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Sam is looking at the roof of the adjacent building from top of his flat. His height is 5 feet. He knows that the height of his building and the distance between the two buildings is 50 feet. Sam measures the angle of elevation of his line of sight of the tip of the other building to be ${30}^{\circ }$. Based on the information in the question, find the height of the adjacent building?

The value of $(\sqrt{3}+\sqrt{2}{)}^2$ is equal to ____.

Two-fifth of the cube of a certain number is 50. Find the number.

Given below are the heights of 20 students in centimetres. Find the number of students whose height is greater than 169 cm.

$$\begin{array}{cc}150& 178\\ 153& 156\\ 162& 184\\ 170& 176\\ 186& 173\\ 153& 186\\ 162& 159\\ 180& 183\\ 165& 180\\ 150& 156\end{array}$$

Question 3
In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:


Find the probability that a student of the class was born in August.

Question 33

If a cube fits exactly in a cylinder with height h, then the volume of the cube is ___ and surface area of the cube is ___.

Multiply:
(i) $\sqrt{3}(\sqrt{7}-\sqrt{3})$

(ii) $(\sqrt{5}-\sqrt{7})\sqrt{2}$

(iii) $(3\sqrt{2}-\sqrt{3})(4\sqrt{3}-\sqrt{2})$

Match the following graphs of an ideal gas with their coordinates.

In the picture below, the sides of the two triangles are parallel:

Prove that they are similar:

What is linear pair axiom

2

In $\Delta ABC$, right angled at $B$. The value of $\cos (A+C)$ =

Solve the following pair of linear equations by substitution method:

$2x+3y=13$

$4x-y=5$

Given that x and y are in inverse proportion, and $y_1,y_2$ are values of y corresponding to the values $x_1,x_2$ of x, respectively. Which of the following is correct?

In the given figure, AB||CD. If $\angle EAB={50}^{\circ }$ and $\angle ECD={60}^{\circ }$ then $\angle AEB=?$

$\left(a\right){50}^{\circ }$

$\left(b\right){60}^{\circ }$

$\left(c\right){70}^{\circ }$

$\left(d\right){55}^{\circ }$

Classify the following numbers as rational or irrational:

(i) (ii) (iii) 0.3796

(iv) 7.478478 (v) 1.101001000100001…

1. 85

Four times a number added to thrice another number gives 43. Twice the second number, subtracted from thrice the first gives 11. What are the numbers?

Determine the probability of three coins falling all heads up when tossed simultaneously.

Help Jerry solve the problem and choose the correct answer.

$\frac{8}{19}÷2$

1. 1250

Lines PQ and RS are parallel. It is given that $\angle RSP={52}^{\circ }$, then find $\angle SPQ$.

In the figure, AB || CD and XY is the transversal.



Which of the following is incorrect?

In the given figure, DE and CF are perpendicular to line AB and its value is 15 cm and 24 cm respectively. Find the length of AB.

The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.

The factors of $2y^3+10y^2-48y$ are:

The area of a triangle formed by tips of vectors, $\overline{a},\overline{b}$ and $\overline{c}$ is

$\stackrel{⟷}{AB}and\stackrel{⟷}{CD}$, are straight lines. Which one of these lines is a transversal with respect to the other?

If the ratio of opposite angles of a cyclic quadrilateral is 5:1, then the values of the angles is

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is

If x + 2 is a factor of x² + mx + 14, then m =
(a) 7
(b) 2
(c) 9
(d) 14

Diagonal $AC$ of a parallelogram $ABCD$ bisects $\angle A$ (see the given figure). Show that

(i) It bisects $\angle C$ also.

(ii) $ABCD$ is a rhombus.