Coordinate Geometry Class 10 Practice Questions

CSCE TUTORIAL

Coordinate Geometry

Class – X                                                                                                                                                                            Mathematics
  1. Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).
  2. Find a point on the y-axis equidistant from (-5, 2) and (9, -2)
  3. Find the distance of the point (-3, 4) from the x-axis.
  4. Find the distance of the point P (2, 3) from the x-axis.
  5. Find the coordinates of the points of trisection (i.e., points dividing into three equal parts) of the line segment joining the points A(2, – 2) and B(– 7, 4).
  6. Find the value of a when the distance between the points (3, a) and (4, 1) is √10.
  7. Find the value of x, y if the distances of the point (x, y) from (- 3, 0) as well as from (3, 0) are 4.
  8. If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that
x + 3y = 0.
  1. Which point on the x-axis is equidistant from (5, 9) and (-4, 6)?
  2. Find a point on the x-axis which is equidistant from the points (7, 6) and (-3, 4).
  3. The length of a line segment is of 10 units, and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.
  4. Show that the points A(- 4, -1), B(-2, – 4), C(4, 0) and D(2, 3) are the vertices points of a rectangle.
  5. The points A (2, 9), B (a, 5) and C (5, 5) are the vertices of a triangle ABC, right-angled at B. Find the values of a and hence the area of triangle ABC.
  6. Prove that the points (-2, 5), (0, 1) and (2, -3) are collinear.
  7. The coordinates of point P are (-3, 2). Find the coordinates of the point Q, which lies on the line joining P and origin such that OP = OQ.
  8. The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.
  9. Find a point which is equidistant from points A (-5, 4) and B (-1, 6). How many such points are there?
  10. The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, -9) and has diameter 10√2 units.
  1. Ayush starts walking from his house to the office. Instead of going to the office directly, he goes to the bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching the office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in kilometers.
  2. Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
  3. Find the coordinates of point A, where AB is the diameter of the circle whose centre is (2, -3) and B is (1, 4).
  4. If (a, b) is the mid-point of the line segment joining the points A (10, -6), B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
  5. If P(9a – 2, -b) divides the line segment joining A(3a + 1, -3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b.
  6. If the points (-2, 1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.

Acid Bases and Salts Class 10 Important Questions

CSCE TUTORIAL

Acid, Bases and Salt

 

  1. What colour do the following indicators turn when added to a base or alkali (such as sodium hydroxide)?
    (a) Methyl orange                       (b) litmus                                    (c) red cabbage extract
  1. What will be the action of the following substances on litmus paper?
    a. Dry HCI gas
    b. Moistened NH3 gas
    c. Lemon juice
    d. Carbonated soft drinks
    e. Curd
    f. Soap solution
  1. Name the acid present in ant sting and give its chemical formula. Also, give the common method to get relief from the discomfort caused by the ant sting.
  1. Name an indicator which is pink in an alkaline solution but turns colourless in an acidic solution.
  1. When a solution is added to a cloth strip treated with onion extract, then the smell of onion cannot be detected. State whether the given solution contains an acid or base.
  1. How will you test for the gas which is liberated when hydrochloric acid reacts with an active metal?
  1. Name the gas that evolved when dilute HCl reacts with sodium hydrogen carbonate. How is it recognized?
  1. (a) Write the chemical name and formula of marble.
    (b) It has been found that marbles of Taj are getting corroded due to development of industrial areas around it. Explain this fact giving a chemical equation.
  1. How would you distinguish between baking powder and washing soda by heating?
  1. Salt A is commonly used in bakery products on heating gets converted into another salt B, which is used to remove the hardness of water, and a gas C is evolved. The gas C, when passed through lime water, turns it milky. Identify A, B and C.
  2. In one of the industrial processes used to manufacture sodium hydroxide, a gas X is formed as a byproduct. The gas X reacts with lime water to give a compound Y used as a bleaching agent in the chemical industry. Identify X and Y giving the chemical equation of the reactions involved.
  3. When zinc metal is treated with a dilute solution of a strong acid, a gas is evolved, which is utilised in the hydrogenation of oil. Name the gas evolved. Write the chemical equation of the reaction involved and also write a test to detect the gas formed.
  4. For making cake, baking powder is taken. If your mother uses baking soda instead of baking powder in cake at home,
    (a ) How will it affect the taste of the cake and why?
    (b ) How can baking soda be converted into baking powder?
    (c ) What is the role of tartaric acid added to baking soda?
  1. A metal carbonate X reacting with acid gives a gas that gives the carbonate back when passed through a solution Y. On the other hand, a gas G obtained at the anode during electrolysis of brine is passed on dry Y, it gives a compound Z, used for disinfecting drinking water. Identity X, Y, G and Z.
  1. Name on natural source of each of the following acids:
    (a) Citric acid            (b) Oxalic acid               (c) Lactic acid                       (d) Tartaric acid
  1. Fresh milk has a pH will change as it turns into curd? Explain.
  1. A milkman adds a very small amount of baking soda to fresh milk.
    (i)  Why does he shift the pH of the fresh milk from 6 to slightly alkaline?
    (ii) What do you expect to observe when milk comes to boil?
  1. What happens when sodium carbonate reacts with dilute HCl acid?
  1. Why are metallic oxides called basic oxides?
  1. State the number of water molecules present in crystals of washing soda and plaster of paris. What are these water molecules called as?
  2. A white powder is used by doctor to support fractured bones write the chemical name of it. Write the chemical equation of its preparation. Why should it be stored in a dry place? Give one more use of the white powder.
  3. State the chemical property in each case on which of the following uses of baking soda are based :
    a. as an antacid
    b. as a constituent of baking powder

