CBSE Class 10 - Science - Human eye and the colourful World - Numericals

 

CBSE Class 10 – Science

Human Eye & The Colourful World

 1.     If the concave lens of focal length (f = 1.5m) used to restore the proper vision, then what is the power of lens? (-0.67 D)

 2.     A person having a myopic eye used the concave lens of focal length 50 cm. What is the power of the lens? (-2.0 D)

 3.     The far point of a myopic person is 80 cm in front of the eye. What is the nature and power of the lens required to correct the problem? (-1.25 D)

 4.     A short-sighted person cannot see clearly beyond 2 m. Calculate the power of lens required to correct his vision. (-0.5 D)

5.     A myopic person uses specs of power – 0.5 D. What is the distance of far point of his eye? (200 cm in front of the eyes)

6.     The far point of a myopic person is 150 cm in front the eye. Calculate the focal length and power of a lens required to enable him to see distant objects clearly. (-150 cm, -0.67 D) 

7.     A person wears eye glass of focal length 70 cm what is the far point of the person? (70 cm in front of the eyes)

8.     If your eye glasses have focal length 60 cm what is your near point? (42.9 cm in front  of the eyes)

9.     A person suffering from far – sightedness wears a spectacle having a convex lens of focal length 50 cm. What is the distance of the near point of his eye? (50 cm in front of the eyes)

10.  The near point of a hypermetropic eye is at 75 cm from the eye. What is the power of the lens required to enable him to read clearly a book held at 25 cm from the eye? (+2.67 D)

11.  A person wants to read a book placed at 20 cm, whereas near point of his eye is 30 cm. calculate the power of the lens required. (+1.67 D)

12.  A certain person has minimum distance of distinct vision of 150 cm. He wishes to read at a distance of 25 cm. What focal length glass should he use? What is the nature of eye defect? (+30 cm, convex lens)

13.  The near point of a hypermetropic eye is 1 m. What is the power of the lens required to correct this defect? Assume that near point of the normal eye is 25 cm. (+3.0 D)

14.  A person needs a lens of power +3 D for correcting his near vision and -3 D for correcting his distant vision. Calculate the focal lengths of the lenses required to correct these defects. (+33.33 cm, -33.33 cm)

15.  A 52-year-old near-sighted person wears eye glass of power of –5.5D for distance viewing. His doctor prescribes a correction of +1.5D in the near-vision section of his bifocals this measured relative to the main parts of the lens:

a.      What is the focal length of his distance viewing part of the lens? (-18.18 cm)

b.     What is the focal length of the near vision section of the lens? (+66.67 cm)

16.  A person is able to see objects clearly only when these are lying at distance between 50 cm and 300 cm from his eye.

a.      What kind of defect of vision he is suffering from? (Myopia and Hypermetropia)

b.     What kind of lenses will be required to increase his range of vision from 25 cm to infinity? (Concave lens and Convex lens)

 

CBSE Class 10 - Mathematics - Linear equations in two variables MCQ

CBSE Class 10 – Mathematics

Linear equations in two variables MCQ

1.      The nature of the graph lines of the equations 5x – 2y + 9 = 0 and 15x – 6y + 1 = 0 will be

a.      Parallel

b.      Coincident

c.      Intersecting

d.      Perpendicular to each other

2.      What will be the nature of the graph lines of the equations 2x+5y+15 and 6x+15y+45?

a.      Parallel

b.      Coincident

c.      Intersecting

d.      Perpendicular to each other

3.      What will be the value of k, if the lines given by 3x+ky-4 and 5x+(9+k)y+41 represent two lines intersecting at a point?

a.      k ≠ 7/2

b.      k ≠ 27/8

c.      k = 27/2

d.      k ≠ 27/2

4.      What will be the value of k, if the lines given by x+ky+3 and 2x+(k+2)y+6 are coincident?

a.      4

b.      2

c.      6

d.      8

5.      The lines 5x-7y=13 and 10x-14y=15 are

a.      Consistent

b.      Inconsistent

c.      May be consistent

d.      None of the above

6.      If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:

a.      -6x+10y-4=0

b.      6x-10y-4=0

c.      6x+10y-4=0

d.      -6x+10y+4=0

7.      If a pair linear equations is consistent then lines represented by them are

a.      Parallel

b.      Always coincident

c.      Always intersecting

d.      Intersecting or coincident

8.      The values for which the pair of equations (a – 1)x + 3y = 2 and 6x + (1 – 2b) = 6 has infinitely many solutions are

a.      a = -7, b = -4

b.      a = -4, b = -7

c.      a =3, b = -4

d.      a = -4, b = 3 

9.      The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have

a.      a unique solution

b.      exactly two solutions

c.      infinitely many solutions

d.      no solution

10.   The pair of equations y = 0 and y = –7 has

a.      One solution

b.      No solution

c.      Two solutions

d.      Infinitely many solutions

11.   If the pair of linear equations has a unique solution, then the lines representing these equations will

a.      coincide

b.      intersect at one point

c.      parallel to each other

d.      parallel to x-axis

12.   The pair of equations x = a and y = b graphically represents lines which are

a.      Parallel to each other

b.      Intersecting at point (a, b)

c.      Intersecting at point (b, a)

