Board Paper of Class 10 2021 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.

Question 1

The exponent of 5 in the prime factorisation of 3750 is

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

Ans: (b)

Question 2

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.

Question 3

The values of x and y satisfying the two equations 32x + 33y = 34, 33x + 32y = 31 respectively are:

  1. –1, 2
  2. –1, 4
  3. 1, –2
  4. –1, –4

Ans: (a)

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Question 4

If A(3, √3), B(0, 0) and C(3, k) are the three vertices of an equilateral triangle ABC, then the value of k is

  1. 2
  2. –3
  3. –√3
  4. –√2

Ans: (c)

Math-Stand-C10-Ques-4

Question 5

In figure, DE || BC, AD = 2 cm and BD = 3 cm, then ar(ΔABC) : ar(ΔADE) is equal to

Math-Stand-C10-Ques-5
  1. 4 : 25
  2. 2 : 3
  3. 9 : 4
  4. 25 : 4

Ans: (d)

Math Stand C10 Ques-5 sol

Question 6

If cot θ=13, the value of sec2 θ + cosec2 θ is

  1. 1
  2. 409
  3. 389
  4. 513

Ans: (d)

Math Stand C10 Ques-6 sol

Question 7

The area of a quadrant of a circle where the circumference of circle is 176 m, is

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

Ans: (c)

Math Stand C10 Ques-7 sol

Question 8

For an event E, P(E) + P(E¯) = x, then the value of x3 – 3 is

  1. –2
  2. 2
  3. 1
  4. –1

Ans. (a)

Math Stand C10 Ques-8 sol

Question 9

What is the greatest possible speed at which a girl can walk 95 m and 171 m in an exact number of minutes?

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

Ans: (b)

Math Stand C10 Ques-9 sol

Question 10

In figure, the graph of a polynomial P(x) is shown. The number of zeroes of P(x) is

Math Stand C10 Ques-10
  1. 1
  2. 2
  3. 3
  4. 4

Ans: (c)

Math Stand C10 Ques-10

Question 11

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)

Math Stand C10 Ques-11

Question 12

Three vertices of a parallelogram ABCD are A(1, 4), B(–2, 3) and C(5, 8). The ordinate of the fourth vertex D is

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

Ans: (b)

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Question 13

In ΔABC and ΔDEF, F = C, B = E and AB = 12 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)

Math Stand C10 Ques-13

Question 14

In ΔABC right angled at B, sin A = 725, then the value of cos C is

  1. 725
  2. 2425
  3. 724
  4. 247

Ans: (a)

Math Stand C10 Ques-14

Question 15

The minute hand of a clock is 84 cm long. The distance covered by the tip of the minute hand from 10:10 am to 10:25 am is

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

Ans: (c)

Math Stand C10 Ques-15

Question 16

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

  1. 913
  2. 3552
  3. 1013
  4. 1926

Ans: (a)

Math Stand C10 Ques-16

Question 17

Three alarm clocks ring their alarms at regular intervals of 20 min, 25 min and 30 min respectively. If they first beep together at 12 noon, at what time will they beep again for the first time?

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

Ans: (c)

Math Stand C10 Ques-17

Question 18

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)

Math Stand C10 Ques-18

Question 19

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)

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Question 20

Math Stand C10 Ques-20

Ans: (a)

Math Stand C10 Ques-20-Sol
Section – B
Q. No. 21 to 40 are of 1 mark each. Attempt any 16 from Q. 21 to 40.

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

Ans: (d)

Math Stand C10 Ques-21-Sol

Question 22

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

  1. 0.01
  2. 3%
  3. 1617
  4. 1716

Ans: (d)

Math Stand C10 Ques-22-Sol

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

Ans: (b)

Math Stand C10 Ques-23-Sol

Question 24

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

Math Stand C10 Ques-24

Ans: (c)

Math Stand C10 Ques-24-Sol

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

Ans: (c)

Math Stand C10 Ques-25-Sol

Question 26

If x – 1 is a factor of the polynomial p(x) = x3 + ax2 + 2b and a + b = 4, then

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

Ans: (b)

Math Stand C10 Ques-26-Sol

Question 27

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

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

Ans: (a)

Math Stand C10 Ques-27-Sol

Question 28

The area of a square that can be inscribed in a circle of area 14087 cm2 is

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

Ans: (c)

Math Stand C10 Ques-28-Sol

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

Ans: (c)

Math Stand C10 Ques-29-Sol

Question 30

Math Stand C10 Ques-30

  1. –7
  2. 7
  3. -3
  4. 3

Ans: (b)

Math Stand C10 Ques-30-Sol

Question 31

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

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

Ans: (d)

Math Stand C10 Ques-31-Sol

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

Ans: (d)

Math Stand C10 Ques-32-Sol

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

Ans: (b)

Math Stand C10 Ques-33-Sol

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

Ans: (d)

Math Stand C10 Ques-34-Sol

Question 35

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

  1. 1136
  2. 13
  3. 1336
  4. 2536

Ans: (d)

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

Math Stand C10 Ques-35-Sol

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

Ans: (c)

Math Stand C10 Ques-36-Sol

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

Math Stand C10 Ques-37-Sol
  1. 567 cm
  2. 756 cm
  3. 257 cm
  4. 247 cm

Ans: (d)

Math Stand C10 Ques-37-Sol

Question 38

In a ΔABC, A = x°, B = (3x  2)°, C = y°. Also C  B = 9°

  1. 107°
  2. 135°
  3. 155°
  4. 145°

Ans: (a)

Math Stand C10 Ques-38-Sol

Question 39

If sec θ + tan θ = p, then tan θ is

  1. p2 +12p
  2. p2 -12p
  3. p2 -1p2+1
  4. p2 +1p2-1

Ans: (b)

Math Stand C10 Ques-39-Sol

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?

Math Stand C10 Ques-40

Ans: (c)

Math Stand C10 Ques-40-sol
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.
Math Standard Sec C Case study I
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.

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

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

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

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

Question 43

What are the fixed charges for a book?

  1. ₹9
  2. ₹10
  3. ₹13
  4. ₹15

Ans: (b)

Math Stand C10 Ques-43-sol

Question 44

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).)

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

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.
Math Stand C-10 Sec-C Case-II
Based on the above information, answer any four of the following questions :

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

Ans: (a)

Math Stand C10 Ques-46-sol

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

Ans: (b)

Math Stand C10 Ques-47-sol

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

Ans: (d)

Math Stand C10 Ques-48-sol

Question 49

If in Δs AOD and BOC, AOBC = ADBO =ODOC , then

  1. AOD ~BOC
  2. AOD ~BCO
  3. ADO ~BCO
  4. ODA ~BCO

Ans: (b)

Math Stand C10 Ques-49-sol

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.

Ans: (b)

Math Stand C10 Ques-50-sol
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