 

Metals and Non Metals Class 10 important questions

CSCE TUTORIAL

Metals and Non-Metals

Class – X                                                                                                                                                                        Chemistry

 

  1. Iron is a ________________ metal widely used in construction.
  2. Non-metals generally have ________________ conductivity of electricity.
  3. Aluminium is a ________________ metal used in making beverage cans.
  4. Non-metals tend to be ________ at room temperature.
  5. Chlorine is a ______________ gas with a pungent odor.
  6. Metals are generally ______________ conductors of heat.
  7. ____________ is a shiny and ductile metal often used in jewelry.
  8. Non-metals such as sulphur and phosphorus are often found in _____________ form.
  9. Aluminium is a ________________ metal used in aircraft manufacturing.
  10. ________________ is the lightest and most abundant element in the universe.
  11. Non-metals tend to ________________ electrons during chemical reactions.
  12. Copper is a good ________________ of heat, making it ideal for cooking utensils.
  13. Carbon dioxide is a ________________ gas that is essential for photosynthesis.
  14. ________________ is a reactive non-metal used in the treatment of drinking water.
  15. ________________ is a non-metal that is essential for the formation of bones and teeth.
  16. Helium is a ________________ gas used to inflate balloons and airships.
  17. Non-metals generally have low ________________ points and low densities.
  18. Gold is a highly ________________ metal, often used in electronic devices.
  19. In the periodic table, metals are found on the ________ side.
  20. Oxygen gas is a ________________ of combustion reactions.
  21. Non-metals like nitrogen and oxygen make up the majority of the ________________.
  22. Mercury is the only metal that is ________________ at room temperature.
  23. Metals have a tendency to ________________ electrons to form positive ions.
  24. ________________ is a non-metallic element used in making matchsticks.
  25. Neon is a noble gas and is used in ________________ signs.
  26. _________________ is an essential metal for the transportation of oxygen in the blood.
  27. ________________ is a non-metal that is essential for the formation of proteins.
  28. The ________________ of metalloids allows them to exhibit properties of both metals and non-metals.
  29. Non-metals like chlorine and iodine are used in ________________ substances.
  30. The most abundant metal in the earth’s crust is ________________ .
  31. The process in which a carbonate ore is heated strongly in the absence of air to convert it into metal oxide is called ________________ .
  32. Oxides of moderately reactive metals like Zinc, Iron, Nickel, Tin, Copper etc. are reduced by using ________________ as reducing agent.
  33. Galvanisation is a method of protecting iron from rusting by coating with a thin layer of ______________ .
  34. Amalgam is an alloy of ______________ .
  35. Copper objects lose their shine and form green coating of ______________
  36. Two metals which melt when kept on the palm are ______________ and ______________ .
  37. A non-metal which is a good conductor of electricity is ______________.
  38. Metals can form positive ions by ______________.
  39. A non-metal which is lustrous is ______________.
  40. A metal which burns in air with a dazzling white flame is ______________ .
  41. Metals above hydrogen in the activity series can displace ______________ from dilute acids.
  42. The extraction of metals from their ores and then refining them for use is known as ______________ is an allotroph of carbon and is the hardest natural substance.
  43. Metals which are so soft that they can be cut with a knife are __________ and __________
  44. Metal oxides ______________ and ______________ dissolve in water to form alkalis.
  45. A non-metal used to preserve food material is ______________
  46. The metals that float when treated with water are ______________ and ______________ .
  47. When a pellet of sodium is dropped in water, it __________________ and __________________
  48. Aqua regia is a freshly prepared mixture of concentrated HNO3 and concentrated HCl in the ratio of __________________ and __________________.
  49. _________________ is a metal which is stored in kerosene oil.
  50. _________________ is a non-metal which is stored under water.

