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Q1) A car travel 47 km with 4 litres of petrol. How much petrol will be needed to travel a distance of 235km?
Q2) If twenty cans of 1 litre fruit juice are packed in one carton, then How many cartons are needed to pack 500 such cans ?
Q3) 120 books of the same size are packed in 5 box . How many such boxes are needed to pack 216 similar books ?

The salaries of A, B, C together amounts to RS. 333. If they spend 80%, 85% , 75% of their respective salaries and their savings are in the ratio of 7:6:9, then their respective salaries are ______

Find LCM of $x^2-1$ and $x+1$.

Dividing $2x^2+13x+15$ by $x+5$ and then substituting $x=2$ in the resulting expression gives

Question 34

The volume of a cylinder becomes ___ the original volume if its radius becomes half of the original radius.

What is the value of 'x' in the following equation?

$22x-12=36-2x$

Assertion: The expression $3x^4-4x^{\frac{3}{2}}+x^2$ is not a polynomial because the term $-4x^{\frac{3}{2}}$ contains a rational power of x.

Reason: The highest exponent(of the variable) in various terms of a polynomial in one variable is called its degree.

Which of the following is true?

‘A’ is a manufacturer of ‘Geysers’. The cost price of each Geyser is Rs. 3447. He sells to ‘B’, and ‘B’ sells to ‘C’. ‘C’ sells them to ‘D’, the retailer. The tax rate is 11.5% and the profit is Rs. 305 at each stage of the selling chain. Find:
(i) the total amount of VAT; and
(ii) the amount that the purchaser will have to pay.

Statement 1: Area of a rectangle with length ‘l’ and breadth ‘b’ is equal to $‘l\times b^{\prime }$.

Statement 2: All squares are rectangles with $l=b$

Pick the correct option from the following

In a regular polygon if the ratio of inner and outer angle is 3:2 then the inner angle of the polygon is

How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?

The minimum number that should be added to 300 so that we can get a perfect square is:

Sign of abscissa and ordinate of a point in the third quadrant will be

Factorize each of the following algebraic expressions.

4 (x + y) (3a - b) + 6 (x + y) (2b - 3a)

A shop worth ₹ 80000 was insured for 90% of its value. How much would the owner get in case of any mishap?

40% of the rat population in Hamelin perished due to a famine. The remaining 60% were drawn out of the town by the Pied Piper of Hamelin. If there were 48000 rats in the town originally, how many rats died due to the famine?

Question 3(vi)
Simplify:
(1.5x-4y)(1.5x+4y+3)-4.5x+12y

Arrange the given numbers in ascending order

5$\sqrt{2}$ , 3$\sqrt{3}$ , 7$\sqrt{5}$ , 9

In the figure shown, ABCD is a parallelogram. It is divided into triangles in such a way that $\angle BEC=\angle BCE$. Which one of the following is correct?

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Find the cube root of $3375\times 512$

The cube of $2\frac{1}{2}$ is ____.

Aditi, Kavya and Sohail were partners in a firm sharing profits in the ratio of 2 : 2 : 1. The firm closes its books on 31st March every year. On 30th September, 2017 Sohail died. According to the partnership deed, his legal representatives are entitled to the following :

(a) Capital as per Balance Sheet (Rs 60,000)

(b) Interest on capital 6$\%$ p.a., till the date of death.

(c) Share of profit to the date of death on the basis of the average profits of the last four years.

(d) Share of goodwill to be determined on the basis of the three years purchase of the average profits of last four years. The profits of last four years were : Rs 30,000, Rs 50,000, Rs 40,000 and Rs 60,000

Factorise each of the following:

$27y^3+125z^3$​ [ 3 MARKS]

Find the value of $\left(3x^3\right)\times (-5x{y}^2)\times \left(2x^{2}y{z}^3\right)$ for x=1,y=2 and z=3.

Question 5(b)
Add : 2x (z - x - y ) and 2y (z - y - x)

Using an identity expand :
$(2y+5)(2y+5)$

Rajan has 50 notes of ₹ 50 with him. Rehaan has 20 notes of ₹ 100. What is the ratio between the overall money that Rajan and Rehaan have respectively?

If $x\text{and}y$ vary directly,
then find the value of $p,q\text{and}r$.

Using the given number Line find the difference between Point A and point B :

2m wide path is built along the border and inside a square garden of side 11m. The area of the path is ___.

Factorise:
$x^2-9x+20$

Adding $5a^{2}b$ + 6ab + 7bc + 54 with 14ab + 8ac + 16, we get:

A glass contains $\frac{1}{4}$ liter of milk. How many glasses of milk is required to fill a bucket of $\frac{10}{2}$ liters ?
[4 MARKS]

1. 16.25

Pawan is a cashier in a bank. He has currency notes of denominations 1000, 500 and 100 respectively. The ratio of the number of these notes is 2:3:5. If the total cash with Pawan is ₹5,00,000, then how many notes of ₹1000 denomination does he have?

In a party my friends start eating a round piece of pizza. They eat in such a way that after each time they have pizza the quantity of pizza reduces by half. What type of decrease is this?

The distances of points that lie above the origin, which are measured along the Y axis, are taken as ____, and the distances of points that lie below the origin, which are measured along the Y axis, are taken as ____.

Question 5
The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Which of the following is not a perfect cube?