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Question 48

State whether the statement given is True or False.

In like terms, the numerical coefficients should also be the same.

Express $\frac{1}{27}$ in exponential form

On their way back home, Rina and Tina were looking for similar milestones on the road. This time, they noticed one that read ‘Chennai 15,645 m’. How many kilometres more would they have to travel to reach Chennai? ___

Question 2(g)
Give first the step you will use to separate the variable and then solve the equation:
$\frac{a}{5}=\frac{7}{15}$

Which of the following is the smallest number that leaves a remainder of 5 when divided by 7, 15, 16 and 21?

The price of the blanket was ₹ 2644.644. Find the number of significant digits in the one -fourth of the price of the blanket ?

If the speed of a boat in downstream is 22 km/hr and in upstream is 10 km/hr. Then the speed of the water stream is?

Thrice a number added to 3 gives 7 can be expressed as:

Tap on the day which had maximum sales if one apple represents 5 units.

Question 19

The following is the map of a town. Based on it answer the question.

The number of hospitals in the town is
(a) 1
(b) 2
(c) 3
(d) 4

Evaluate $(2x+5{)}^2-(2x-5{)}^2$

Incentre of triangle whose vertices are A(-36,7), B(20,7), C(0,-8), is

Question 84

State whether the statement is True or False.

A right-angled triangle may have all sides equal.

Question 11:

Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes.

$$\begin{array}{ccccc}\text{Outcome}& 3\text{heads}& 2\text{heads}& 1\text{heads}& 0\text{heads}\\ \text{Frequency}& 22& 76& 83& 19\end{array}$$

What is the probability of getting

(i) not more than one head?
(ii) at least two heads?
(iii) exactly two heads? [3MARKS]

Which number is a whole number but not a natural number

Evaluate
${\left(\frac{5}{3}\right)}^2\times {\left(\frac{5}{3}\right)}^{14}$

The area of a triangle whose sides are 13cm, 14cm and 15cm is:___.

How does the value of a digit change as it moves from the right to the left in a place value chart?

Name the quadrilateral which has both line and rotational symmetry of order more than 2.

Question 7 (iv)

Simplify these expressions and find their values if x = 3, a = -1, b = -2:
10 - 3b - 4 - 5b

Factorise: $21x^2{y}^3+27x^3{y}^3$

In the following figure, find the area of the shaded portion:

Ted went with number $13$ to his house.There, he was surprised to see that all the houses were placed in a straight line at equal distances. Neighbors of $13$ were $12$ and $14$; similarly $14$ had $13$ and $15$ as neighbors. $13$ said, “This line, mathematically, is called a ______.”

Rohit's friend's house is 2.87 km away from his house. If Rohit has covered a distance of 1500 m, find how much more distance he has to cover to reach his friends's house

Question 5 (a)

PQRS is a parallelogram QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find the area of the parallelogram PQRS

The measure of two supplementary angles are $(3x+15{)}^{\circ }$ and $(2x+5{)}^{\circ }$. Find the value of x.

A line segment AP is divided into 2 parts by a point O. If the length of the smaller segment AO is 15 cm less than the larger segment OP and the ratio of lengths of AO and OP = 4 : 7, find the length of OP.

Question 8(iii)
Verify a−(−b) = a + b for the following values of a and b.
a = 75, b = 84

Rashi can travel 4 hours after having a Pizza, while Rashid can travel for 6 hours after having a pizza. How many more hours can Rashid travel than Rashi after having a Pizza? Express in terms of percentage.
[2 MARKS]

The set {$x:x$ is a letter in the word 'SELECT'} in roster form is

Question 1(d)
Following number line shows the temperature in degree Celsius (°C)at different places on a particular day.



Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

If the revenue from exports across different product groups were to be represented by a pie-chart, what angle would the sector depicting export earnings from Internet form at the centre of the piechart in year 2000?

Find the value of

$(2\times {10}^4)+(3\times {10}^3)+(1\times {10}^2)+(6\times {10}^1)+(7\times {10}^0)+(4\times {10}^{-1})+(2\times {10}^{-2})+(8\times {10}^{-3})$

Simplify $(-4x^2-2xy+9y^2)-(3x^2-3xy+7y^2)$

If $\frac{2x}{9}=8$, what is the value of $x$ which balances the equation?

Approximate weight (in gm) of $H_2$$O_2$ in 560ml of 20 volumes $H_2$$O_2$ solution is

State whether a given pair of terms is of like or unlike terms:

(i) $1,100$
(ii) $-7x,\frac{5}{2}x$
(iii) $–29x,-29y$
(iv) $14xy,42yx$
(v) $4m^{2}p,4m{p}^2$
(vi) $12xz,12x^2{z}^2$

Three cans contain 23.260 ml, 60.5 ml and 71.486 ml of kerosene. What should be the minimum capacity of a can that can hold the total quantity of kerosene?

3 $\pi$

find a number such that one fourth of a number is 3 more than 7.

A cone has ___ edge(s).

Two numbers are 25% and 30% greater than a third number respectively. What percent of the first number is the second number?

The following pictograph shows the number of vehicles parked in the basement of an apartment, each picture represents 5 vehicles.

The total number of vehicles parked in the basement is ___

There are 10 good shirts and 5 defective shirts in a box of 15 shirts. What is the probability of finding a defective shirt?

Question 56 (b)

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

$x^4+3x^{3}y+3x^2{y}^2-3x^{3}y-3x{y}^2+y^4-3x^2{y}^2$

Question 1
Is zero a rational number? Can you write it in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$?