Class 11 Sets Important Questions Solutions

Answer Key

  1. 2x– 1 is always an odd number for all positive integral values of x since 2x is an even number.
  • In particular, 2x– 1 is an odd number for x = 1, 2, … , 9.
    Therefore, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
  • x2+ 7x – 8 = 0
    (x + 8) (x – 1) = 0
    x = – 8 or x = 1
    Therefore, C = {– 8, 1}

 

  1. For “CATARACT”, Distinct letters are
    {C, A, T, R} = {A, C, R, T}
    For “TRACT”, Distinct letters are
    {T, R, A, C} = {A, C, R, T
    The letters needed to spell cataract are equal to the set of letters needed to spell tract.
    Hence, the two sets are equal.

 

  1. (i) A = {x | x ∈ N and x is odd}

A = {1, 3, 5, 7, …, 99}
(ii) B = {y | y = x + 2, x ∈ N}

1 ∈ N, y = 1 + 2 = 3

2 ∈ N, y = 2 + 2 = 4, and so on.

Therefore, B = {3, 4, 5, 6, … , 100}

 

  1. A = All natural numbers, i.e., {1, 2, 3…..}

B = All even natural numbers, i.e., {2, 4, 6, 8…}

C = All odd natural numbers, i.e., {1, 3, 5, 7……}

D = All prime natural numbers, i.e., {1, 2, 3, 5, 7, 11, …}

(i) A ∩ B

A contains all elements of B.

∴ B ⊂ A = {2, 4, 6, 8…}

         ∴ A ∩ B = B

(ii) A ∩ C

A contains all elements of C.

∴ C ⊂ A = {1, 3, 5…}

         ∴ A ∩ C = C

(iii) A ∩ D

A contains all elements of D.

∴ D ⊂ A = {2, 3, 5, 7..}

         ∴ A ∩ D = D

(iv) B ∩ C

B ∩ C = ϕ

         There is no natural number which is both even and odd at the same time.

(v) B ∩ D

B ∩ D = 2

         {2} is the only natural number which is even and a prime number.

C ∩ D

C ∩ D = {1, 3, 5, 7…}

= D – {2}

         Every prime number is odd except {2}.

