__Chapter – 6 ( Square And Square Roots)__
·

**Very Short Answer Type Questions (1 Mark)****Q1.**Which of the following can be a perfect square?

(i) A
number ending in 3 or 7

(ii) A
number ending with odd number of zeros

(iii) A number
ending with even number of zeros

(iv) A number
ending in 2.

**Q2.**Which of the following is the number non-perfect square numbers’ between the square of the numbers n and n + 1?

(i) n + 1 (ii) n (iii) 2n (iv) 2n + 1

Q3. Which of the following is the number of non-perfect square
number between 172 and 182?

(i) 613 (ii) 35 (iii) 34 (iv) 70

Q4. Which of the following is the number of zeros in the square of
900?

(i) 3 (ii) 4 (iii) 5 (iv) 2

Q5. Which of the following can be a perfect square?

(i) A
number ending in 3 or 7

(ii) A
number ending with odd number of zeros

(iii) A number
ending with even number of zeros

(iv) A number
ending in 2.

·

**Short Answer Type Questions (2 Mark)****Q6.**Find the square root of 144 by the method of repeated subtraction.

Q7. Q8. Factorise: p

^{2}– 10p + 25.
Q8. Write a Pythagorean triplet whose smaller
member is 6.

Q9. Find the square root of

·

**Long Answer Type Questions (3 Mark)****Q10.**The area of a square field is 8281 m2. Find the length of its side.

Q11.
Is 2352 a perfect square? if not, find the smallest number by which 2352
must be multiplied so that the product is a perfect square. Find the square
root of new number.

Q12. 1225 plants are to be planted in a
garden in such a way that each row contains as many plants as the number of
rows. Find the number of rows and the number of plants in each row.

Q13. Find the smallest number by which 3645
should be divided so as to get a perfect square. Also, find the square root of
the number so obtained.

·

**Very Long Answer Type Questions ( 4 Mark)**
Q14.

**For each of the following numbers, find the smallest number by which we divide it so as to get a perfect square. Also find the square root of the square numbers so obtained.**
(a) 37845 (b) 2800 (c) 45056

Q15. The students of Class VIII of a school
donated Rs 2401 for Prime Ministerï¿½ï¿½s National Relief Fund. Each student
donated as many rupees as the number of students in the Class. Find the number
of students in the Class.

Q16. There are 500 children in a school. For a
P.T. drill they have to stand in such a manner that the number of rows is equal
to number of columns. How many children would be left out in this arrangement?

Q17. A school collected Rs 2304 as fees from its
students. If each student paid as many paise as there were students in the
school, how many students were there in the school?

·

**HOTS**
Q18. Find

Q19. Find the smallest number by which 1800 must
be multiplied so that it becomes a perfect square. Also find the square root of
the perfect square so obtained.

Q20. Q18. 2025 plants are to be planted in a
garden in such a way that each row contains as many plants as the number of
rows. Find the number of rows and the number of plants in each row.

__CHAPTER – 11 ( MENSURATION )__
·

**Very Short Answer Type Questions ( 1 Mark)**
Q1. Which of the following is the once of a rhombus?

(i) Product of its diagonals (ii) (sum of its diagonals)

(iii) 2 (Product of its diagonals) (iv) 2
(Product of its diagonals)

Q2. If the edge of a cube is 1 cm then which of the following is
its total surface area?

(i) 1 cm

^{2}(ii) 4 cm^{2}(iii) 6 cm^{2}(iv) none of these
Q3. If base area of a room 12 m

^{2}and height is 3 m then its volume is:
(i) 4 m

^{3}(ii) 36 m^{3}(iii) 12 m^{3}(iv) 18 m^{3}
Q4. Which of the following has its area and perimeter numerically
equal?

(i) an equilateral triangle of side
1 cm (ii) a square of side 1 cm

(iii) a square of side 1 cm (iv) a regular
pentagon of side 1 cm.

·

**Short Answer Type Questions ( 2 Mark)****Q5.**The length, breadth and height of a cuboid are 20 cm, 15 cm, 10 cm respectively. Find its total surface area.

