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Two quantities were in the ratio 1 : 4. On increasing the smaller one by 6 and decreasing the Larger one by 6, The quantities are now in the ratio 7 : 13.

What were the original quantities ?

If the amount paid at the end of 4 years is equal to Rs. 6000 at 5% per annum, find the principal.

(a) Which of the following is greater? 10₍₂₎ or 11₍₂₎

(b) Write in ascending order: 1011₍₂₎, 110₍₂₎, 1000₍₂₎

(c) Find the value of: (1 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰)

(d) Expand and write: (1) 10101₍₂₎ (2) 11110₍₂₎

Consider this calendar. Select the numbers 1,2,3,8,9,10,15,16,17 such that they form a square. The sum of the selected numbers of the square, is ____ times the middle number of the square.

Which of these shapes can be rolled into a cylinder?

Express the following numbers using the exponential notation:

(i) $512$ (ii) $343$

(iii) $729$ (iv) $3125$

Question 101
Construct an equilateral triangle ABC of side 6 cm.

In the given figure, ABCD is a parallelogram and PD is parallel to QC.

S1 : $△$APD $\cong$ $△$BQC

S2 : area($△$APD) + area(PBCD) = area($△$BQC) + area(CDPB)

The number of ways when $5$ distinct balls can be put into $2$ boxes

In a right angled triangle , the 2 smaller angles are in the ratio 1 : 5. Find the measure of the smallest angle

A floor tile is in the shape of a parallelogram of base is 24 cm and height 10 cm. The number of such tiles required to cover a floor of area 1080 $m^2$ is___ .

What does the top view of a cylinder look like?

Copy the
figures with punched holes and find the axes of symmetry for the
following:

Two trains moving in the same direction and at the same speed will be ___.

Question 74

People of Khejadli village take good care of plants, trees and animals. They say that plants and animals can survive without us, but we cannot survive without them. Inspired by her elders Amrita marked some land for her pets (Camel and Ox) and plants. Find the ratio of the areas kept for animals and plants to the living area. What value depicted here?

Find the value of x + y + z.

Question 63

In the following question, state whether the statement is True (T) or False (F):

The product of one negative and one positive term is a negative term.

The total length of the pencil is .

Question 1(iii)
Find the value of:
(iii) ${11}^2$

In a park, there are rectangular and circular paths with width 1.5 m. The rectangular paths pass through center of the park. The local community decided to put grass beds on entire pathway. The inner radius of the circular path is 8 m. If the distance between any of the gates and the circular path is 2.5 m, find the cost of putting grass beds on the entire pathway at 0.1 paise per square cm.

The cube of $2\frac{1}{2}$ is ____.

$(7\times 82)+(7\times 18)=$

In a triangle ABC, right angled at A, AB = AC. Find the value of angle B and angle C.

$(3\times \frac{1}{5})+(3\times 5)$ = __________

Grade $6$ students participated in the Physics test. The class teacher prepared the data of the test as shown below:





If the passing marks is $40$, then how many students have failed the test?

If the HCF of 60 and 168 is 12, what is the LCM?

Area of the following triangle is

1. 300