 

  1. (i) A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

A ∪ B = {x: x ∈ A or x ∈ B}

                        = {1, 2, 3, 4, 5, 6, 7, 8}

         (ii) A = {1, 2, 3, 4, 5}

C = {7, 8, 9, 10, 11}

A ∪ C = {x: x ∈ A or x ∈ C}

              = {1, 2, 3, 4, 5, 7, 8, 9, 10, 11}

         (iii) B = {4, 5, 6, 7, 8}

C = {7, 8, 9, 10, 11}

B ∪ C = {x: x ∈ B or x ∈ C}

                  = {4, 5, 6, 7, 8, 9, 10, 11}

         (iv)  B = {4, 5, 6, 7, 8}

D = {10, 11, 12, 13, 14}

B ∪ D = {x: x ∈ B or x ∈ D}

                = {4, 5, 6, 7, 8, 10, 11, 12, 13, 14}

(v) A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

C = {7, 8, 9, 10, 11}

A ∪ B = {x: x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 6, 7, 8}

A ∪ B ∪ C = {x: x ∈ A ∪ B or x ∈ C}

                        = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

(vi) A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

D = {10, 11, 12, 13, 14}

A ∪ B = {x: x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 6, 7, 8}

A ∪ B ∪ D = {x: x ∈ A ∪ B or x ∈ D}

                         = {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14}

(vii) B = {4, 5, 6, 7, 8}

C = {7, 8, 9, 10, 11}

D = {10, 11, 12, 13, 14}

B ∪ C = {x: x ∈ B or x ∈ C}

= {4, 5, 6, 7, 8, 9, 10, 11}

B ∪ C ∪ D = {x: x ∈ B ∪ C or x ∈ D}

                        = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

(viii) A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

C = {7, 8, 9, 10, 11}

B ∪ C = {x: x ∈ B or x ∈ C}

= {4, 5, 6, 7, 8, 9, 10, 11}

A ∩ B ∪ C = {x: x ∈ A and x ∈ B ∪ C}

                = {4, 5}

(ix) A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

C = {7, 8, 9, 10, 11}

(A ∩ B) = {x: x ∈ A and x ∈ B}

= {4, 5}

(B ∩ C) = {x: x ∈ B and x ∈ C}

= {7, 8}

(A ∩ B) ∩ (B ∩ C) = {x: x ∈ (A ∩ B) and x ∈ (B ∩ C)}

                                   = ϕ

(x) A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

C = {7, 8, 9, 10, 11}

D = {10, 11, 12, 13, 14}

A ∪ D = {x: x ∈ A or x ∈ D}

= {1, 2, 3, 4, 5, 10, 11, 12, 13, 14}

B ∪ C = {x: x ∈ B or x ∈ C}

= {4, 5, 6, 7, 8, 9, 10, 11}

(A ∪ D) ∩ (B ∪ C) = {x: x ∈ (A ∪ D) and x ∈ (B ∪ C)}

                                 = {4, 5, 10, 11}

 

  1. U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}

A′ = {1, 4, 5, 6}

B′ = { 1, 2, 6 }.

A′ ∩ B′ = { 1, 6 }

A ∪ B = { 2, 3, 4, 5 }

(A ∪ B)′ = { 1, 6 }

Therefore, ( A ∪ B )′ = { 1, 6 } = A′ ∩ B′

 

  1. (i) A = {x : x is an integer and –3 ≤ x < 7}

Integers are …-5, -4, -3, -2, -2, 0, 1, 2, 3, 4, 5, 6, 7, 8,…..

A = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {x : x is a natural number less than 6}

Natural numbers are 1, 2, 3, 4, 5, 6, 7, ……

B = {1, 2, 3, 4, 5}

 

  1. U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {3, 5} and C = {1, 2, 4, 7}

(i)  A′ = {1, 3, 5, 7}

C′ = {3, 5, 6}

B ∩ C′ = {3, 5}

A′ ∪ (B ∩ C′) = {1, 3, 5, 7}

(ii) B – A = {3, 5}

A – C = {6}

(B – A) ∪ (A – C) = {3, 5, 6}

 

  1. Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}

U = { 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {2, 4, 6, 8}

A U B = {2, 3, 4, 5, 6, 7, 8}

(A U B)’ = {1, 9}

 

  1. n (A ∪ B) = 50

n (A) = 28

n (B) = 32

n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

Substituting the values, we get

50 = 28 + 32 – n (A ∩ B)

50 = 60 – n (A ∩ B)

–10 = – n (A ∩ B)

∴ n (A ∩ B) = 10

 

  1. n (P) = 40

n (P ∪ Q) = 60

n (P ∩ Q) =10

We know, n (P ∪ Q) = n (P) + n (Q) – n (P ∩ Q)

Substituting the values, we get

60 = 40 + n (Q)–10

60 = 30 + n (Q)

N (Q) = 30

∴ Q has 30 elements.

