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MODEL PAPER 1 (STANDARD) Maths - MODEL PAPER 1 (STANDARD)

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

Question types

MODEL PAPER 1 (STANDARD) 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 1 (STANDARD) 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
The distribution below gives the marks obtained by 80 students on a test:
MarksLess than 10Less than 20Less than 30Less than 40Less than 50Less than 60
Number of Students31227577580
The modal class of this distribution is:
  • ✓
    30 - 40
  • B
    20 - 30
  • C
    50 - 60
  • D
    $10 - 20$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
3 rotten eggs are mixed with 12 good ones. One egg is chosen at random. The probability of choosing a rotten egg is
  • A
    $\frac{1}{15}$
  • B
    $\frac{4}{5}$
  • ✓
    $\frac{1}{5}$
  • D
    $\frac{2}{5}$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
A pendulum swings through an angle of $30^{\circ}$ and describes an arc $8.8 \ cm$ in length. Find the length of the pendulum.
  • A
    $8.8 \ cm$
  • B
    $17 \ cm$
  • C
    $15.8 \ cm$
  • ✓
    $16.8 \ cm$

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark
In a circle of radius $14 \ cm$ , an arc subtends an angle of $120^{\circ}$ at the centre. If $\sqrt{3}=1.73$ then the area of the segment of the circle is
  • A
    $124.63 \ cm^2$
  • B
    $130.57 \ cm^2$
  • ✓
    $120.56 \ cm^2$
  • D
    $118.24 \ cm^2$

Answer: C.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): Sum of first $n$ terms in an A.P. is given by the formula: $S_n=2 n \times[2 a+(n-1) d]$
Reason (R): Sum of first 15 terms of $2,5,8 \ldots$ is 345 .
  • ✓
    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.
  • C
    A is true but R is false.
  • D
    A is false but R is true.

Answer: A.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is $1 m, 463.39 cm^2$ is the area of cloth required.
Reason (R): Surface area of hemisphere $=2 \pi r ^2$.
  • 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 92 Marks Questions2 Marks
A horse is tethered to one corner of a rectangular field of dimensions $70 m \times 52 m$, by a rope of length $21 m .$ How much area of the field can it graze?
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Q 122 Marks Questions2 Marks
Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P.
Image
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Q 133 Marks Question3 Marks
In figure, $O$ is the centre of a circle of radius $5 \ cm. T$ is a point such that $OT = 13 \ cm$ and $OT$ intersects circle at $E$. If $AB$ is a tangent to the circle at $E,$ find the length of $AB$. where $TP$ and $TQ$ are two tangents to the circle.
Image
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Q 143 Marks Question3 Marks
A plane left $30$ minutes late than its scheduled time and in order to reach the destination $1500 \ km $ away in time, it had to increase its speed by $100 \ km/h$ from the usual speed. Find its usual speed.
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Q 153 Marks Question3 Marks
The percentage of marks obtained by $100$ students in an examination are given below:
Marks $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$
Frequency $14$ $16$ $18$ $23$ $18$ $8$ $3$
Determine the median percentage of marks.
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Q 173 Marks Question3 Marks
In the given figure, a circle is inscribed in a quadrilateral $\text{ABCD }$ in which $\angle B =90^{\circ}$. If $AD =17 \ cm, AB =20 \ cm $ and $DS =3 \ cm,$ then find the radius of the circle.
Image
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Q 185 Marks Questions5 Marks
A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is $19 \ cm$ and the diameter of the cylinder is $7 \ cm$ . Find the volume and total surface area of the solid $($Use $\pi=22 / 7 )$
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Q 195 Marks Questions5 Marks
$₹ 9000$ were divided equally among a certain number of persons. Had there been $20$ more persons, each would have got $₹ 160$ less. Find the original number of persons.
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Q 205 Marks Questions5 Marks
Find the mean from the following frequency distribution of marks at a test in statistics:
Marks$ (x):$ $5$ $10$ $15$ $20$ $25$ $30$ $35$ $40$ $45$ $50$
No. of students $(f):$ $15$ $50$ $80$ $76$ $72$ $45$ $39$ $9$ $8$ $6$
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Q 215 Marks Questions5 Marks
A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm , find the cost of polishing its surface at the rate of ₹ 10 per $dm ^2$.
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Q 225 Marks Questions5 Marks
In Fig., $\text{DEFG}$ is a square in a triangle $\text{ABC}$ right angled at $A$ . Prove that
$i. \triangle AGF \sim \triangle DBG$
$ii. \triangle AGF \sim \triangle EFC$
Image
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Q 23Case study (4 Marks)4 Marks
Read the text carefully and answer the questions:
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections $A$ and $B$ . Tower is supported by wires from a point $O$ .Distance between the base of the tower and point $O$ is $36 \ cm$ . From point $O,$ the angle of elevation of the top of the Section B is $30^{\circ}$ and the angle of elevation of the top of Section $A$ is $45^{\circ}$.

Image
$(a)$ Find the length of the wire from the point $O$ to the top of Section $B$ .
$(b)$ Find the distance $AB$ .
OR
Find the height of the Section $A$ from the base of the tower.
$(c)$ Find the area of $\triangle OPB$.
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Q 24Case study (4 Marks)4 Marks
Read the text carefully and answer the questions:
Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play $\text{“PUBG’’}$ can get easily stressed out. To raise social awareness about ill effects of playing $\text{PUBG,}$ a school decided to start $\text{‘BAN PUBG’}$ campaign, in which students are asked to prepare campaign board in the shape of a rectangle. One such campaign board made by class $X$ student of the school is shown in the figure.

Image

$(a)$ Find the coordinates of the point of intersection of diagonals $AC$ and $BD.$
$(b)$ Find the length of the diagonal $AC.$
OR
Find the ratio of the length of side $AB$ to the length of the diagonal $AC.$
$(c)$ Find the area of the campaign Board $\text{ABCD.}$
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Q 25Case study (4 Marks)4 Marks
Read the text carefully and answer the questions:
A fashion designer is designing a fabric pattern. In each row, there are some shaded squares and unshaded triangles.
Image

$(a)$ Identify $A.P. $for the number of squares in each row.
$(b)$ Identify $A.P.$ for the number of triangles in each row.
$OR$
Write a formula for finding total number of triangles in $n$ number of rows. Hence, find $S_{10}.$
$(c)$ If each shaded square is of side $2\  cm,$ then find the shaded area when $15$ rows have been designed.
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