Q6. Find the height of cylinder whose radius is 7
cm and total surface area is 968 cm

^{2}.
Q7. A roller takes 750
complete revolutions to move once over a level of road. Find the area of road
if the diameter of the roller is 84 cm and length is 1 m.

·

**Long Answer Type Questions ( 3 Mark)****Q8.**In a building there are 24 cylindrical pillars with each having a radius 28 cm and height 4 m. Find the cost of painting the curved surface area of all pillars at the rate of Rs. 8 per meter square.

Q9. A box is in the form of cuboid of dimensions
(80*30*40) cm. The base the side faces and back faces are to be covered with a
coloured paper. Find the area of paper needed.

Q10. The lateral surface area of a hollow
cylinder is 4224 cm

^{2}. It is cut along its height and formed a rectangular sheet of width 33 cm. find the perimeter of rectangular sheet.
·

**Very Long Answer Type Questions ( 4 Mark)**
Q11.
If each side of a cube is
doubled, how many times will its surface area increase?

Q12. Find the height of a cuboid whose base
area is 180 cm

^{2}and volume is 900 cm^{3}.
Q13. Find the height of the cylinder whose
volume is 1.54 m

^{3}and diameter of base is 140 cm.
Q14. Find the area of rhombus whose diagonals are
8cm and 10cm.

Q15. If each side of a cube is doubled, how
many times will its volume increase?

·

**HOTS**
Q16. A cuboid is of dimensions (60*50*30)cm.How
many small cubes with side 6 cm can be placed in the given cuboid?

Q17. Find the area of trapezium where
length of parallel sides are 15 cm and 25 cm and the third side measures 12 cm.

Q18. A rectangular sheet of paper is having
measures 11 cm* 4 cm. it is folded without overlapping to make a cylinder of
height 4 cm. Find the volume of the cylinder.

__CHAPTER – 2(LINEAR EQUATIONS IN ONE VARIABLE)__
·

**Very Short Answer Type Questions ( 1 Mark)**
Q1.Find
‘x’, if 8x -3 =25+17x.

Q2.
Solve : y + 3 = 10.

Q3.
Solve : +
x =

Q4.

**Solve 3x/4 – 7/4 = 5x + 12****Q5. Find the solution of 3x-4 = 12**

·

**Short Answer Type Questions ( 2 Mark)**
Q6.

**What should be subtracted from thrice the rational number -8/3 to get 5/2?****Q7. The sum of three consecutive multiples of 7 is 63. Find these multiples.**

**Q8. Perimeter of a rectangle is 13cm. if its width is**

**cm, find its length.**

**Q9. anjay will be 3 times as old as he was 4 years ago after 18 years. Find his present age.**

·

**Long Answer Type Questions ( 3 Mark)**
Q10.

**The present of Sita’s father is three times the present age of Sita. After six years sum of their ages will be 69 years. Find their present ages.****Q11. The digits of a two-digit number differ by 3. If digits are interchanged and the resulting number is added to the original number, we get 121. Find the original number.**

**Q12. The numerator of a fraction is 2 less than the denominator. If one is added to its denominator, it becomes 1/2 find the fraction.**

**Q13.**

**x + 3x/2 = 35. Find x.**

·

**Very Long Answer Type Questions ( 4 Mark)**
Q14. Show that x = 4 is
a solution of the equation x + 7 – 8x/3 = 17/6 – 5x/8

Q15. Find x for the
equation: (2 + x)(7 – x)/(5 – x)(4 + x) = 1

Q16. The digits of a
2-digit number differ by 5. If the digits are interchanged and the resulting
number is added to the original number, we get99. Find the original number.

**·**

**HOTS**

**Q17.**Divide 40 into two parts such that 1/4th of one part is 3/8th of the other.

Q18. x
+ 3x/2 = 35. Find x.

**Q19.**A is twice old as B. Five years ago A was 3 times as old as B. Find their present ages.

Q20. Solve : (x +
3)/6 + 1 = (6x – 1)/3

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