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Question 4 (i)

If a = 2, b = -2, find the value of:
$a^2+b^2$

The measures of the angles of a quadrilateral are $(p+{25}^{\circ }),2p,(2p-{15}^{\circ })$ and $(p+{20}^{\circ })$. What is the measure of the largest angle?

A jeweler makes a profit of 30% after offering a discount of 20% on the labelled price of a jewelry. If he makes a profit of ₹9,000 on the sale, then find the labelled price of the jewelry.

Which of the following could represent the sides of a triangle?

Mac cuts a chocolate into 8 equal pieces and puts 3 pieces in the freezer.

Fraction of the chocolate put by Mac in the freezer is .

How fast do you need to travel to cover 150 miles in 3 hours?

Karan spends Rs.$5000$ on food which is ${\left(\frac{5}{8}\right)}^{th}$ of his income. Karan's income is ___ (in rupees).

Karan deposited 24% of the cost of her house.
If he paid 124,800 rupees for the deposit, what was the cost of the house?

In the given figure, $\angle$ DAB = $\angle$ CBA and AD = BC. Then which angle is equal to $\angle$​ ​​​​​​ACD?

Question 4 (x)

Find the square roots of the following numbers by the Prime Factorization method:

8100

The symmetries which are exhibited by the following figures are:

Taking into account of the significant figures, what is the value of $9.99\text{m}-0.0099\text{m}$ ?

In the adjoining figure, if $BC=a,AC=b,AB=c$ and $\angle CAB={120}^{\circ }$,

then which of the following is the correct relation?

1. 7

An aquarium is in the form of a cuboid whose length $\left(l\right)$ is 50 cm, breadth $\left(b\right)$is 40 cm and height $\left(h\right)$ is 30 cm. The base, back face and side faces are to be covered with a coloured paper. Find the area of the paper required to cover the aquarium. (Note that the front face and top face are not covered.)

Number of unit cubes in the following solid is:

The additive inverse of $\frac{3}{5}$ is

For the construction of a ${60}^{\circ }$ angle, drawing which of the following is the starting step?

1. 12

1. 200

The weights of Shankar and Shyla are 45 kg and 30 kg respectively. Express these weights as a ratio.

Using prime factorization, find the square roots of

a) 11025

b) 4761

Question 20

Radhika bought a car for Rs. 250000. Next year, its price decreased by 10% and further next year, it decreased by 12%. In the two years, overall decrease per cent in the price of the car is

(a) 3.2%

(b) 22%

(c) 20.8%

(d) 8%

The following data relates to the expenses of a household in Bangalore.
$\begin{array}{cc}\text{Items}& \text{Expenditure(in Rs)}\\ \text{Food}& 4000\\ \text{Clothing}& 2000\\ \text{Rent}& 1500\\ \text{Education}& 1500\\ \text{Miscellaneous}& 1000\end{array}$
What will be the central angle of clothing?

In Fig. the line segment joining the mid-points M and N of opposite sides AB and DC of quadrilateral ABCD is perpendicular to both these sides. Prove that the other sides of the quadrilateral are equal. [4 MARKS]

What is the total in an account if ₹500 is deposited at 5% simple interest for 5 years?

Solve the following.

30% of which number is 21?

1. 2

Which of the following are not triangular numbers?

Find the square roots of 2025.

Which of these follow the closure property of rational numbers?

Question 1

Only one of the four options is correct. Write the correct one.

The ratio of 8 books to 20 books is

a) 2 : 5

b) 5 : 2

c) 4 : 5

d) 5 : 4

Compare and arrange these numbers on the number line.

-2, 2, 0, -4

Question 58

Solve the following:

8x-7-3x=6x-2x-3

Find:

(i) 4.8 ÷
10 (ii) 52.5 ÷ 10 (iii) 0.7
÷ 10

(iv) 33.1
÷ 10 (v) 272.23 ÷
10 (vi) 0.56 ÷ 10

(vii) 3.97
÷ 10