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Sum of supplementary angles is equal to:

If we have a polyhedron, which of the following is true about its faces? Explain. [3 MARKS]

(i) It has 3 triangular faces.

(ii) It has 4 triangular faces.

(iii) It has 1 square and 4 triangular faces.

Subtract the sum of $(a+b+c)$ and $(2a-b+2c)$ from $3a-b+3c$. Name the type of expression formed. [3 MARKS]

(a) For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?
(b) Which of the following congruency conditions is preferred to draw a triangle exactly congruent to a right-angled triangle? [2 MARKS]

In algebra, terms are added to form ___________.

Match the following.

Check whether $6^n$ can end with the digit 0 for any natural number n. [2 MARKS]

50 bells B1 , B2 , B3 ,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Bells $B_{11}$ , $B_{22}$, $B_{33}$ and $B_{44}$ ring together in $2^2.a^1.b^1$ sec sec.Which of the following is always true about a and b ?

Question 21
In which of the following cases, a unique triangle can be drawn?
a) AB = 4 cm, BC = 8 cm and CA = 2 cm
b) BC = 5.2 cm, $\angle \text{B}={90}^{\circ }\text{and}\angle \text{C}={110}^{\circ }$
c) XY = 5 cm, $\angle \text{X}={45}^{\circ }\text{and}\angle \text{Y}={60}^{\circ }$
d) An isosceles triangle with the length of each equal side 6.2 cm

(a) Find out the unknown $\angle BOD$ in the given quadrilateral ABDC in which $AB\parallel CD$. Given that AD & BC are angle bisectors of $\angle BAC$ & $\angle DCA$ respectively.

(b) What is the value of (x+y) in the figure below?

[4 MARKS]

If BD is the angle bisector of ∠ABC, and ∠ABD = 25°, then what is the measure of ∠ABC ?

The additive inverse of -55 is ___

If $\frac{p}{q}={\left(\frac{2}{3}\right)}^2÷{\left(\frac{6}{7}\right)}^0$ then the value of ${\left(\frac{q}{p}\right)}^3$ is

Consider the figure of an opened die given below:

What is the value of A?

Question 90

Two complementary angles differ by ${20}^{\circ }.$ Find the angles.

Question 12

The circumference of a circle is 31.4 cm. Find the radius and the area of the circle.
$(Take\pi =3.14)$

The value of - 8765+985

Among the cities given, is the hottest.
(Temperatures are given in celcius)

Find the breadth of the rectangle if the length of the rectangle is 40 m and diagonal of the rectangle is 50 m.

Find the area of the given quadrilateral by using area of triangles

When Ted entered the class, Mr. McMurphy was teaching integers!! Ted didn’t even know what was going on in the class before, but, the moment he heard the word ‘integer’ from his mouth, he became super attentive. Suddenly, Mr. McMurphy started asking questions.

He said: “If you add or subtract two integers, the result will always be an integer. What is this property called?” Thinking that anytime he could ask him, Ted started looking at the book for the answer. To his relief, one of his classmates gave right answer. The right answer was -

In the given figure if AB = 20 cm DC = 10 cm and BC = 24 cm, then AD = _________ cm.

What are the uses of the NUMBER LINE

The sum of three consecutive odd numbers is 153. What is the first number in sequence?

Question 36

Fill in the blanks to make the statement true.

If x, y and z are integers, then (x + ___ ) + z = ___ + ( y + ___)

Factorize : $2x^2-18y^2$

How many student like red colour?

Find the median of the following data:

15, 22, 8, 16, 0, 10, 16

Select the brand with least cost/unit

Question 79(iii)

In the given figure P, Q and R are collinear points and TQ$\perp$ PR. Name four pairs of adjacent angles.

If P(0, 1, 2), Q(4, -2, 1) and O(0, 0, 0) are three points, then -POQ =

A __ is a number on its own, or sometimes a letter such as a or b to stand for a fixed number.

Divide 40 into 2 parts such that one fourth of one part is three eighth of other.

In a hall, 225 chairs are arranged in such a way that the number of rows is equal to the number of columns. If one more row and column of chairs is added, find the new number of chairs in the hall.

Solve $:-2z-15\ge 11;xϵR$

A gardener uses pipes to water his garden from a tank. For his entire garden he uses 6 pipes to water and it takes him 1 hour 20 minutes to completely empty the tank. Now if he uses only 5 pipes to water his garden, how long it will take to empty the tank?

A die is dropped at random on the rectangular region of sides $3m\times 2m$. What is the probability that it will land inside a circle(lying inside the rectangle) with diameter 1 m?

Find $x$ if $5:4::125:x$

Question 78

State whether the statement is True or False.

(-23) + 47 is same as 47 + (-23).

On subtracting $\frac{-3}{4}$ from $\frac{-5}{6}$ we get :

If $\sqrt[n]{n{x}^P}=x^m$, then $p$ is equal to:

Which of the following figures are polygons?

Question 1(f)
Evaluate the following
0 $÷$ (- 12)

Find the area of the 1.5 m wide pathways (green) if length is twice of breadth which is equal to 6 m (in square cm).

Study the table below and answer the question that follows :

$\begin{array}{ccccc}\text{Beverages}& \text{\% of vitamin}& \text{\% of minerals}& \text{\% of micronutrients}& \text{Cost/250gm~(In)}\\ \text{Orange juice}& 20& 10& 40& 8\\ \text{Pineapple juice}& 15& 20& 10& 10\\ \text{Litchi juice}& 12& 18& 30& 8\end{array}$

Which of the following beverages contains the maximum amount of Vitamins :
i) Litchi juice worth ₹ 16

ii) Pineapple juice worth ₹ 15

iii) Orange juice worth ₹ 8

iv) All the three worth ₹ 12.5 (125 grams each)

Divide -90 by 15.