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Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22)


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Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 1

The product of two numbers is 1900 and their LCM is 100, then the HCF of the numbers is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 1

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 2

If a number when divided by 71 gives 37 as quotient and 42 as remainder, then the number is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 2

Here, divisor = 71, quotient = 37 and remainder = 42.
∴ Dividend = Divisor × Quotient + Remainder
= (71 × 37) + 42
= 2669.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 3

The decimal expansion of the rational number   will terminate after:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 3

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 4

The number 0.121212 ...... is the form of p/q will be equal:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 4

Let x =0.121212.... ...(i)
100x =12.1212.... ...(ii)
On subtracting eqn. (i) from (ii)

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 5

If the sum of the zeroes of the quadratic polynomial 5x2 – px + 8 is 4, then the value of k is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 5

Let the zeroes of the given polynomial be a and b, then sum of the zeroes = 4
i.e  p/5  = 4
⇒  p = 20

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 6

If the polynomial is p(x) = x3 - 3x2 + x + 1, then the value of p(- 3) is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 6

We have,
p(x) = x3 – 3x2 + x + 1
Then, p(– 3) = (-3)3 – 3(– 3)2 + (– 3)
+ 1
= – 27 – 27 – 3 + 1
= – 56.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 7

If α, β and γ are the zeroes of the polynomial 2x3 + x2 – 13x + 6, then abg is equal to:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 7

Let the polynomial be f(x), then

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 8

The distance of the point P(– 4, 3) from the origin is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 8

Here, two points (–4, 3) and
(0, 0) are given, then
x1 = – 4, y1 = 3 and x2 = 0, y2 = 0
∴ Distance between them

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 9

If   is the mid point of the line segment joining the points A(–7, 3) and B(– 3, 7), then the value of a is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 9

Then, comparing on both sides, we get
a/3 = – 5
⇒ a = – 15.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 10

The point   divide the line segment joining the points A(3, 5) and (– 3, – 2) is the ratio:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 10

Let the required ratio be k : 1, then the coordinates of P are


⇒ –15k + 15 = 3k + 3 and –10k + 25 = 11k + 11
⇒ –18k = –12 and –21k = –14
⇒ k = 2/3  and k = 2/3
Hence the point P divides AB in the ratio
2 : 3.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 11

The distance between the points 

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 11

Distance between 

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 12

In a given ABC, DE || BC and AB/DB = 3/5. If AC = 5.6 cm, then AE = .

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 12

Let AE = x cm,
then EC = (5.6 – x) cm
and DE || BC   (given)

⇒ 3(5.6 – x) = 5x
⇒ 16.8 – 3x = 5x
⇒ 8x = 16.8
⇒ x = 2.1

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 13

If sin A = 1/√2, then the value of tan A + cot A is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 13

∵ sin A = 1/√2,
∴ sin A = sin 45°
⇒ A = 45°
Now, tan A + cot A = tan 45° + cot 45°
= 1 + 1
= 2.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 14

If x = 0, then the value of 

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 14

We have,
x = 0
or cos x = cos 0
or cos x = 1

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 15

The value of sin2 30° – cos2 30° is: 

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 15


= - 2/4
= - 1/2.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 16

The circumference of a circle of radius 4 cm is: (Use π = 3.14)

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 16

Given, radius (r) = 4 cm
∴ Circumference, (C) = 2πr
= 2 × 3.14 × 4 cm
= 25. 12 cm.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 17

Aarti had bought a circular pot wherein area of cross-section is mentioned as 38.5 cm2. She wantedto calculate the radius of the circle and observed its value.

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 17

Area of a circle = 38.5 cm2

πr2 = 38.5

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 18

If a piece of wire 30 cm long is bent into the form of an arc of a circle, subtending an angle of 60° at its centre, then radius of the circle is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 18

Length of arc = 30 cm
So, 2 x 5 – 5p + 2 = 0
⇒ 10 + 2 – 5p = 0
⇒ 5p = 12
⇒ p = 2.4

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 19

Which of the following can not be the probability of an event ?

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 19

Probability of an event can not be more than one or negative 9/8 > 1.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 20

A box contains 80 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 30, is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 20

Total number outcomes = 80
i.e., n(S) = 80
Prime number less than 30 = 2, 3, 5, 7, 11,
13, 17, 19, 23, 29
i.e., n(E) = 10
∴ Required probability,

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 21

What number must be added to numerator and denominator of 2/7 to make fraction equal to 2/3 ?

