Mathematics Official 2022-2023 (English Medium) ICSE Class 10 Question Paper Solution

If `[(2, 0),(0, 4)][(x),(y)] = [(2),(-8)]`, the value of x and y respectively are ______.

1, –2

–2, 1

1, 2

–2, –1

If x – 2 is a factor of x³ – kx – 12, then the value of k is ______.

3

2

–2

–3

In the given diagram RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is equal to ______.

40°

30°

60°

90°

A letter is chosen at random from all the letters of the English alphabets. The probability that the letter chosen is a vowel, is ______.

`4/26`

`5/26`

`21/26`

`5/24`

If 3 is a root of the quadratic equation x² – px + 3 = 0 then p is equal to ______.

4

3

5

2

In the given figure ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm, then PD : DB is ______.

5 : 3

3 : 5

3 : 2

2 : 3

The printed price of an article is ₹ 3080. If the rate of GST is 10%, then the GST charged is ______.

₹ 154

₹ 308

₹ 30.80

₹ 15.40

(1 + sin A)(1 – sin A) is equal to ______.

cosec²A

sin²A

sec²A

cos²A

The coordinates of the vertices of ΔABC are respectively (–4, –2), (6, 2) and (4, 6). The centroid G of ΔABC is ______.

(2, 2)

(2, 3)

(3, 3)

(0, –1)

The n^th term of an Arithmetic Progression (A.P.) is 2n + 5. The 10^th term is ______.

7

15

25

45

The mean proportional between 4 and 9 is ______.

4

6

9

36

Which of the following cannot be determined graphically for a grouped frequency distribution?

Median

Mode

Quartiles

Mean

Volume of a cylinder of height 3 cm is a 48π. Radius of the cylinder is ______.

48 cm

16 cm

4 cm

24 cm

Naveen deposits ₹ 800 every month in a recurring deposit account for 6 months. If he receives ₹ 4884 at the time of maturity, then the interest he earns is ______.

₹ 84

₹ 42

₹ 24

₹ 284

The solution set for the inequation 2x + 4 ≤ 14, x ∈ W is ______.

{1, 2, 3, 4, 5}

{0, 1, 2, 3, 4, 5}

{1, 2, 3, 4}

{0, 1, 2, 3, 4}

Find the value of 'a' if x – a is a factor of the polynomial 3x³ + x² – ax – 81.

Salman deposits ₹ 1000 every month in a recurring deposit account for 2 years. If he receives ₹ 26000 on maturity, find:

1. the total interest Salman earns.
2. the rate of interest.

In the given figure O, is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26° find:

1. ∠BDA
2. ∠BAD
3. ∠CAD
4. ∠ODB

Solve the following quadratic equation:

x² + 4x – 8 = 0

Give your Solution correct to one decimal place.

(Use mathematical tables if necessary.)

Prove the following identity:

(sin²θ – 1)(tan²θ + 1) + 1 = 0

Use graph sheet to Solution this question. Take 2 cm = 1 unit alogn both the axes.

1. Plot A, B, C where A(0, 4), B(1, 1) and C(4, 0)
2. Reflect A and B on the x-axis and name them as E and D respectively.
3. Reflect B through the origion and name it F. Write down the coordinates of F.
4. Reflect B and C on the y-axis and name them as H and G respectively.
5. Join points A, B, C, D, E, F, G, H and A in order and name the closed figure formed.

If A = `[(1, 3),(2, 4)]`, B = `[(1, 2),(2, 4)]`, C = `[(4, 1),(1, 5)]` and I = `[(1, 0),(0, 1)]`. Find A(B + C) – 14I.

ABC is a triangle whose vertices are A(1, –1), B(0, 4) and C(– 6, 4). D is the midpoint of BC. Find the coordinates of D.

ABC is a triangle whose vertices are A(1, –1), B(0, 4) and C(– 6, 4). D is the midpoint of BC. Find the equation of the median AD.

In the given figure, O is the centre of the circle. PQ is a tangent to the circle at T. Chord AB produced meets the tangent at P.

AB = 9 cm, BP = 16 cm, ∠PTB = 50° ∠OBA = 45°

Find:

1. Length of PT 
2. ∠BAT
3. ∠BOT
4. ∠ABT

Mrs. Arora bought the following articles from a departmental store:

Find the:

1. Total GST paid,
2. Total bill amount including GST.

Solve the following inequation. Write down the solution set and represent it on the real number line.

–5(x – 9) ≥ 17 – 9x > x + 2, x ∈ R

In the given figure, AC || DE || BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm, BF = 30 cm.

1. Prove ΔGED ∼ ΔGBF
2. Find DE
3. DB : AB

The following distribution gives the daily wages of 60 workers of a factory.

Use graph paper to Solution this question.

Take 2 cm = ₹ 100 along one axis and 2 cm = 2 workers along the other axis.

Draw a histogram and hence find the mode of the given distribution.

The 5^th term and the 9^th term of an Arithmetic Progression are 4 and – 12 respectively.

Find:

1. the first term
2. common difference
3. sum of 16 terms of the AP.

A and B are two points on the x-axis and y-axis respectively.

1. Write down the coordinates of A and B.
2. P is a point on AB such that AP : PB = 1 : 1.
   Using section formula find the coordinates of point P.
3. Find the equation of a line passing through P and perpendicular to AB.

A bag contains 25 cards, numbered through 1 to 25. A card is drawn at random. What is the probability that the number on the card drawn is multiple of 5?

A bag contains 25 cards, numbered through 1 to 25. A card is drawn at random. What is the probability that the number on the card drawn is a perfect square?

A bag contains 25 cards, numbered through 1 to 25. A card is drawn at random. What is the probability that the number on the card drawn is a prime number?

A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed.

A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height. If the radius of the cylinder is 14 cm, find the rise in the water level.

The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution by using the short cut method.

What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?

Using ruler and compass construct a triangle ABC in which AB = 6 cm, ∠BAC = 120° and AC = 5 cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle.

Using Componendo and Dividendo solve for x:

`(sqrt(2x + 2) + sqrt(2x - 1))/(sqrt(2x + 2) - sqrt(2x - 1))` = 3

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?

Hence find the sum of all the terms of the Arithmetic Progression (A.P.)

From the top of a tower 100 m high a man observes the angles of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line find the distance between the two ships A and B to the nearest metre.

(Use Mathematical Tabels for this question)

Factorize completely using factor theorem:

2x³ – x² – 13x – 6

Use graph paper to Solution this question.

During a medical checkup of 60 students in a school, weights were recorded as follows:

Taking 2 cm = 2 kg along one axis and 2 cm = 10 students along the other axis draw an ogive. Use your graph to find the:

1. median
2. upper Quartile
3. number of students whose weights is above 37 kg