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The weight of a piece of wire is directly proportional to its length. A piece of wire is 25 cm long and has a weight of 6 grams. Another piece of the same wire is 30 cm long. Calculate the weight of the 30 cm piece of wire.

$$\begin{array}{cc}Colours& No.ofpeople\\ Blue& 18\\ Green& 9\\ Red& 6\\ Yellow& 3\\ Total& 36\end{array}$$

Draw a pie chart showing the given information. The table shows the colours preferred by a group of people. Calculate the respective proportion of each colour and use that proportion to find the central angle. What is the percentage of the colour red?

$\begin{array}{cc}Season& No.ofvotes\\ Summer& 90\\ Rainy& 120\\ Winter& 150\end{array}$

A group of 360 people were asked to vote for their favourite season from the three seasons: rainy, winter and summer. Find the central angle of each sector in a pie chart for the above information. [4 MARKS]

Question 48

Fill in the blanks to make the statements true.

Cube of a number ending in 7 will end in the digit ___

Question 50

Solve the following:

$\frac{5x}{2x-1}=2$

What does Baudhayan theorem (Baudhayan Sulva Sutra) relate to?

$\text{If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.}$

Factorise :

$x^3-3x^2+x-3$

Factorize the following :

$72x^6{y}^7-96x^7{y}^6$

Question 92 (vi)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$9x^2-1$

Question 41
Fill in the blank to make statement true.
Out of ___ faces of a triangular prism, ___ are rectangles and ___ are triangles.

If x=6a+8b+9c;y=2b-3a-6c and z=c-b+3a ; find

(i) x+y+z (ii) x-y+z

(iii) 2x-y-3z (iv) 3y-2z-5x

Simplify and express in exponential form:
$4^3$ x $4^{-2}$ x ${16}^2$

Which of the following is an identity?

Compound interest for a certain sum of money for two years is 10% per annum is ₹ 315. Find the sum of money.

In what ratio should two kinds of sugar at Rs. 180 and Rs. 250 per quintal be mixed so that the price of each quintal of the mixed sugar will be Rs. 220?

Using suitable identity, evaluate $(-13{)}^3+(5{)}^3+(8{)}^3$

1A*A=9A

One A is multiplied by A

And the answer is 9A

What is the range of lengths of chord of contact of a circle with radius R.

Given that $7^{\text{m}}>7^{\text{n}}$, then m-n is

A person sells a article for ₹550, gaining ${\frac{1}{10}}^{th}$ of its CP. Find the gain%

Kunal has a recurring deposit account in a post office for 3 years at an interest of 8.5% per annum. If he gets Rs. 5661 as interest at the time of maturity then the monthly instalment is

Question 4 (iii)

Subtract $4p^{2}q-3pq+5p{q}^2-8p+7q-10from18-3p-11q+5pq-2p{q}^2+5p^{2}q.$

1. 98

What is the number of zeroes in the cube of 100?

Two ordered pairs (x,y) and (a,b) are equal if ______.

Rahul borrows a sum of Rs.10,000 for 2 years at a rate of interest 4% per annum. Find the simple interest he pays.

In a right angled triangle if the base is 3 cm and perpendicular is 4 cm. What is the area of that triangle?

Pavan tried to draw a line parallel to a given line, 'l'. Few steps are shown below. What will be the next step?

Step 1: Mark a point A, not on the line 'l'.
Step 2: Mark point B on line 'l'.
Step 3: Draw line segment joining points A and B.
Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and AB at E.

If $a+\frac{1}{a}=2\sqrt{3}$, then find the value of $a^3+\frac{1}{a^3}$

The area of a trapezium is 1586 cm²and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, then find the other parallel side.

If number of end points in a line, ray and a line segment are represented by X, Y and Z, what is the value of X + Y + Z? [2 MARKS]

The following pie-chart represents the marks scored by a student. If he obtained 540 as total marks, then the difference in the marks obtained in Maths and English is _______.

One of the factors of $x^2-2x-15$ is _____.

If $a+b+c=12$ and $a^2+b^2+c^2=50$, then ab + bc + ca = .

Ramesh invests ₹ 12800 for three years at the rate of $10\%$ per annum compounded annually. Find the sum Ramesh receives at the end of the first year.

Ram says that 22 bags of cement were required to cement a circular platform. If one bag of cement is required to cement an area of 7 m², then the area and the radius of the circular platform respectively are

An almirah is sold at ₹ 5225 after allowing a discount of 5%. Find its marked price.

₹ 5000

₹ 5500

₹ 4500

₹ 6000

Factorize:

$12(x+y{)}^2-(x+y)-35$

Find the value of A and B.

$AB\times B\underset{–}{}8A\underset{–}{}$

The probability of picking the letter K from the word TREKKING is $\frac{x}{4}$. Then the value of x is ___.

Pass journal entries for the Forfeiture and Re-issue in the following cases:

(a) X Ltd. forfeited 200 shares of Ravi of Rs 10 each Rs 8 called up, on which he had paid application and allotment money of Rs 3 per share. Out of these, 100 shares were re-issued as fully paid up for Rs 8 per share.

(b) Y Ltd. forfeited 300 shares of Rs 10 each, Rs 7 called up, for non-payment of First Call of Rs 2 per share. Out of these, 100 shares were immediately re-issued at Rs 6 per share.

(c) Z Ltd. forfeited 600 shares of Rs 10 each, on which first call of Rs 3 per share was not received; the second and final call of Rs 2 per share has not yet been called. Out of these, 200 shares were re-issued as Rs 8 paid-up for Rs 7 per share.

The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2).

Find the value of m and c.