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Which of the following measurements can be used to construct a unique triangle?

Question 82 (c)

Express the following numbers in standard form.
5,83,00,00,00,000

Question 19

In the given figure, PQ|| SR and SP|| RQ. Then, angles a and b are respectively

(a) ${20}^{\circ },{50}^{\circ }$
(b) ${50}^{\circ },{20}^{\circ }$
(c) ${30}^{\circ },{50}^{\circ }$
(d) ${45}^{\circ },{35}^{\circ }$

Express $[\frac{-1}{4}-\left(\frac{-1}{6}\right)]÷[\frac{1}{3}+\left(\frac{-1}{2}\right)]$

Raw data is:

The cost price of a pen is Rs. 12. A shopkeeper sold it for Rs. 18. What is the percentage of profit obtained by the shopkeeper?

Sushant reads $\frac{1}{3}$ part of a book in 1 hour. How much will he read in $2\frac{1}{5}$ hours?

Question 51

A line segment 56cm long is to be divided into two parts in the ratio of 2 : 5. Find the length of each part.

Question 85(i)

If principal = Rs. 100000, rate if interest = 10 $\%$ compounded half - yearly.
Find Interest for 6 months.

On a map, the distance between two cities is marked as 18 cm and the actual distance between the two cities is 99 km. Find the scale on the map.

If the mean of the given data is 250, then find the value of p.

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 0-100& 7\\ 100-200& 11\\ 200-300& 15\\ 300-400& p\\ 400-500& 8\end{array}$ [2 MARKS]

Question 108
Draw an isometric view of a cuboid $6cm\times 4cm\times 2cm$.

Ram drew a line segment $AB$ of length $3cm$ and another line segment $CB$ of length $4cm$, which is perpendicular to line segment $AB$. What is the length of the third side of the triangle?

In the figure x, y and z are the internal angles of ∆ABD. Line ED || AB and side AD is extrapolated to point P and the value of $\angle$EDP and $\angle$EDB are m and n, respectively. Then, the values of n and m are ______ and _______, respectively.

Question 1 (v)

Simplify combining like terms:

$5x^{2}y-5x^2+3y{x}^2-3y^2+x^2-y^2+8x{y}^2-3y^2$

In the given figure, ∠ABC = ${90}^{\circ }$ and BM is a median, AB = 8 cm and BC = 15 cm. Then, the value of CM is

Why is every rational no. not a fraction even though every fraction is a rational number

which of the following indicates sum of 5 taken 6 times ?

Simplify : (3a/10)+(2a/5)=(7a/25)+(29/25)

A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the $9^{th}$ step.

(i) He jumps $3$ steps down and then jumps back $2$ steps up. In how many jumps will he reach the water level?

If two complementary angles are in the ratio 3 :2, then find the measure of the greater angle.

A man starts from his house and goes 5km north, turns right and goes 5km. Again he goes 5km to his left, turns left and goes 15km further. Now in which direction is he from the house?

The sides$BC$,$CA$ and $AB$ of $\Delta ABC$ are produced in order to form exterior angles $\angle ACD$,$\angle ABG$, and $\angle CAE$ then $\angle ACD+\angle CAE+\angle ABG$ is

What is the probability of getting an even number on rolling a die?

The point (8, 2) is at a distance of ____ units from the y-axis.

Question 37
Fill in the blank to make statement true.
A solid with no vertex is ___.

Add the following rational numbers:
(i) $\frac{3}{4}$ and $\frac{-3}{5}$
(ii) $\frac{5}{8}$ and $\frac{-7}{12}$
(iii) $\frac{-8}{9}$ and $\frac{11}{6}$
(iv) $\frac{-5}{16}$ and $\frac{7}{24}$
(v) $\frac{7}{-18}$ and $\frac{8}{27}$
(vi) $\frac{1}{-12}$ and $\frac{2}{-15}$
(vii) $-1$ and $\frac{3}{4}$
(viii) $2$ and $\frac{-5}{4}$
(ix) $0$ and $\frac{-2}{5}$

Question 20
Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle?
a) 3 cm, 4 cm, 6 cm
b) 9 cm, 16 cm, 26 cm
c) 1.5 cm, 3.6 cm, 3.9 cm
d) 7 cm, 24 cm, 26 cm

${\left(\frac{2}{3}\right)}^3\times {\left(\frac{5}{7}\right)}^3$ is equal to

$\left(a\right){(\frac{2}{3}\times \frac{5}{7})}^9$
$\left(b\right){(\frac{2}{3}\times \frac{5}{7})}^6$
$\left(c\right){(\frac{2}{3}\times \frac{5}{7})}^3$
$\left(d\right){(\frac{2}{3}\times \frac{5}{7})}^0$

Question 58

Express the given statement as an equation.

One-fifth of a number is 5 less than that number.

Question 93

Translate the given algebraic expression into words.

$\frac{7}{8-x}$

Tina noticed juicy oranges in a shop and asked the shopkeeper for the price. He said each costs Rs. x. She bought 3 of them.
What is the coefficient of x after calculating the total amount spent by Rina and Tina, if Rina had already spent Rs. 6x + 4y?
___

The given expression (11n + 10) is for numbers in a series (taking n = 1, 2, 3, 4…… in order).

Which of the following number belong to the given series.

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)

The amount of surface enclosed by a closed figure is called its___

A polygon is said to be a regular polygon if

Choose the correct ratio for the angle bisector theorem for this triangle.

An oil container is of the shape of a cuboid whose length is 10 cm more than its breadth, while its height is 10 cm more than its length. The total cost of the metallic sheet required for making 25 such containers at the rate of Rs 30 per square metre is Rs 705.

How much oil can the container hold?

Find the sum of money which increases by $\frac{1}{10}$th of itself every year and amounts to ₹ 450 in 5 years, if calculated as per simple interest formula.

In a village, out of 60 couples, 15 couples were married at the age of 21 to 24, 25 couples were married at the age of 24 to 28 and 16 couples were married at the age of 28 to 30. After an age of 30, no one marries. What is the probability that a couple will remain unmarried?

What will be the value of x if $\frac{x+1}{x+4}$ = $\frac{2}{3}$?

Mark the option which contains set of prime numbers.

The Ages of A and B are in the ratio of 5:3, after six years their ages will be in the ratio of 7:5. The present age of A is