List of top Mathematics Questions

Classify the following numbers as rational or irrational : 

(i) \(\sqrt23 \)

(ii) \(\sqrt225 \)

(iii) 0.3796 

(iv) 7.478478... 

(v) 1.101001000100001...

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?
Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Classify the following numbers as rational or irrational:

(i) \(2 - \sqrt5\)  

(ii) \((3 + \sqrt23) - \sqrt23\) 

(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}\)

(iv) \(\frac{1}{\sqrt{2}}\)

(v) 2π 

Write the degree of each of the following polynomials: 

(i) 5x 3 + 4x 2 + 7x (ii) 4 – y 2 (iii) 5t – √7 (iv) 3.

Simplify each of the following expressions: 

(i) (3 + √3)(2 + √2) 

(ii) (3 + √3)(3 - √3) 

(iii) (√5 + √2 )2 

(iv) (√5 - √2)(√5 + √2)

Classify the following as linear, quadratic and cubic polynomials: 

(i) x 2 + x (ii) x – x 3 (iii) y + y 2 + 4 (iv) 1 + x (v) 3t (vi) r 2 (vii) 7x 3

Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π =\(\frac{ c}{d}\). This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
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.

 

Represent √9.3 on the number line

Find the zero of the polynomial in each of the following cases: 

(i) p(x) = x + 5 (ii) p(x) = x – 5 (iii) p(x) = 2x + 5 (iv) p(x) = 3x – 2 (v) p(x) = 3x

(vi) p(x) = ax, a ≠ 0 (vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.

The height of a cone is 15 cm. If its volume is 1570 cm3, find the diameter of its base. [Use \(\pi\) = 3.14]
Factorise: 27x3+y3+z3–9xy.

Rationalise the denominators of the following: 

(i) \(\frac{1 }{ \sqrt{7 }}\)

(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)

(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)

(iv) \(\frac{1 }{ \sqrt{7}-2}\)

Verify that x 3 + y 3 + z 3 – 3xyz = \(\frac{1}{2}\) (x + y + z) [(x - y)2 + (y - z)2 + (z - x)2].

Find: (i) 9 \(\frac{3}{2}\) (ii) 32 \(\frac{2}{5}\) (iii) 16 \(\frac{3}{4}\) (iv) 125 -\(\frac{1}{3}\)

If x+y+z=0, show that x3+y3+z3= 3xyz.
If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian Society is given below:

Section    

Number of girls per thousand boys

Scheduled Caste (SC)

940 

Scheduled Tribe (ST)

970

Non-SC/ST    

920

Backward districts 

950

Non-backward districts   

920

Rural    

930

Urban 

910

(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Find: (i) 64 \(\frac{1}{2}\) (ii) 32 \(\frac{1}{2}\) (iii) 125 \(\frac{1}{3}\)

Without actually calculating the cubes, find the value of each of the following: 

(i) (–12)3 + (7)3 + (5)3 

(ii) (28)3 + (–15)3 + (–13)3

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kiloliters?

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:

(i) Area : 25a 2 – 35a + 12 

(ii) Area : 35y 2 + 13y –12

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find. 
(i) height of the cone 
(ii) slant height of the cone 
(iii) curved surface area of the cone

What are the possible expressions for the dimensions of the cuboids whose volumes are given below? 

(i) Volume : 3x 2 – 12x 

(ii) Volume : 12ky2 + 8ky – 20k