 

  1. Total number of people = 70

Number of people who like Coffee = n (C) = 37

Number of people who like Tea = n (T) = 52

Total number = n (C ∪ T) = 70

Person who likes both would be n (C ∩ T)

n (C ∪ T) = n (C) + n (T) – n (C ∩ T)

Substituting the values, we get

70 = 37 + 52 – n (C ∩ T)

70 = 89 – n (C ∩ T)

n (C ∩ T) =19

∴ There are 19 people who like both coffee and tea.

 

  1. Teachers teaching physics or math = 20

Teachers teaching physics and math = 4

Teachers teaching Maths = 12

Let teachers who teach physics be ‘n (P)’ and for Maths be ‘n (M)’

20 teachers who teach physics or math = n (P ∪ M) = 20

4 teachers who teach physics and math = n (P ∩ M) = 4

12 teachers who teach Maths = n (M) = 12

n (P ∪ M) = n (M) + n (P) – n (P ∩ M)

Substituting the values, we get,

20 = 12 + n (P) – 4

20 = 8 + n (P)

n (P) =12

∴ There are 12 physics teachers.

 

  1. Let total number of people be n (P) = 950

People who can speak English n (E) = 460

People who can speak Hindi n (H) = 750

(i) How many can speak both Hindi and English.

People who can speak both Hindi and English = n (H ∩ E)

n (P) = n (E) + n (H) – n (H ∩ E)

Substituting the values, we get

950 = 460 + 750 – n (H ∩ E)

950 = 1210 – n (H ∩ E)

n (H ∩ E) = 260

∴ The number of people who can speak both English and Hindi is 260.

(ii) How many can speak Hindi only.

We can see that H is disjoint union of n (H–E) and n (H ∩ E).

(If A and B are disjoint then n (A ∪ B) = n (A) + n (B))

∴ H = n (H–E) ∪ n (H ∩ E)

n (H) = n (H–E) + n (H ∩ E)

750 = n (H – E) + 260

n (H–E) = 490

∴ 490 people can speak only Hindi.

(iii) How many can speak English only.

We can see that E is disjoint union of n (E–H) and n (H ∩ E)

(If A and B are disjoint then n (A ∪ B) = n (A) + n (B))

∴ E = n (E–H) ∪ n (H ∩ E).

n (E) = n (E–H) + n (H ∩ E).

460 = n (H – E) + 260

n (H–E) = 460 – 260 = 200

∴ 200 people can speak only English.

 

  1. 15 students do not play any of three games.

n(H ∪ B ∪ C) = 60 – 15 = 45

n(H ∪ B ∪ C) = n(H) + n(B) + n(C) – n(H ∩ B) – n(B ∩ C) – n(C ∩ H) + n(H ∩ B ∩ C)

45  = 23 + 15 + 20 – 7 – 5 – 4 + d

45  = 42 + d

d = 45- 42 = 3

Number of students who play all the three games = 3

Therefore, the number of students who play hockey, basketball and cricket = 3

a + d = 7

a = 7 – 3 = 4

b + d = 4

b = 4 – 3 = 1

a + b + d + e = 23

4 + 1 + 3 + e = 23

e = 15

Similarly, c = 2, g =14, f = 6

Number of students who play hockey but not cricket = a + e

= 4 + 15

= 19

Number of students who play hockey and cricket but not basketball = b = 1

 

 

Click here for questions based on above assignment

 

 

 

Class 11 Sets Important Questions

CSCE TUTORIAL

SETS

Important Questions

Class – XI

Maths

 

  1. Write the following sets in the roster form.
    (i)  A = {x : x is a positive integer less than 10 and 2x – 1 is an odd number}
    (ii) C = {x : x2 + 7x – 8 = 0, x ∈ R}

 

  1. Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.
  1. Given that N = {1, 2, 3, …, 100}, then
    (i) Write the subset A of N, whose elements are odd numbers.
    (ii) Write the subset B of N, whose elements are represented by x + 2, where x ∈ N.

