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1. Fill in the boxes.
2. A car travels 432 km on 48 liters of petrol. How far would it travel on 20 liters of petrol?
3. An electric pole,24 meters high casts a shadow of 20 meters. Find the height of a tree. If it casts a shadow of 15 meters under similar conditions
4. A train 315 m long is running at 54 km/h.How much time will it take to cross a pole?
5. In an examination John secured 372 marks. If she secured 62% marks, find the maximum marks.
6. Length of a rectangle is 8m less than twice its breadth. If the perimeter of the rectangle is 56m,find the length and breadth.
7. Factorize 9m² -12 m n + 4 n²
8.The length of the sides of a right triangle are 6 cm and 8 cm. What is the length of its hypotenuse?
9. A rectangular lawn of length 40m and breadth 25 m is to be surrounded externally by a path which is 2m wide. Find the area of the path.
10. Capacity of a tank is 60 kl. If the length and breadth of the tank are 5 m and 4 m respectively, find its depth.
Question 1 |
Here the given fractions are equal. Let "x" be the denominator of the second fraction
90/165 = -6/x
90 x = -6 x 165 from this we have to find the value of "x" so, x = (-6 x 165)/90 x = -990/90 x = -11 Let "y" be the numerator of the third fraction 90/165 = y/-55 90 (-55) = y x 165 y = 90(-55)/165 y = -4950/165 y = -30 So the correct answer for this question is -11 & -30 option B |
Question 2 |
The car covers the distance 432 km by consuming 48 liters of petrol.Now we have to find the number of km covered by the car using 20 liters of petrol.
432 x 20 = x x 48 8640 = 48 x 8640/48 = x x = 180 km So the correct answer for this question is 180 km option A |
Question 3 |
Now we need to find the length of the tree when it casts a shadow of 15 meters
24 x 15 = x x 20 360 = 20 x 360/20 = x x = 18 m So the correct answer for this question is 18 m option C |
Question 4 |
Now,we are going to use the formula to find time
Time = Distance/Speed Length of the train = distance covered by the train = 315 m Speed of the train = 54 km/hr To convert the speed from km/hr to m/second we have to multiply by 5/18 = 54 x (5/18) = 15 m/sec Time = 315/15 = 21 seconds So the correct answer for this question is 21 seconds option B |
Question 5 |
Marks secured by John = 372
Let "x" be the maximum marks 62 % of x = 372 (62/100) x x = 372 x = 372 x (100/62) x = 37200/62 x = 600 So,the maximum mark is 600. So the correct answer for this question is 600 option B |
Question 6 |
Let "x" be the breadth of the rectangle
So,length of the rectangle = 2 x - 8 Perimeter of the rectangle = 56 m Perimeter of a rectangle = 2 (length + breadth) 2 (2 x - 8 + x) = 56 2 (3x - 8) = 56 6 x - 16 = 56 6 x = 56 + 16 6 x = 72 x = 72/6 x = 12 breadth of the rectangle = 12 m length of the rectangle = 2 (12) - 8 = 24 - 8 = 16 m So the correct answer for this question is 12 m & 16 m option C |
Question 7 |
Here 9 can be written as 3^{2} and 4 can be written as 2^{2}
= 3^{2}m^{2} - 2 (6 m n) + 2^{2}n^{2} = (3 m)^{2} - 2 (3 m)(2 n) + (2 n)^{2} This exactly matches the algebraic identity a^{2} - 2 a b + b^{2} So, we shall written it as (3 m - 2 n)^{2} Therefore the factors are (3 m - 2 n) (3 m - 2 n) So the correct answer for this question is (3 m - 2 n) (3 m - 2 n) option C |
Question 8 |
Here we need to find the length of the hypotenuse side
In any right triangle the square of hypotenuse side is equal to the sum of squares of other two sides. Length of other two sides are 6 cm and 8 cm respectively (Hypotenuse side)^{2} = 6^{2} + 8^{2} = 36 + 64 = 100 hypotenuse side = √ 100 = 10 cm So the correct answer for this question is 10 cm option C |
Question 9 |
Width of the path = 2 m
Length of rectangular lawn = 40 m Breadth of the rectangular lawn = 25 m Area of path = Area of large rectangle - area of small rectangle Area of a rectangle = Length x breadth = (44 x 29) - (40 x 25) = 1276 - 1000 = 276 m^{2} So the correct answer for this question is 276 m^{2} option C |
Question 10 |
From the given information we come to know that the tank is in the form of cuboid
Volume of the tank = 60 kl Length x breadth x height = 60 length of the tank = 5 m breadth of the tank = 4 m From this we have to find the height 5 x 4 x h = 60 20 x h = 60 h = 60/20 h = 3 m So the correct answer for this question is 3 m option A |