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Question 99(i)

Find the value of x, so that

${\left(\frac{5}{3}\right)}^{-2}\times {\left(\frac{5}{3}\right)}^{-14}={\left(\frac{5}{3}\right)}^{8x}$

In the given figure, ABCD is a quadrilateral and AO and DO are bisectors of $\angle Aand\angle D$. The value of 'x ' is _____.

From the above pie chart, find

The fraction of students interested in science

The fraction of students interested in social studies and maths

The roster form of the set $\{x:x=2r+3,\text{where}rϵI\text{and}-2<r\le 3\}$.

Area of a sector of angle $\theta$ with radius r is:

Which of the following represents the prime factorization of 24?

Dividing $(a^4+2a^2+a)÷3a$ gives ______.

From the following figure, choose the correct pair of corresponding angles.

Divide as directed.

(i)$5(2x+1)(3x+5)÷(2x+1)$

(ii)$26xy(x+5)(y-4)÷13x(y-4)$

(iii)$52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)$

(iv)$20(y+4)(y^2+5y+3)÷5(y+4)$

(v)$x(x+1)(x+2)(x+3)÷x(x+1)$

Which of these options, can best replace the ‘?’ in the given figure?

The area of quadrilateral ABCD in the given figure is

(a) $57c{m}^2$

(b) $108c{m}^2$

(c) $114c{m}^2$

(d) $195c{m}^2$

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.

(i) $252$ (ii) $2925$ (iii) $396$ (iv) $2645$ (v) $2800$ (vi) $1620$

Find the area of the triangle if the sides of the triangle are in the ratio 12:17:25 and the perimeter of the triangle is 270 m.

Mary gets an increment of 200 rupees on her salary every year. Write an equation connecting the number of years she works and the total increase in salary over the years. Is the total increase in salary proportional to the number of years of work?

Complete the following table of products of two monomials:

Find the values of the letters in the following and give reasons for
the steps involved.

From the graph identify the fruit that has same sales on both Monday and Tuesday.

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

My friend bought me a gift. He had left the price tag intact, so I saw that the item cost him ₹ 200. The sales tax levied on the item was 5%. What was the total amount paid by him for the gift?

The given graph shoes the performance of the cricket team in a match, observe it and find out the correct table.

Find the cube of $(2a-6b)$

Anshul and Balendu have 50 cubes of side 1 cm. They decided to make a larger cube by joining these smaller cubes. The number of larger cubes (all of different sizes) they can make is

With what number should 1715 be divided to get a perfect cube?

Question 1

In a cricket match, a batswoman hits a boundary 6times out of 30 balls she plays.

Find the probability that she did not hit a boundary.

A. The likelihood of an accident is determined by how carefully the motorist drives and how carefully the pedestrian crosses the street.

B. An accident involving a motorist and a pedestrian is such a case.

C. Each must decide how much care to exercise without knowing how careful the other is.

D. The simplest strategic problem arises when two individuals interact with each other, and each must decide what to do without knowing what the other is doing.
___

The table below shows the details of the leave availed by 40 workers in a factory, during one year:

Draw the line graph of this data.

(i) How many workers were on leave for atleast one day?

(ii) How many workers were on leave for more than 5 days?

(iii) How many workers were on leave for 6 or 7 days?

Find the quotient when $9p^5{q}^5-15p^3{q}^3+27p^2{q}^2$ is divided by $-3pq$.