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 21

Let x be added to numerator and denominator of 2/7, so

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 22

The difference of LCM and HCF of 28 and 42 is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 22

28 = 22 × 7
and 42 = 2 x 3 x 7
∴ HCF (28, 42) = 2 x 7 = 14
and LCM (28, 42) = 22 x 3 x 7 = 84
Now, difference = 84 – 14 = 70.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 23

If the sum of ages of father and son is 40 years and its difference is 20 years then age of father will be:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 23

Let father's age be x years and son's age be y, then
x + y = 40 ...(i)
and x – y = 20
On adding eq. (i) and (ii), we get
2x = 60
⇒ x = 30.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 24

If 2 sin 5θ = √3, then the value of q is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 24

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 25

The system of equations 2x + ay = 1 and 5x – 7y = 9 are given.
If the system has a unique solution, then all real values except :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 25

∵ The system of equations has unique
solution


i.e., all real values except - 14/5

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 26

If the radius of a circle with centre O is 3.5 cm and two radii OA and OB are drawn at right angles toeach other, then the area of minor segment is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 26

Here,
r = 3.5 cm, θ = 90°

∴ Area of minor segment

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 27

If the area of a sector of the circle of radius 18 cm is 72π cm2, then the angle q is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 27

Here, r = 18 cm and area of sector = 72 π
cm2

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 28

The zeroes of the quadratic polynomial 3x2 + 2x – 1 = 0 are :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 28

Given, 3x2 + 2x – 1 = 0
⇒ 3x2 + 3x – x – 1 = 0
⇒ 3x(x + 1) – 1 (x + 1) = 0
⇒ (x + 1) (3x – 1) = 0
⇒ x = – 1 and 1/3

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 29

In the given figure, if PQ = 8 cm and PR = 6 cm, then the radius of the circle is ..... cm, where O is thecentre of circle.

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 29

Since ∠P in a semicircle, so
∠P = 90°
∴ In DRPQ, RQ2 = PR2 + PQ2
(Using Pythagoras theorem)
= (6)2 + (8)2
= 100
∴ RQ = 10 cm
∴ Radius = 1/2RQ
= 5 cm

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 30

In the given figure, If DE || BC, AD = 2 cm, BD = 2.5 cm, AE = 3.2 cm and DE = 4 cm, then BC = 9 cmFind AC.

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 30

∵ DE || BC (given)
∴ ∠ADE = ∠ABC (corresponding angles)
and ∠AED = ∠ACB (corresponding angles)
∴ DADE ~ DABC (By AA similarity)

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 31

If cot (A + B – C) = √3 and cos (B + C – A) = 1/2, then the value of B is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 31

cot (A + B + C) = √3 = cot 30°
⇒ A + B – C = 30° ...(i)
and cos (B + C – A) = 1/2
⇒ cos (B + C – A)= cos 60°
⇒ B + C – A = 60° ...(ii)
Adding eq. (i) and (ii), we get
2B = 90°
⇒ B = 45°

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 32

If sin θ = 3/4, then cot θ =

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 32

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 33

If cos θ = 4/5, then tan θ =

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 33

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 34

If two positive integers p and q are written as p = a3b4 and q = a4b4, where a and b are prime numbers,then LCM (p, q) × HCF (p, q) is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 34

p = a3b4
and q = a4b4
Then LCM (p, q) = a4 b4
and HCF (p, q) = a3 b4
∴ LCM (p, q) x HCF (p, q)
= a4 b4 x a3 b4
= a7 b8

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 35

In evening, during family time, Radha observed the dimensions of room. If the length, breadth andheight of a room are 24 m, 18 m and 9 m respectively, then the length of the longest rod that canmeasure the dimensions of the room exactly is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 35

Length = 24 m, breadth = 18 m and height = 9 m
Since, the length of the longest rod is equal to HCF (24, 18, 9), i.e., 24 = 23 × 3
18 = 2 × 32
and 9 = 32
Then, HCF (24, 18 and 9) = 3
Thus, the longest rod that can measure the dimensions of the room exactly = 3 m.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 36

The value of    is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 36

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 37

If DABC ~ DQRP   and AC = 18 cm then the value of QR is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 37

∵  DABC ~ DQRP, then


Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 38

Rational number 7/125 will terminate after ........ decimal places.

