List of top Mathematics Questions

Let $A=\{1,2,3,5,8,9\}$ Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to______

Find the product:
(i)$\frac{9}{2}$×(-$\frac{7}{4}$)
(ii) $\frac{3}{10}$×(-9)
(iii) -$\frac{6}{5}$×$\frac{9}{11}$
(iv) $\frac{3}{7}$×(-$\frac{2}{5}$)
(v) $\frac{3}{11}$×$\frac{2}{5}$
(vi) $\frac{3}{-5}$ ×$\frac{-5}{3}$

Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
\includegraphics[width=\linewidth]{latex.png} The relation between fuel consumption $ F $ (liters per 100 km) and speed $ V $ (km/h) under some constraints is given as: \[ F = \frac{V^2}{500} - \frac{V}{4} + 14. \] On the basis of the above information, answer the following questions: [(i)] Find $ F $, when $ V = 40 \, \text{km/h} $. [(ii)] Find $ \frac{dF}{dV} $. [(iii)] (a) Find the speed $ V $ for which fuel consumption $ F $ is minimum.
\hspace*{0.8cm} OR
(b) Find the quantity of fuel required to travel $ 600 \, \text{km} $ at the speed $ V $ at which $ \frac{dF}{dV} = -0.01 $.

The following table gives the distribution of students of two sections according to the marks obtained by him:

Section A		Section B
Marks	Frequency	Marks	Frequency
0 − 10	3	0 − 10	5
10 − 20	9	10 − 20	19
20 − 30	17	20 − 30	15
30 − 40	12	30 − 40	10
40 − 50	9	40 − 50	1

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

Draw, wherever possible, a rough sketch of

a triangle with both line and rotational symmetries of order more than 1.
a triangle with only line symmetry and no rotational symmetry of order more than 1.
a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

The family of curves whose x and y intercepts of a tangent at any point are respectively double the x and y coordinates of that point is

A survey conducted by an organization for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):

S.No.	Causes	Female fatality rate (%)
1.	Reproductive health conditions	31.8
2.	Neuropsychiatric conditions	25.4
3.	Injuries	12.4
4.	Cardiovascular conditions	4.3
5.	Respiratory conditions	4.1
6.	Other causes	22.0

(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women’s ill health and death worldwide?
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.

Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

In Fig. 9.26, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.

four points on a circle. AC and BD intersect at a point

Multiply and reduce to the lowest form and convert into a mixed fraction:
(i) 7 × $\frac{3}{5}$
(ii) 4 × $\frac{1}{3}$
(iii) 2 × $\frac{6}{7}$
(iv) 5 ×$\frac{2}{9}$
(v) $\frac{2}{3}$× 4
(vi) $\frac{5}{2}$ × 6
(vii) 11 × $\frac{4}{7}$
(viii) 20 × $\frac{4}{5}$
(ix) 13 × $\frac{1}{3}$
(x) 15 × $\frac{3}{5}$

Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

If $ x = at, y = \frac{a}{t} $, then $ \frac{dy}{dx} $ is:

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 9.27). Prove that ∠ACP = ∠ QCD

Two circles intersect at two points B and C.

Using laws of exponents, simplify and write the answer in exponential form:
(i) 32 × 34 × 38 (ii) 615 ÷ 610 (iii) a³ × a² (iv) 7x×7² (v) (5²) ÷ 5³ (vi) 2⁵ × 5⁵ (vii) a⁴ × b⁴ (viii) (34)³(ix) (220 ÷ 215)×23 (x) 8t ÷ 82