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How many rational numbers p/q are there between 0 and 1 for which q < p?

Question 14

The volume of a cylinder whose radius r is equal to its height is

(a) $\frac{1}{4}\pi r^3$ (b) $\frac{\pi r^3}{32}$ (c) $\pi r^3$ (d) $\frac{\pi r^3}{8}$

Question 5(iv)

Obtain the product of:

a,2b,3c,6abc

Question 90

Solve the following question:

Express 81 as the sum of first nine consecutive odd numbers.

Factorise:

$x^2+\frac{1}{x^2}-11$

In a class, the number of girls is $20\%$ more than that of boys. The strength of the class is $66.$ If $4$ more girls are admitted to the class, then the ratio of the number of boys to that of girls is

By using the formula, find the amount and compound interest on:

In how many years will Rs 1800 amount to Rs 2178 at $10\%$ per annum when compounded annually ?

In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel. How long will these provisions last ?

Question 9

A regular hexagon is inscribed in a circle of radius r. The perimeter of the regular hexagon is

(a) 3 r (b) 6 r (c) 9 r (d) 12 r

Factorise $(a^3-8b^3)$.

Question 98(iv)

Simplify
$(2^5÷2^8)\times 2^{-7}$

In a cricket match of India and Pakistan, what is the probability that India would win the toss?

What
is the sum of the measures of the angels of a convex quadrilateral?
Will this property hold if the quadrilateral is not convex? (Make a
non-convex quadrilateral and try!)

Aman's age is three times his son's age. Ten years ago he was five times his son's age. Find their present ages.

Question 81

The cost of 27 kg of iron is ₹1080, what will be the cost for 120 kg of iron of the same quality?

A cuboid has dimentions of $\sqrt{7}\text{unit}\times \sqrt[3]{34}\text{unit}\times \sqrt[4]{49}\text{unit}.$ Find the volume of the cuboid.

In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={50}^{\circ }$, then $\angle CAO$ is equal to.

Question 177(ii)

Find x.

${\left(\frac{2}{5}\right)}^{2x+6}\times {\left(\frac{2}{5}\right)}^3={\left(\frac{2}{5}\right)}^{x+2}$

Construct a triangle PQR in which PQ = 4 cm, ∠P = 60° and ∠Q = 60°

A line PQ is drawn and with P as centre, a circle is drawn with radius greater than half of PQ but less than PQ. Again with same radius and Q as centre, draw another circle. If the two circles meet at X and Y, then the triangles PXQ and PYQ are

A customer orders 3 pizzas with pepperoni on
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$\frac{7}{3}$ of the pizzas. Choose the correct pizzas that has been ordered.

A half is repesented as and a quarter is represented as respectively.

Question 37

If amount on the principal of Rs 6000 is written as $6000{(1+\frac{5}{100})}^3$ and compound interest payable half-yearly, then rate of interest per annum is ___ and time (in years) is ___.

Which of the following is an equivalent fraction of $\frac{1}{5}$?

Find the value of:

$\left(i\right)\frac{\sqrt{80}}{\sqrt{405}}$ $\left(ii\right)\frac{\sqrt{441}}{\sqrt{625}}$ $\left(iii\right)\frac{\sqrt{1587}}{\sqrt{1728}}$ $\left(iv\right)\sqrt{72}\times \sqrt{338}$ $\left(v\right)\sqrt{45}\times \sqrt{20}$

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

If $\frac{p}{q}$ is a rational number, then