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

#### General Instructions:

1. This question paper contains 50 questions out of which 40 questions are to be attempted. All questions carry equal marks.
2. This question paper contains three Sections: A, B, and C.
3. Section A has 20 questions. Attempt any 16 questions from Q.No. 1 to 20.
4. Section B has 20 questions. Attempt any 16 questions from Q.No. 21 to 40.
5. Section C contains two Case Studies containing 5 Questions in each case. Attempt any 4 questions from Q.No. 41 to 45 and 4 another from Q.No. 46 to 50.
6. There is only one correct option for every multiple choice question (MCQ). Marks will not be awarded for answering more than one option.
7. There is no negative marking.
Q. No. 1 to 20 are of 1 mark each. Attempt any 16 from Q. 1 to 20.

1. 3
2. 4
3. 5
4. 6

Ans: (b)

## The graph of a polynomial P(x) cuts the x-axis at 3 points and touches it at 2 other points. The number of zeroes of P(x) is

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

Ans: (d)

Sol: The number of zeroes of P(x) is 5.

1. –1, 2
2. –1, 4
3. 1, –2
4. –1, –4

Ans: (a)

1. 2
2. –3
3. –√3
4. –√2

Ans: (c)

1. 4 : 25
2. 2 : 3
3. 9 : 4
4. 25 : 4

Ans: (d)

## If cot $\mathbf{\theta }\mathbf{=}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}$, the value of sec2$\mathbf{\theta }$ + cosec2$\mathbf{\theta }$ is

1. 1
2. $\frac{40}{9}$
3. $\frac{38}{9}$
4. $5\frac{1}{3}$

Ans: (d)

1. 2464 m2
2. 1232 m2
3. 616 m2
4. 308 m2

Ans: (c)

1. –2
2. 2
3. 1
4. –1

Ans. (a)

1. 17 m/min
2. 19 m/min
3. 23 m/min
4. 13 m/min

Ans: (b)

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

Ans: (c)

## Two lines are given to be parallel. The equation of one of the lines is 3x – 2y = 5. The equation of the second line can be

1. 9x + 8y = 7
2. –12x – 8y = 7
3. –12x + 8y = 7
4. 12x + 8y = 7

Ans: (c)

1. 8
2. 9
3. 7
4. 6

Ans: (b)

## In ΔABC and ΔDEF, DE. Then, the two triangles are

1. Congruent, but not similar.
2. Similar, but not congruent.
3. Neither congruent nor similar.
4. Congruent as well as similar.

Ans: (b)

## In ΔABC right angled at B, sin A , then the value of cos C is

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

Ans: (a)

1. 44 cm
2. 88 cm
3. 132 cm
4. 176 cm

Ans: (c)

## The probability that the drawn card from a pack of 52 cards is neither an ace nor a spade is

1. $\frac{9}{13}$
2. $\frac{35}{52}$
3. $\frac{10}{13}$
4. $\frac{19}{26}$

Ans: (a)

1. 4 : 00 pm
2. 4 : 30 pm
3. 5 : 00 pm
4. 5 : 30 pm

Ans: (c)

## A quadratic polynomial, the product and sum of whose zeroes are 5 and 8 respectively is

1. k [x2 – 8x + 5]
2. k [x2 + 8x + 5]
3. k [x2 – 5x + 8]
4. k [x2 + 5x + 8]

Ans: (a)

## Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y). The values of y are

1. 1, –7
2. –1, 7
3. 2, 7
4. –2, –7

Ans: (b)

#### Question 20

Ans: (a)

Section – B
Q. No. 21 to 40 are of 1 mark each. Attempt any 16 from Q. 21 to 40.

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

Ans: (d)

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

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

Ans: (d)

1. 104
2. 105
3. 106
4. 103

Ans: (b)

Ans: (c)

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

Ans: (c)

## If x – 1 is a factor of the polynomial p(x) then

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

Ans: (b)

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

Ans: (a)

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

Ans: (c)

## 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

Ans: (c)

1. –7
2. 7
3. -3
4. 3

Ans: (b)

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

Ans: (d)

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

Ans: (d)

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

Ans: (b)

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

Ans: (d)

## 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. $\frac{25}{36}$

Ans: (d)

Sol: A dice is rolled twice. Then possible outcomes are :

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

Ans: (c)

## 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

Ans: (d)

Ans: (a)

Ans: (b)

## 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?

Ans: (c)

Section – C
Q. No. 41-45 are based on Case Study–I, you have to answer any (4) four questions. Q. No. 46-50 are based on Case Study-II, you have to answer any (4) four questions.
Case Study-I
A book store shopkeeper gives books on rent for reading. He has variety of books in his store related to fiction, stories and quizzes etc. He takes a fixed charge for the first two days and an additional charge for subsequent day. Amruta paid ₹22 for a book and kept for 6 days; while Radhika paid ₹16 for keeping the book for 4 days.
Assume that the fixed charge be ₹x and additional charge (per day) be ₹y.
Based on the above information, answer any four of the following questions :

Given information:

Let, fixed charge for 2 days = ₹x.

and additional charge (per day) = ₹y.

## 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

Ans: (d)

The amount paid by Radhika, for keeping the book for 4 days = ₹16

$⇒$ Fixed charge for two days + additional charge (per day) for next 2 days = ₹16

$⇒$ x + 2y = 16

## 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

Ans: (c)

Sol: The amount paid by Amruta, for keeping the book for 6 days = ₹22

$⇒$ Fixed charge for two days + additional charge (per day) for next 4 days = ₹22.

$⇒$ x + 4y = 22

1. ₹9
2. ₹10
3. ₹13
4. ₹15

Ans: (b)

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

1. ₹6
2. ₹5
3. ₹4
4. ₹3

Ans: (d)

Sol: The additional charges for each subsequent day for a book = y = ₹3 (As solved in Q. 43 equation (3).)

## 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

Ans: (c)

Sol: Total amount = Amount paid by Radhika for keeping the book for 6 days + Amruta for keeping the book for 8 days

= Radhika for keeping the book for 4 days + 2 days additional
+ Amruta keeping the book for 6 days + 2 days additional

= 16 + 2y + 22 + 2y

= 38 + 4y

= 38 + 4 × 3

= 38 + 12

= ₹50

Case Study – II
A farmer has a field in the shape of trapezium, whose map with scale 1 cm = 20 m, is given below : The field is divided into four parts by joining the opposite vertices.
Based on the above information, answer any four of the following questions :

## 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

Ans: (a)

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

Ans: (b)

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

Ans: (d)

Ans: (b)

## 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.

Ans: (b)