 

  1. Let A = {x: x ∈N}, B = {x: x = 2n, n ∈ N), C = {x: x = 2n – 1, n ∈ N} and, D = {x: x is a prime natural number} Find:
    (i) A ∩ B                                                     (ii) A ∩ C                                               (iii) A ∩ D
    (iv) B ∩ C                                                   (v) B ∩ D                                               (vi) C ∩ D

 

  1. If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}. Find:
    (i) A ∪B                                                     (ii) A ∪ C                                               (iii) B ∪ C
    (iv) B ∪ D                                                   (v) A ∪ B ∪ C                                         (vi) A ∪ B ∪ D
    (vii) B ∪ C ∪ D                                           (viii) A ∩ (B ∪ C)                                   (ix) (A ∩ B) ∩ (B ∩ C)
    (x) (A ∪ D) ∩ (B ∪ C).

 

  1. Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}.
    Find A′, B′, A′ ∩ B′, A ∪ B and hence show that ( A ∪ B )′ = A′∩ B′.
  1. Write the following sets in roster form:
    (i) A = {x : x is an integer and –3 ≤ x < 7}
    (ii) B = {x : x is a natural number less than 6}
  1. Let U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {3, 5} and C = {1, 2, 4, 7}, find
    (i) A′ ∪ (B ∩ C′)
    (ii) (B – A) ∪ (A – C)
  1. Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}. Write the set (A U B)’.
  1. If A and B are two sets such that n (A ∪ B) = 50, n (A) = 28 and n (B) = 32, find n (A ∩ B).
  2. If P and Q are two sets such that P has 40 elements, P ∪ Q has 60 elements, and P ∩ Q has 10 elements, how many elements does Q have?
  3. In a group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. How many like both coffee and tea?
  4. In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics, and 4 teach physics and mathematics. How many teach physics?
  1. In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find:
    (i) How many can speak both Hindi and English?
    (ii) How many can speak Hindi only?
    (iii) How many can speak English only?
  2. In a class of 60 students, 23 play hockey, 15 play basketball,20 play cricket and 7 play hockey and basketball, 5 play cricket and basketball, 4 play hockey and cricket, 15 do not play any of the three games. Find
    (i) How many play hockey, basketball and cricket
    (ii) How many play hockey but not cricket
    (iii) How many play hockey and cricket but not basketball

 

Click on the link for the answers

 

CSCE Tutorial aims to provide comprehensive support for Class 11 students in their mathematics exam preparation. We understand the importance of not only practicing questions but also having access to solutions and answers to gauge your progress. That’s why we ensure that all the practice questions on our web page come with detailed solutions and explanations.

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Remember, consistent practice, understanding the concepts, and utilizing the provided solutions are key to your success in mathematics. Stay motivated, keep practicing, and excel in your exams!

Fundamental Unit of Life Extra Questions

CSCE TUTORIAL

Class – IX                                                                                                                                                                                    Science

