Board Paper of Class 10 2022 Mathematics Standard Term-1 Set-4 Solutions - Solutions

Question 21

The greatest number which when divides 1251, 9377 and 15628 leaves remainder 1, 2 and 3 respectively is

1. 575
2. 450
3. 750
4. 625

Question 22

Which of the following cannot be the probability of an event?

1. 0.01
2. 3%
3. $\frac{16}{17}$
4. $\frac{17}{16}$

Question 23

The diameter of a car wheel is 42 cm. The number of complete revolutions it will make in moving 132 km is

1. 10⁴
2. 10⁵
3. 10⁶
4. 10³

Question 24

If θ is an acute angle and tan θ + cot θ = 2, then the value of sin³ θ + cos³ θ is

Question 25

The ratio in which the line 3x + y – 9 = 0 divides the line segment joining the points (1, 3) and (2, 7) is

1. 3 : 2
2. 2 : 3
3. 3 : 4
4. 4 : 3

Question 26

If x – 1 is a factor of the polynomial p(x) $\mathbf{=}\mathbf{ }{\mathbf{x}}^{\mathbf{3}}\mathbf{ }\mathbf{+}\mathbf{ }{\mathbf{ax}}^{\mathbf{2}}\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{2}\mathbf{b}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{a}\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{b}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{4}\mathbf{,}$ then

1. a = 5, b = –1
2. a = 9, b = –5
3. a = 7, b = –3
4. a = 3, b = 1

Question 27

If a and b are two coprime numbers, then a³ and b³ are

1. Coprime
2. Not coprime
3. Even
4. Odd

Question 28

The area of a square that can be inscribed in a circle of area $\frac{\mathbf{1408}}{\mathbf{7}}$ cm² is

1. 321 cm²
2. 642 cm²
3. 128 cm²
4. 256 cm²

Question 29

If A(4, –2), B(7, – 2) and C(7, 9) are the vertices of a ΔABC, then ΔABC is

1. equilateral triangle
2. isosceles triangle
3. right angled triangle
4. isosceles right angled triangle

Question 30

1. –7
2. 7
3. -3
4. 3

Question 31

If n is a natural number, then 2(5ⁿ + 6ⁿ) always ends with

1. 1
2. 4
3. 3
4. 2

Question 32

The line segment joining the points P(–3, 2) and Q(5, 7) is divided by the y-axis in the ratio

1. 3 : 1
2. 3 : 4
3. 3 : 2
4. 3 : 5

Question 33

If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p² – q² =

1. a² – b²
2. b² – a²
3. a² + b²
4. b – a

Question 34

If the perimeter of a circle is half to that of a square, then the ratio of the area of the circle to the area of the square is

1. 22 : 7
2. 11 : 7
3. 7 : 11
4. 7 : 22

Question 35

A dice is rolled twice. The probability that 5 will not come up either time is

1. $\frac{11}{36}$
2. $\frac{1}{3}$
3. $\frac{13}{36}$
4. $\frac{25}{36}$

Question 36

The LCM of two numbers is 2400. Which of the following CANNOT be their HCF?

1. 300
2. 400
3. 500
4. 600

Question 37

In fig., PA, QB and RC are each perpendicular to AC. If x = 8 cm and z = 6 cm, then y is equal to

1. $\frac{56}{7}$ cm
2. $\frac{7}{56}$ cm
3. $\frac{25}{7}$ cm
4. $\frac{24}{7}$ cm

Question 38

In a $\mathrm{\Delta ABC}, \angle \mathrm{A} = \mathrm{x}°, \angle \mathrm{B} = (3\mathrm{x} – 2)°, \angle \mathrm{C} = \mathrm{y}°. \mathrm{Also} \angle \mathrm{C} – \angle \mathrm{B} = 9°$

1. 107°
2. 135°
3. 155°
4. 145°

Question 39

If sec θ + tan θ = p, then tan θ is

1. $\frac{{\mathrm{p}}^2 +1}{2\mathrm{p}}$
2. $\frac{{\mathrm{p}}^2 -1}{2\mathrm{p}}$
3. $\frac{{\mathrm{p}}^2 -1}{{\mathrm{p}}^2+1}$
4. $\frac{{\mathrm{p}}^2 +1}{{\mathrm{p}}^2-1}$

Question 40

The base BC of an equilateral ΔABC lies on the y-axis. The coordinates of C are (0, –3). If the origin is the mid-point of the base BC, what are the coordinates of A and B?

Question 41

The situation of amount paid by Radhika, is algebraically represented by

1. x – 4y = 16
2. x + 4y = 16
3. x – 2y = 16
4. x + 2y = 16

Question 42

The situation of amount paid by Amruta, is algebraically represented by

1. x – 2y = 11
2. x – 2y = 11
3. x + 4y = 22
4. x – 4y = 11

Question 43

What are the fixed charges for a book?

1. ₹9
2. ₹10
3. ₹13
4. ₹15

Question 44

What are the additional charges for each subsequent day for a book?

1. ₹6
2. ₹5
3. ₹4
4. ₹3

Question 45

What is the total amount paid by both, if both of them have kept the book for 2 more days?

1. ₹35
2. ₹52
3. ₹50
4. ₹58

Question 46

The two triangular regions AOB and COD are

1. Similar by AA criterion
2. Similar by AA criterion
3. Similar by RHS criterion
4. Not similar

Question 47

The ratio of the area of the ΔAOB to the area of ΔCOD, is

1. 4 : 1
2. 1 : 4
3. 1 : 2
4. 2 : 1

Question 48

If the ratio of the perimeter of ΔAOB to the perimeter of ΔCOD would have been 1 : 4, then

1. AB = 2 CD
2. AB = 4 CD
3. CD = 2 AB
4. CD = 4 AB

Question 49

If in Δs AOD and BOC, $\frac{\mathbf{A}\mathbf{O}}{\mathbf{B}\mathbf{C}}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{A}\mathbf{D}}{\mathbf{B}\mathbf{O}}\mathbf{ }\mathbf{=}\frac{\mathbf{O}\mathbf{D}}{\mathbf{O}\mathbf{C}}\mathbf{ }$, then

1. $∆\mathrm{AOD} ~∆\mathrm{BOC}$
2. $∆\mathrm{AOD} ~∆\mathrm{BCO}$
3. $∆\mathrm{ADO} ~∆\mathrm{BCO}$
4. $∆\mathrm{ODA} ~∆\mathrm{BCO}$

Question 50

If the ratio of areas of two similar triangles AOB and COD is 1 : 4, then which of the following statements is true?

1. The ratio of their perimeters is 3 : 4.
2. The corresponding altitudes have a ratio 1 : 2.
3. The medians have a ratio 1 : 4.
4. The angle bisectors have a ratio 1 : 16.