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 38


which terminates after 3 places.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 39

The difference of (3 + 2 √3) and (3 − 2 √3) is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 39

Difference = (3 + 2√3) −(3 − 2√3)
= 3 + 2√3 − 3 + 2√3
= 4√3 ,
which is irrational.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 40

In the given figure, MN || QR. The length of PN is :

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 40

In DPQR, MN || QR

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 41

Case Study
Places A and B are 80 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour.

Assuming that the speed of first car and second car be u km/h and v km/h respectively.

What is the relative speed of both cars while they are travelling in the same direction ?

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 41

Relative speed of both cars while they are travelling in same direction
= (50 – 35) km/hr = 15 km/h.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 42

Case Study
Places A and B are 80 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour.

What is the relative speed of both cars while they are travelling towards each other ?

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 42

Relative speed of both cars while they are travelling in opposite directions i.e., travelling towards each other
= (50 + 35) km/hr = 85 km/h.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 43

Case Study
Places A and B are 80 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour.

What is the actual speed of one car?

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 43

Let the speeds of first car and second car be u km/hr and v km/hr respectively.
According to the given information.
4 (u – v) = 80
i.e,. u – v = 20 ...(i)
and u + v = 80 ...(ii)
Solving eqs. (i) and (ii), we get u = 50 km/hr.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 44

Case Study
Places A and B are 80 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour.

What is the actual speed of other car?

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 44

Let the speeds of first car
and second car be u km/hr and v km/hr
respectively.
According to the given information.
4 (u – v) = 80
i.e,. u – v = 20 ...(i)
and u + v = 80 ...(ii)
Solving eqs. (i) and (ii), we get u = 50
km/hr and v = 30 km/hr.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 45

Case Study
Places A and B are 80 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour.

The given problem is based on which mathematical concept

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 45

The given problem is based
on pair of linear equations.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 46

Case Study

The diagram show the plans for a sun room. It will be built onto the wall of a house. The four walls of
the sun room are square clear glass panels. The roof is made using,

  • Four clear glass panels, trapezium in shape, all of the same size
  • One tinted glass panel, half a regular octagon in shape

Refer to Top View, find the mid-point of the segment joining the points J(6, 17) and I(9, 16).

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 46

Mid-point of J(6, 17) and I (9, 16) is

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 47

Case Study

The diagram show the plans for a sun room. It will be built onto the wall of a house. The four walls of
the sun room are square clear glass panels. The roof is made using,

  • Four clear glass panels, trapezium in shape, all of the same size
  • One tinted glass panel, half a regular octagon in shape

Refer to front View, the distance of the point P from the y-axis is:

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 47

The distance of the point P from the Y-axis = 4.

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 48

Case Study

The diagram show the plans for a sun room. It will be built onto the wall of a house. The four walls of
the sun room are square clear glass panels. The roof is made using,

  • Four clear glass panels, trapezium in shape, all of the same size
  • One tinted glass panel, half a regular octagon in shape

Refer to front view, the distance between the points A and S is

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 48

A's coordinates = (1, 8)
S's coordinates = (15, 8)

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 49

Case Study

The diagram show the plans for a sun room. It will be built onto the wall of a house. The four walls of
the sun room are square clear glass panels. The roof is made using,

  • Four clear glass panels, trapezium in shape, all of the same size
  • One tinted glass panel, half a regular octagon in shape

Refer to front view, find the co-ordinates of the point which divides the line segment joining the points
A and B in the ratio 1 : 3 internally.

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 49

The coordinates of A = (1, 8)
The coordinates of B = (4, 10)
Also, m = 1 and n = 3
Then,

Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 50

Case Study

The diagram show the plans for a sun room. It will be built onto the wall of a house. The four walls of
the sun room are square clear glass panels. The roof is made using,

  • Four clear glass panels, trapezium in shape, all of the same size
  • One tinted glass panel, half a regular octagon in shape

Refer to front view, if a point (x, y) is equidistant from the Q(9, 8) and S(17, 8), then

Detailed Solution for Test: Class 10 Mathematics: CBSE Sample Question Paper- Term I (2021-22) - Question 50

Let point be P(x, y)
PQ2 = PS2
or, (x – 9)2 + (y – 8)2 = (x – 17)2 + (y – 8)2
or, x – 13 = 0

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