List of top Mathematics Questions

Numbers \(1\) to \(10\) are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of . 

1. getting a number \(6\)? 
2. getting a number less than \(6\)? 
3. getting a number greater than \(6\)? 
4. getting a \(1\)-digit number?

List the outcomes you can see in these experiments. 

1. Spinning a wheel 
2. Tossing two coins together

The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
 

Language	Hindi	English	Marathi	Tamil	Bengali	Total
Number of students	40	12	9	7	4	72

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions: 

1. In which subject did the student score 105 marks? (Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?) 
2. How many more marks were obtained by the student in Mathematics than in Hindi? 
3. Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles).

Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
 

Colours	Number of people
Blue	18
Green	9
Red	6
Yellow	3
Total	36

Obtain the product of
(i) xy, yz, zx
(ii) a, – a² , a³
(iii) 2, 4y, 8y² , 16y³
(iv) a, 2b, 3c, 6abc
(v) m, – mn, mnp

A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey.

From this pie chart answer the following: 

1. If 20 people liked classical music, how many young people were surveyed? 
2. Which type of music is liked by the maximum number of people? 
3. If a cassette company were to make 1000 CD’s, how many of each type would they make?

Obtain the volume of rectangular boxes with the following length, breadth and height, respectively.
(i) 5a, 3a², 7a⁴
(ii) 2p, 4q, 8r
(iii) xy, 2x²y, 2xy²
(iv) a, 2b, 3c

\(ABC\) is a right-angled triangle and \(O\) is the mid point of the side opposite to the right angle. Explain why \(O\) is equidistant from \(A, B\) and \(C\). (The dotted lines are drawn additionally to help you).

Explain why a rectangle is a convex quadrilateral.

Name the quadrilaterals whose diagonals. 

1. bisect each other 
2. are perpendicular bisectors of each other 
3. are equal.

Identify all the quadrilaterals that have 

1. four sides of equal length 
2. four right angles

State whether True or False. 

1. All rectangles are squares. 
2. All rhombuses are parallelograms. 
3. All squares are rhombuses and also rectangles. 
4. All squares are not parallelograms. 
5. All kites are rhombuses. 
6. All rhombuses are kites. 
7. All parallelograms are trapeziums. 
8. All squares are trapeziums.

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths, respectively.
(p, q) ; (10m, 5n) ; (20x² , 5y²) ; (4x, 3x²) ; (3mn, 4np)

Find the measure of \(∠P\) and \(∠S\) if \(\bar {SP} || \bar{RQ}\) in Figure. (If you find \(m∠R\), is there more than one method to find \(m∠P\) ?)

Find \(m∠C \) in Figure if \(\bar {AB}|| \bar{DC}\)

Find the product of the following pairs of monomials.
(i) 4, 7p
(ii) – 4p, 7p
(iii) – 4p, 7pq
(iv) 4p³, – 3p
(v) 4p, 0

In the above figure both \(RISK\) and \(CLUE\) are parallelograms. Find the value of \(x\).

The following figures \(GUNS\) and \(RUNS\) are parallelograms. Find \(x\) and \(y\). (Lengths are in cm)

The adjacent figure \(HOPE\) is a parallelogram. Find the angle measures \(x, y\) and \(z\). State the properties you use to find them.

The measures of two adjacent angles of a parallelogram are in the ratio \(3 : 2\). Find the measure of each of the angles of the parallelogram.

Add the following ab– bc, bc – ca, ca – ab.

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y-cos y=x :(ysin y+cosy+x)y'=y

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: xy = log y+C : y'= \(\frac{y^2}{1-xy}\,(xy\neq 1)\)

Can a quadrilateral \(ABCD\) be a parallelogram if 

1. \(\angle D + ∠B = 180°\)? 
2. \(AB = DC = 8 \;cm\), \(AD = 4 \;cm\) and \(BC = 4.4 \;cm\)? 
3. \(∠A = 70°\) and \(∠C = 65°\)?