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The price of 1 kg of potato is Rs. 60. 1 kg of onions costs 10% less than 1 kg potato. If I pay Rs. 180 for potatoes, what will be the cost of onions of the weight same as the weight of the potatoes?

Which basic property of a square will you use, if you are asked to draw a square with diagonal measuring 5 cm?

Sum of three consecutive integers is 51. The middle one is

(a) 14

(b) 15

(c) 16

(d) 17

Factorise:

$3y^2+14y+8$

Draw a line segment AB = 6.2 cm. Mark a point P in AB such that BP= 4 cm. Through point P draw perpendicular to AB.

A Ltd issued 50,00,000, 8% Debenture of Rs.100 at a discount of 6% on April 1, 2000 redeemable at premium of 4% by draw of lots as under.

20,00,000 Debentures on March, 2002

20,00,000 Debentures on March, 2004

20,00,000 Debentures on March, 2005

Compute the amount of discount to be written-off in each year till debentures are paid. Also prepare discount/ loss on issue of debentures account.

A cylindrical container of length 10m and radius 7m starts pouring water into a cubical tank of side 10m. Find the amount of water that will spill out of the cubical tank (in litres)?

Divide 184 into two parts such that one third of one part may exceed one seventh of another party by 8.

Question 2(iv)
Use the identity $(x+a)(x+b)=x^2+(a+b)x+ab$ to find the following products:
$(4x+5)(4x-1)$

Factorize

i) x⁴ - y⁴ + x² - y²

When 0 is divided by a non zero integer the quotient is

Which of the below is a mapping?

For x = ______, the equation 2x + 4 = x + 8 is satisfied.

The given pictograph shows the votes given by a group of students for their favourite flavour of ice cream. How many students voted for Chocolate Chip?

Divide -15x³y²z⁴ +25x²y²z² –20x²yz³ by 5xyz.

What should be multiplied with 20x²y³ to get 40x⁴y⁵?

The ratio of areas of a circular and rectangular field is 1:2. If the area of a circular field is 50 m², then area of the rectangular field is ___ m²

A shopkeeper purchases an article for Rs. 12,400 and sells it to a customer for Rs. 17,000. If the tax under VAT is 8%, find the VAT paid by the shopkeeper.

The degree of the polynomial P(x) = 11$x^6$ + $x^5$ + 3$x^4$ + $x^3$ + $x^2+x+1$ is ___

Ajay is constructing a square PQRS with PQ = 5 cm. The steps of construction are as follows.

(i) Draw a line segment PQ of length 5 cm. Construct 90° at the points P and Q. Extend the rays from P and Q.
(ii) Draw arcs of radius 5 cm keeping P and Q as centre on the extended rays.
(iii) Mark the intersecting points to be S and R.
Which of the following figure represents the completion of the construction of above mentioned steps?

The value of the given expression using multiplication identities will be equal to

$35\times 64+6\frac{2}{3}\times 12\times \frac{1}{2}$

If $6x+2=20$, then the value of $x$ is ___

For each of the following, find the least number that must be added so that the resulting number is a perfect square.

(i) 511 (ii) 7172 (iii) 55078

Factorise:
$a^{3}b-a^{2}b+5ab-5b$

Find which of the following numbers are divisible by 2:

(i) 192 (ii) 1660

(iii) 1101 (iv) 2079

In a class, the teacher asks the students to name few scientists. Following names came - Einstein, Newton, Einstein, Faraday, Tesla, Hawking, Einstein, Tesla, Tesla, Faraday, Einstein. Who is the most famous scientist?

Construct, if possible, a quadrilateral ABCD given,AB=6 cm BC=3.7 cm, CD=5.7 cm,AD=5.5 cm, and BD=6.1 cm, Give reasons for not able to construct, if you cannot.

Tick $\left(✓\right)$ the correct answer in each of the following:
$(x^2-4x+4)÷(x-2)=?$

(a) $(x-2)$
(b) $(x+2)$
(c) $(2-x)$
(d) $(2+x+x^2)$

The compound interest on a sum of ₹ 7500 at 4% per annum for a period of 2 years, compounded annually will be equal to

When the cube root of 8 is multiplied to the cube root of -8, the result which can be obtained is

Find the compound interest on Rs. 64000 for 1 year at the rate of $10\%$ per annum compounded quarterly.

The length of the side of a square with an area of 1600 m² is __ metres.

$(-69)÷69=$ ___

Question 107

Write 0.000005678 in the standard form.

Divide $x^5-4x^3+x^2+3x+6$ by $x^3-3x+1$,and then find the remainder and quotient.

Ravish sold his motorcycle to Vineet at a loss of 28% . Vineet spent

₹1680 on its repairs and sold the motorcycle to Rahul for ₹35910,

there by making a profit of 12.5% , find the cost price of motorcycle

for Ravish

Which of the following statements are true or false?
(i) $-\frac{3}{5}$ lies to the left of O on the number line.
(ii) $\frac{-12}{7}$ lies to the right of O on the number line.
(iii) The rational numbers $\frac{1}{3}$ and $\frac{-5}{2}$ are on opposite sides of O on the number line.
(iv) The rational number $\frac{-18}{-13}$ lies to the left of O on the number line.

Mohan wants to buy a trapezium shaped field.Its side along the river is parallel and twice the side along the road.If the area of this field is 10500 $m^2$ and the perpendicular distance between the two parallel sides is 100 m,find the length of the side along the river.