Fundamental Unit of Life

  1. Name two unicellular organisms.
  2. Name the smallest known cell.
  3. Who coined the term ‘Protoplasm’ for the fluid substance of the cell?
  4. Name two structures that are found in plant cell but not in animal cell.
  5. Name the process in which diffusion takes place through a semi permeable membrane.
  6. Name the process by which unicellular freshwater organisms and most plant cell tend to gain water.
  7. Name the cell organelle which serves as a channel for transport of material between cytoplasm and nucleus.
  8. What is the function of cellulose?
  9. Write the full form of DNA.
  10. Name the energy currency of cell.
  11. Name the cell organelle called as the power house of a cell.
  12. Name the organelle that imparts red and yellow colours to the flower.
  13. Name the type of plastid that helps in the process of photosynthesis.
  14. Which of the organelle is present only in plants and possess their own genome and ribosomes.
  15. Which organelle is called the factory of ribosomes?
  16. Where is stroma is present in the cell?
  17. Who discovered cell?
  18. What are all organisms made up of?
  19. Name the largest animal cell.
  20. Who discovered bacteria?
  21. Who discovered nucleus in the cell?
  22. Who gave the term protoplasm?
  23. What are the three functional regions of the cell?
  24. What happens when dried raisins or apricots are put into
    (i).   Pure water
    (ii).  Concentrated solution of sugar
    (iii). Concentrated solution of salt
  25. How do unicellular fresh water organisms and plant cells gain water?
  26. What is plasma membrane made up of?
  27. Name the process through which amoeba acquires its food.
  28. Name the outer covering of an animal cell.
  29. Name the outer covering of the plant cell.
  30. Why are mitochondria called ‘power house of the cell’?

Class – 10 Real Numbers Important Questions

CSCE TUTORIAL
Real Numbers
Chapter – 1
Most Important Questions
  1. Write the HCF of the smallest composite number and the smallest prime number.
  2. Using prime factorization, find HCF and LCM of 96 and 120.
  3. Explain whether (3 × 5 × 13 × 46) + 23 is prime or composite number.
  4. The HCF of two numbers a and b is 5 and their LCM is 200. Find the Product of ab.
  5. Two positive integers a and b can be written as a = x³y² and b = xy³. If x and y are the prime numbers, then find the LCM of (a, b).
  6. Prove that √2 is an irrational number.
  7. Prove that 3 – 2√5 is an irrational number, given that √5 is an irrational number.
  8. If HCF (253, 440) = 11 and LCM (253, 440) = 253 × R, Find the value of R.
  9. Explain, why (7 × 11 × 13) + 13 and (7 × 6 × 5 × 4 × 3 × 2 × 1) + 5 are composite numbers?
  10. The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm, respectively. Find the length of the longest rod that can measure the three dimensions of the room exactly.

Force and Laws of Motion

CSCE TUTORIAL

Force and Laws of Motion

Worksheet-1

 

  1. Which of the following has more inertia:
         (a)  a rubber ball and a stone of the same size?
         (b)  a bicycle and a train?
         (c)  a five rupees coin and a one-rupee coin?
  1. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.
  1. Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?
  1. A constant force acts on an object of mass 5 kg for a duration of 2 s. It increases the object’s velocity from 3 m s–1 to 7 m s-1. Find the magnitude of the applied force. Now, if the force was applied for a duration of 5 s, what would be the final velocity of the object?
  1. A motorcar is moving with a velocity of 108 km/h and it takes 4 s to stop after the brakes are applied. Calculate the force exerted by the brakes on the motorcar if its mass along with the passengers is 1000 kg.
  1. A force of 5 N gives a mass m1 , an acceleration of 10 m s–2 and a mass m2 , an acceleration of 20 m s-2 . What acceleration would it give if both the masses were tied together?
  1. Explain why it is difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity.
  1. When a carpet is beaten with a stick, dust comes out of it. Explain.
  1. A stone of 1 kg is thrown with a velocity of 20 m s–1 across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice?
  1. An object of mass 100 kg is accelerated uniformly from a velocity of 5 m s–1 to 8 m s–1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.
  1. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s–2 .

Class – 9 Motion

CSCE TUTORIAL

MOTION

Worksheet – 1

  1. Can the magnitude of the displacement be equal to the distance travelled by an object? Justify by giving an example.

 

  1. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?

 

  1. What does the odometer of an automobile measure?

 

  1. The odometer of a car reads 2000 km at the start of a trip and 2400 km at the end of the trip. If the trip took 8 h, calculate the average speed of the car in km h–1 and m s–1. 

