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MODEL PAPER 3 (BASIC) Maths - MODEL PAPER 3 (BASIC)

CBSE - STD 10 - Maths (CBSE - English Medium). 44 questions in this chapter.

Question types

MODEL PAPER 3 (BASIC) question types

44 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

44
Questions
6
Question groups
5
Question types
Sample Questions

MODEL PAPER 3 (BASIC) questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Consider the following table:
Class interval $10-14$ $14-18$ $18-22$ $22-26$ $26-30$
Frequency $5$ $11$ $16$ $25$ $19$
The mode of the above data is
  • A
    $25$
  • B
    $23.5$
  • ✓
    $24.4$
  • D
    $24$

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark
A cylindrical vessel of radius $4 \ cm$ contains water. A solid sphere of radius $3 \ cm$ is lowered into the water until it is completely immersed. The water level in the vessel will rise by
  • ✓
    $\frac{9}{4} \ cm$
  • B
    $\frac{9}{2} \ cm$
  • C
    $\frac{2}{9} \ cm$
  • D
    $\frac{4}{9} \ cm$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
Consider the following frequency distribution:
Class0-56-1112-1718-2324-29
Frequency131015811
The upper limit of the median class is
  • A
    18.5
  • ✓
    17.5
  • C
    18
  • D
    17

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark
In a single throw of a die, the probability of getting a multiple of $3$ is
  • A
    $\frac{1}{6}$
  • B
    $\frac{2}{3}$
  • C
    $\frac{1}{2}$
  • ✓
    $\frac{1}{3}$

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark
Pankaj has a motorcycle with wheels of diameter 91 cm. There are 22 spokes in the wheel. Find the length of arc between two adjoining spokes.
  • A
    13 cm
  • B
    26 cm
  • C
    15 cm
  • D
    18 cm
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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion $(A):$ For any two positive integers $a$ and $b, \operatorname{HCF}(a, b) \times \operatorname{LCM}(a, b)=a \times b$
Reason $(R):$ The $\text{HCF}$ of two numbers is $5$ and their product is $150.$ Then their $\text{LCM}$ is $40.$
  • A
    Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
  • B
    Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
  • ✓
    $A$ is true but $R$ is false.
  • D
    $A$ is false but $R$ is true

Answer: C.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): Distance between (3, 7) and its image under x-axis is 6 units.
Reason (R): Coordinates of centroid $=\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}$
  • A
    Both A and R are true and R is the correct explanation of A.
  • ✓
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true

Answer: B.

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Q 133 Marks Question3 Marks
The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of
i. heart
ii. queen
iii. clubs.
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Q 163 Marks Question3 Marks
In the given figure, the incircle $-$ of $\triangle A B C$ touches the sides $BC, CA$ and $AB $ at $P, Q$ and $R$ respectively. Prove that $(AR + BP + CQ) = (AQ + BR + CP) =\frac{1}{2}($ perimeter of $\triangle A B C)$.
Image
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Q 185 Marks Questions5 Marks
The median of the following data is $525.$ Find the values of $x$ and $y,$ if the total frequency is $100.$
Class interval Frequency
$0-100$ $2$
$100-200$ $5$
$200-300$ $x$
$300-400$ $12$
$400-500$ $17$
$500-600$ $20$
$600-700$ $y$
$700-800$ $9$
$800-900$ $7$
$900-1000$ $4$
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Q 195 Marks Questions5 Marks
A cylindrical tub of radius $12 \ cm$ contains water to a depth of $20 \ cm.$ A spherical ball is dropped into the tub and the level of the water is raised by $6.75 \ cm.$ Find the radius of the ball.
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Q 205 Marks Questions5 Marks
In Figure, from a solid cube of side $7 \ cm,$ a cylinder of radius $2.1 \ cm$ and height $7 \ cm$ is scooped out. Find the total surface area of the remaining solid.
Image
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Q 225 Marks Questions5 Marks
A motor boat whose speed is $18 \ km/h$ in still water takes $1$ hour more to go $24 \ km$ upstream, than to return to the same point. Find the speed of the stream and total time of the journey.
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Q 23Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow: A bird is sitting on the top of a tree, which is $80\ m$ high. The angle of elevation of the bird, from a point on the ground is $45^{\circ}$. The bird flies away from the point of observation horizontally and remains at a constant height. After $2$ seconds, the angle of elevation of the bird from the point of observation becomes $30^{\circ}$. Find the speed of flying of the bird.
Image
$i.$ Find the distance between observer and the bottom of the tree?
$ii$. Find the speed of the bird?
$iii$. Find the distance between second position of bird and observer?
OR
Find the distance between initial position of bird and observer?
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Q 24Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow:
Mary and John are very excited because they are going to go on a dive to see a sunken ship. The dive is quite shallow which is unusual because most sunken ship dives are found at depths that are too deep for two junior divers. However, this one is at 40 feet, so the two divers can go to see it.
Image
They have the following map to chart their course. John wants to figure out exactly how far the boat will be from the sunken ship. Use the information in this lesson to help John figure out the following.
i. What are the coordinates of the boat and the sunken ship respectively?
ii. How much distance will Mary and John swim through the water from the boat to the sunken ship?
iii. If each square represents 160 cubic feet of water, how many cubic feet of water will Mary and John swim through from the boat to the sunken ship?
OR
If the distance between the points (x, -1) and (3, 2) is 5, then what is the value of x?
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Q 25Case study (4 Marks)4 Marks
Read the following text carefully and answer the questions that follow:
Elpis Technology is a laptop manufacturer. The company works for many branded laptop companies and also provides them with spare parts. Elpis Technology produced $6000$ units in $3^{rd}$ year and $7000$ units in the $7^{th}$ year.
Image
Assuming that production increases uniformly by a fixed number every year.
$i.$ Find the production in the $1^{st}$ year.
$ii.$ Find the production in the $5^{th}$ year.
$iii$. Find the total production in $7$ years.
OR
Find in which year $10000$ units are produced?
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