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In order to compare two bar graphs, which of the following is/are true?

Karan runs 4/3 times as fast as Sanjay. If Karan gives Sanjay a head start of 20 meters, how far must the winning post be so that both of them reach at the same time?

In the following table, the number of children in six different classes are given.

Which class has the maximum number of children?

Present the following data by a percentage sub-divided bar diagram.

A quadrilateral has an area of $453.6m^2$. The length of a diagonal is 42 m and the perpendicular distance from one vertex to the diagonal is 10 m. What is the perpendicular distance from the other vertex to the diagonal ?

Which of the following is a linear expression ?

a) $x^2\times y+xy+1$

b) $x+y+1$

c) $x^3\times y+xy+1$

d) $4x^2+1$

Write the negation of the following statements :

(i) p : For every positive real number x, the number x - 1 is also positive.

(ii) q : All cats scratch.

(iii) r : For every real number x, either x > 1 or x < 1.

(iv) s : There exists a number x such that 0 < x < 1.

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Question 74

Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:

Write an equation whose solution is not a whole number.

Which of the following is the additive inverse of $\frac{-5}{6}$?

[5-5 X 9 X {(-36) /(-3 X 3 )}]3+1

Question 36

In a right angled $\Delta ABC$, if $\angle B={90}^{\circ }$, BC = 3 cm and AC = 5 cm, then the length of side AB is

a) 3 cm
b) 4 cm
c) 5 cm
d) 6 cm

Question 29

Fill in the blanks to make the statement true.

The unlike terms in perimeters of following figures are ___ and ___.

Question 72 (f)

Find the value of
$(8^0-2^0)\times (8^0+2^0)$

Question 6

If 7x + 4 = 25, then x is equal to

(a) $\frac{29}{7}$

(b) $\frac{100}{7}$

(c) 2

(d) 3

Great! Now that Ted knows about Geometry, he is curious about how it all started. Since Ted wants to become a great mathematician one day, he is also interested in knowing about the great mathematicians. We are talking about Geometry here. Which mathematician is regarded as the father of Geometry?

If a: b= 4:9 and b : c = 3: 2 what is the ratio a: c ?

Sonu and Raju have to collect different kinds of leaves for a science project. They went to a park where Sonu collected 12 leaves and Raju collected $x$ leaves. After sometime Sonu lost 3 leaves and Raju collects $2x$ leaves. Write an algebraic expression to find the total number of leaves collected by both of them. If they collected an equal number of leaves then find the value of $x$. [4 MARKS]

What rational number should be added -3/16to get 11/24?

$\text{Construt a}\Delta ABC\text{in which BC=5cm,AB=3.8cm,and AC=2.6cm.Bisect the largest angle of this triangle.}$

Which number is a whole number but not a natural number?

Which of the following is a closed shape?

Question 47

Fill in the blanks to make the statement true.

Corresponding angles are on the ___ side of the transversal.

Question 3
If the circumference of a circular sheet is 154 m, find its radius. Also, find the area of the sheet. $(Take\pi =\frac{22}{7})$

Question 2 (b)
Draw rough sketches for the following:
In $\Delta$ PQR, PQ, and PR are altitudes of the triangle.

Raju is playing a game with his friends where they have to run a stretch of 1200 m within a specified time limit of 150 seconds. The person exceeding the time limit will have to pay a penalty of Rs 2 for every second exceeded. Raju can run 100 m in 15 seconds. Find the penalty that Raju will have to pay.

Question 2 (ii)

If p = -2, find the value of:
$-3p^2+4p+7$

Which places is 6 present in the number 6046856?

Write an algebraic expression for the series 21, 32, 43, 54 … (taking n = 1, 2, and 3 … in order)

I bought a second-hand car for ₹ 50,000, spent ₹ 5,000 on transportation and sold it for ₹ 59,400. What is my profit %?

Raw data is:

The major segment of a circle is bounded by a ___ of the circle.

Compute and choose the relations that are correct.

Find the value of x in the equation $\frac{x(x-b)+x(x-a)}{(x-a)(x-b)}=2$.

From inside Room I, Bill overheard the following conversation between a group of humans (from Earth 1), who gathered near a job fair in the premises of “The Hall of Operations”, with a banner which read “Vacancies open for numbers which are closed under addition”:

Supriya (looking at the banner): What does “closed” in the banner mean?

Ajit (with a poker face): If a set of numbers is closed for a particular operation, then it is said to possess the closure property under that operation.

Supriya (unimpressed): That’s just a textbook definition. I want to understand what that actually means.

Arjun: Supriya, a set of numbers is said to be closed under a particular mathematical operation when the result of that operation also belongs to the same set of numbers.

Supriya then made 4 statements, each of which is presented in the following options. Chose the correct options made by Supriya. She might make more than one correct statement.

Ramesh does $\frac{1}{10}$th of work in an hour while his friend does $\frac{1}{10000}$th of what Ramesh does in the given time. What part of work did Ramesh's friend complete in an hour ? [2 MARKS]

What per cent of $Rs.4500$ is $Rs.9000$?

(a) $200\%$
(b) $\frac{1}{2}\%$
(c) $2\%$
(d) $50\%$

Two trains of length 150 m and 170 m respectively are running at the speed of 40 km/hr and 32 km/hr on parallel tracks in opposite directions. Find the time taken for them to cross each other.

Consider a rectangle of breadth 5 cm and area 30 sq cm. Then the length of this rectangle is

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Question 129

In the given figure, find the values of x, y and z.

If y is the reciprocal of rational number x, then the multiplicative inverse of y will be:

A wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to its other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

If two lines p and q are cut by a transversal, and the corresponding angles formed are equal, then:

The value of ${\frac{(-7)}{\left(7^6\right)}}^6$ is