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How are prisms and cylinders as well as pyramids and cones alike? [2 MARKS]

A ladder of height 15 m casts a shadow of 12 m and a nearby tree casts a shadow of 14 m. Find the height of the tree assuming that the data is collected at the same place and at the same time.

In the given figure, diagonals are

How can we find the cube root of a 7 , 8 or 9 digit number like 1906624 using estimation method?

Question 35

State whether the statement is true (T) or false (F).

In a 2-digit number, the unit's place digit is x. If the sum of the digits be 9, then the number is (10x-9).

A number increased by 15% becomes 391. Find the number.

Factorise:
$a^2+ab(b+1)+b^3$

Coordinates of point J as shown below is _____.

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Question 112(iv)

Sonia picks up a card from the given cards

Find the probability of getting a B card bearing number greater than 7. ?

In figure AB = CB and O is the centre of the circle. Prove that BO bisects $\angle ABC$. [1 MARK]

Which of the following represents the correct prime factorisation of 272?

The expansion of $(x+\frac{1}{x}+2{)}^2$ is :

If $a^2+b^2=14$ and $ab=3$, find the value of $2(a+b{)}^2-5(a-b{)}^2$.

In a contest, the first gets 1000 rupees as prize, the second 600 rupees and the third 400 rupees. What is the ratio of the prize money?

Simplify ${(2^5÷2^8)}^5$ × $2^{-5}.$

For the given figure, find $\angle ABC+\angle ACB,$ where $O$ is the centre of the circle.

Solve :

15 (y - 4) - 2 (y - 9) + 5 (y + 6) = 0

Multiply the binomials.

(i)(2x + 5) and(4x − 3) (ii) (y − 8) and (3y −4)

(iii)(2.5l −0.5m) and (2.5l + 0.5m)

(iv) (a + 3b)and (x + 5)

(v)(2pq + 3q²)and (3pq − 2q²)

(vi)$(\frac{3}{4}{a}^2+3b^2)$ and $4(a^2-\frac{2}{3}{b}^2)$

EdWear has printing facilities in $y$ cities. Each city has two factories. How many factories are there in total?

For a parallelogram, which of the following is true?

Write a verbal statement for the algebraic expression: 4x + 8

We have a parallelogram ABCD with AC and BD as diagonals. In parallelogram ABCD, $\angle$ ABC = ${110}^{\circ }$, $\angle$ DAC = ${15}^{\circ }$, $\angle$ CAB=${25}^{\circ }$, AB = 5cm, CD = 7cm. Can we construct this parallelogram?

$\text{Rick sold}\frac{2}{6}\text{of the total apples in Street A}$

$\text{and}\frac{5}{12}\text{of the total apples in Street B}.$



Calculate the combined fraction of apples sold by Rick in the two streets.

One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus.

Factorize $3p^2-5pr-3pq+5qr$

Given a rectangle of length $a$ and breadth $b$:





In another rectangle, the length is $2$ units more than the length and breadth is $3$ units less than the breadth of the given rectangle.

Represent the area of another rectangle as an algebraic expression.

Find the mean of following data :

18 , 33 ,30 ,21 and 13 .

Also find the sum of deviation of this data from the mean

Which of the following has non-terminating non-repeating decimal expansion?

Which of the following is not a polygon?

If you subtract $\frac{1}{4}$ from a number and multiply the result by $\frac{1}{2}$, you get $\frac{1}{4}$. What is the number?

The external dimensions of a closed wooden box are 62 cm, 30 cm and 18 cm. If the box 1s made of 2-cm-thick wood, find the capacity of the box.

What is inverse proportion?