $4 \frac{1}{2}$ hours? (ii) How much time does the car take to reach R?(iii) How long does the car take to cover 80 km?(iv) How far is Q from the starting point?(v) When does the car reach the place S after starting? Solution: (i) The car travels $180 \mathrm{~km}$ in $4 \frac{1}{2}$ hours. (ii) The car take...
Read More →The following line graph shows the temperature forecast and the actural temperature for each day of a week.
Question: The following line graph shows the temperature forecast and the actural temperature for each day of a week.Study the above graph carefully and answer the questions given below: (i) On which days was the forecast temperature the same as the actual temperature?(ii) What was the maximum forecast temperature during the week?(iii) What was the minimum actual temperature during the week?(iv) On which day did the actual temperature differ the most from the forecast temperature? Solution: (i) ...
Read More →Find the length of the side of a square,
Question: Find the length of the side of a square, if the length of its diagonal is 10 cm. Solution: Given, length of diagonal $=10 \mathrm{~cm}$ Suppose, the length of side of a square is $x \mathrm{~cm}$. By using Pythagoras theorem, $(10)^{2}=x^{2}+x^{2}$ $\Rightarrow \quad 100=2 x^{2}$ $\Rightarrow \quad x^{2}=50$ $\Rightarrow \quad x=\sqrt{50}$[taking square root on both sides] $\therefore \quad x=5 \sqrt{2} \mathrm{~cm}$ Hence, the length of the side of square is $\sqrt{50}$ or $5 \sqrt{2}...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{2 x-3}{3 x-7}0, x \in R$ Solution: Given: $\frac{2 x-3}{3 x-7}0, x \in R$ Signs of $2 x-3$ : $2 x-3=0 \rightarrow x=\frac{3}{2}$ (Adding 3 on both the sides and then dividing both sides by 2) $2 x-30 \rightarrow x\frac{3}{2}$ (Adding 3 on both the sides and then dividing both sides by 2) $2 x-30 \rightarrow x\frac{3}{2}$ (Adding 3 on both the sides and then dividing both sides by 2) Signs...
Read More →The following line graph shows the change in temperature of a block of ice when heated.
Question: The following line graph shows the change in temperature of a block of ice when heated.Study the above graph carefully and answer the questions given below: (i) For how many seconds did the ice block have no change in temperature?(ii) For how long was there a change in temperature?(iii) After how many seconds of heating did the temperature become constant at 100 C?(iv)What was the temperature after 25 seconds?(v) What will be the temperature after 1.5 minutes? Justify your answer. Solu...
Read More →Find the least square,
Question: Find the least square, number, which is exactly divisible by 3, 4, 5, 6 and 8. Solution: The least square number divisible by each of $3,4,5,6$ and 8 , is equal to the LCM of $3,4,5,6$ and 8 . $\therefore$ LCM of $3,4,5,6$ and $8=2 \times 2 \times 2 \times 3 \times 5=120$ The prime factorisation of $120=(2 \times 2) \times 2 \times 3 \times 5$ Here, prime factors 2,3 and 5 are unpaired. Clearly, to make it a perfect square, it must be multiplied by $2 \times 3 \times 5$, i.e. 30 . Ther...
Read More →For an experiment in botany, two different plants, plant A and plant B, were grown under similar laboratory conditions.
Question: For an experiment in botany, two different plants, plant A and plant B, were grown under similar laboratory conditions. Their heights were measured at the end of each week for three weeks. The results are shown by the line graph given below: Study the above graph carefully and answer the questions given below: (i) How high was plant A after (a) 2 weeks (b) 3 weeks?(ii) How high was plant B after (a) 2 weeks (b) 3 weeks?(iii) How much did plant A grow during the 3rd week?(iv) How much d...
Read More →Find the least number of four digits
Question: Find the least number of four digits that is a perfect square. Solution: Since, the greatest number of three digits is 1000 . Now, find the square root of 1000 by long division method. The least number of four digits that is a perfect square = 1000 + 24 = 1024...
Read More →The following is the distance-time graph of amit's walking.
Question: The following is the distance-time graph of amit's walking. Study the above graph carefully and answer the questions given below: (i) When does Amit make the least progress? Explain your answer.(ii) Find his average speed in km/hr. Solution: (i) Amit make least progress from 25 min to 40 min, as indicated by the line in the graph. (ii) Total distance covered = 2km Total time $=55 \mathrm{~min}=\frac{55}{60} \mathrm{hr}$ Average speed $=\frac{\text { Total } \text { distance covered }}{...
Read More →The line graph given below shows the yearly sales figures for a manufacturing company during the last five years.
Question: The line graph given below shows the yearly sales figures for a manufacturing company during the last five years. Study the above graph carefully and answer the questions given below: (i) What were the sales in (a) 2013 (b) 2015 (c) 2016?(ii) Compute the difference between the sales in 2012 and 2016?(iii) In which year was there the greatest difference between the sales as compared to its previous year? Solution: (i) The sales in (a) 2013 was Rs 7 cr (b) 2015 was Rs10 cr (c) 2016 was R...
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