 

  1. A bus decreases its speed from 80 km h–1 to 60 km h–1 in 5 s. Find the acceleration of the bus.

 

  1. What is the nature of the distance-time graphs for uniform and non-uniform motion of an object? 

 

  1. What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?

 

  1. What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis? 

 

  1. What is the quantity which is measured by the area occupied below the velocity-time graph?

 

  1. He brakes applied to a car produce an acceleration of 6 m s-2 in the opposite direction to the motion. If the car takes 2 s to stop after the application of brakes, calculate the distance it travels during this time.

 

  1. A trolley, while going down an inclined plane, has an acceleration of 2 cm s-2. What will be its velocity 3 s after the start?

 

  1. A stone is thrown in a vertically upward direction with a velocity of 5 m s-1. If the acceleration of the stone during its motion is 10 m s–2 in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

 

  1. Abdul, while driving to school, computes the average speed for his trip to be 20 km h–1. On his return trip along the same route, there is less traffic and the average speed is 30 kmh–1 What is the average speed for Abdul’s trip?

 

  1. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s-2, with what velocity will it strike the ground? After what time will it strike the ground?

 

  1. State which of the following situations are possible and give an example for each of these:

          (a) an object with a constant acceleration but with zero velocity

          (b) an object moving in a certain direction with an acceleration in the perpendicular direction. 

 

  1. An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth.

Ch-3 Pair of Linear Equations in Two Variables

CSCE TUTORIAL

                                                                               Chapter 3                                                                                  Assignment-1

Pair of Linear Equations in two variables

Class – X                                                                                                                                                Mathematics

 

Q-1. The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 do not have a solution if k=

a) = 5                    b) = 10                    c) ≠10                              d) ≠ 5

 

Q-2. The solution of the equation x + y = 5 and x − y = 5 is

a) (0,5)                     b) (5,5)                   c) (5,0)                            d) (10 ,5)

 

Q-3. The pair of linear equations x = 0 , x = −5 has

a) One solution                    b) two solution                    c) infinite no. of solution             d) no solution

 

Q-4. For what value of ‘k’ do the equations 3x – y + 8 = 0 and 6x – ky + 16 = 0 represent coincident lines

a) 1/2                     b) −1/2                      c) 2                                        d) -2

 

Q-5. For what value of ‘k’ for which the system of equations 4x + ky + 8 = 0 and 2x + 2y + 2 = 0 has a unique solution?

 

Q-6. In how many points do the lines represented by the equations x − y = 0 and x + y = 0 intersect?

 

Q-7. Find the value of (x + y) if  3x − 2y = 5 and 3y − 2x = 3.

 

Q-8. Sum of two numbers is 35 and their difference is 13, find the numbers.

 

Q-9. Find the value of ‘p’ for which the pair of linear equations 2px + 3y = 7 and 2x + y = 6 has exactly one solution.

 

Q-10. Do the equations y = x and y = x + 3 represent parallel lines?

 

Case study

  1. The alumni meet of two batches of a college- batch A & batch B were held on the same day in the same hotel in two separate halls “Rose” and “Jasmine”. The rents were the same for both the halls. The expense for each hall is equal to the fixed rent of each hall and proportional to the number of persons attending each meet. 50 persons attended the meet in “Rose” hall, and the organisers had to pay ₹ 10000 towards the hotel charges. 25 guests attended the meet in “Jasmine” hall and the organizers had to pay ₹ 7500 towards the hotel charges. Denote the fixed rent by ₹ x and proportional expense per person by ₹ y.
  2. Represent algebraically the situation in hall “Rose”.
  3. Represent algebraically the situation in hall “Jasmine”.
  4. What is the fixed rent of the halls?
  5. Find the amount the hotel charged per person.

 

Q-2.  Draw the graphs of 2x − 3y + 6 = 0 and 2x + 3y − 18 = 0. Find the ratio of areas of triangles formed by the given lines with X-axis and            Y-axis.

 

Q-3. Determine graphically the vertices of the triangle, the equations of whose sides are given below   2y − x = 8; 5y − x = 14; y − 2x = 1