d.      Coincident

13.   When lines l₁ and l₂ are coincident, then the graphical solution system of linear equations has

a.      Infinitely many solutions

b.      One solution

c.      No solution

d.      Unique solution

14.   The graphical representation of a pair of equations 4x + 3y + 1 = 6 and 12x + 9y = 15 will be

a.      parallel lines

b.      coincident lines

c.      intersecting lines

d.      perpendicular lines

15.   The graph of x = –2 is

a.      Parallel to x-axis

b.      Parallel to y-axis

c.      Passes through origin

d.      Parallel to neither x-axis nor y-axis

16.   Which of the following is not a solution of the pair of equations 3x – 2y = 4 and 6x – 4y = 8?

a.      x = 2 and y = 1

b.      x = 6 and y = 7

c.      x = 5 and y = 3

d.      x = 4 and y = 4

17.   If the system of equations 2x + 3y = 7 and 2ax + (a+b)y = 28 has infinitely many solutions then

a.      a = 2b

b.      b = 2a

c.      a + 2b = 0

d.      2a + b = 0

18.   If x = a and y = b is the solution of the pair of equations x – y = 2 and x + y = 4 then the values of a and b are respectively

a.      3 and 5

b.      5 an 3

c.      3 and 1

d.      -1 and -3

19.   The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are

a.      45°, 75°

b.      50°, 80°

c.      55°, 85°

d.      55°, 95°

20.   If the sum of two numbers is 35 and difference is 13 then the two numbers are

a.      24, 12

b.      24, 11

c.      13, 22

d.      28, 15

 

Answers:

1.   a                     2.   b                     3.   d                     4.   b                     5.   b                     6.   a                    

7.   d                     8.   c                      9.   d                     10. b                     11. b                     12. b

13. a                     14. b                     15. b                     16. c                     17. b                     18. c

19. c                     20. b

CBSE Class 10 - Mathematics - Surface areas and volumes - Exercise 13.3 Solutions

1. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

2. Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

3. A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

4. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

5. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

6. How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

Factors and multiples - 8

In the previous post we discussed about the multiples of a number. We hope that you have solved the given practice problems. Did you realize that the tables of various numbers are nothing but the first 10 multiples of the given number?

 Multiples and LCM

Example:

Table of 2 i.e. First 10 multiples of 2	Table of 7 i.e. First 10 multiples of 7	Table of 13 i.e. First 10 multiples of 13
2 x 1 = 2	7 x 1 = 7	13 x 1 = 13
2 x 2 = 4	7 x 2 = 14	13 x 2 = 26
2 x 3 = 6	7 x 3 = 21	13 x 3 = 39
2 x 4 = 8	7 x 4 = 28	13 x 4 = 52
2 x 5 = 10	7 x 5 = 35	13 x 5 = 65
2 x 6 = 12	7 x 6 = 42	13 x 6 = 78
2 x 7 = 14	7 x 7 = 49	13 x 7 = 91
2 x 8 = 16	7 x 8 = 56	13 x 8 = 104
2 x 9 = 18	7 x 9 = 63	13 x 9 = 113
2 x 10 = 20	7 x 10 = 70	13 x 10 = 130

Let’s explore the concept of multiple further.

Write down first 10 multiples of number 2 and 3.

First 10 multiples of 2	First 10 multiples of 3
2 x 1 = 2	3 x 1 = 3
2 x 2 = 4	3 x 2 = 6
2 x 3 = 6	3 x 3 = 9
2 x 4 = 8	3 x 4 = 12
2 x 5 = 10	3 x 5 = 15
2 x 6 = 12	3 x 6 = 18
2 x 7 = 14	3 x 7 = 21
2 x 8 = 16	3 x 8 = 24
2 x 9 = 18	3 x 9 = 27
2 x 10 = 20	3 x 10 = 30

From the table above we observe that within first 10 multiples of each 2 & 3, the common multiples are 6, 12 and 18. Here the smallest common multiple is 6.  

We know that a number has infinitely many multiple. Hence there can be many common multiples between any two numbers.

Let’s consider some more examples.

Multiples of 4 and 6

First 10 multiples of 4	First 10 multiples of 6
4 x 1 = 4	6 x 1 = 6
4 x 2 = 8	6 x 2 = 12
4 x 3 = 12	6 x 3 = 18
4 x 4 = 16	6 x 4 = 24
4 x 5 = 20	6 x 5 = 30
4 x 6 = 24	6 x 6 = 36
4 x 7 = 28	6 x 7 = 42
4 x 8 = 32	6 x 8 = 48
4 x 9 = 36	6 x 9 = 54
4 x 10 = 40	6 x 10 = 60

From the first 10 multiples of 4 and 6, the common multiples are 12, 24 and 36. The smallest common multiple is 12.

Multiples of 6, 9 and 12

First 10 multiples of 6	First 10 multiples of 9	First 10 multiples of 12
6 x 1 = 6	9 x 1 = 9	12 x 1 = 12
6 x 2 = 12	9 x 2 = 18	12 x 2 = 24
6 x 3 = 18	9 x 3 = 27	12 x 3 = 36
6 x 4 = 24	9 x 4 = 36	12 x 4 = 48
6 x 5 = 30	9 x 5 = 45	12 x 5 = 60
6 x 6 = 36	9 x 6 = 54	12 x 6 = 72
6 x 7 = 42	9 x 7 = 63	12 x 7 = 84
6 x 8 = 48	9 x 8 = 72	12 x 8 = 96
6 x 9 = 54	9 x 9 = 81	12 x 9 = 108
6 x 10 = 60	9 x 10 = 90	12 x 10 = 120

From the first 10 multiples of 6, 9 and 12, the common multiple among all is 36 which is the smallest common multiple as well.

The smallest common multiple of given numbers is called Least common multiple (LCM).

From the given examples:

·         LCM of 2 and 3 is 6.  

·         LCM of 4 and 6 is 12.

·         LCM of 6, 9 and 12 is 36.

Practice time:

Write first 10 multiples of each of the following and find the LCM.

         i.        3, 7

        ii.        5, 8

       iii.        12, 15

      iv.        16, 80

       v.        16, 24