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# Board Paper of Class 10 Maths (Standard) Term-I 2021 Delhi(Set 4) - Solutions

General Instructions :
(i) This question paper contains 50 questions out of which 40 questions are to be attempted. All questions carry equal marks.
(ii) The question paper consists of three Sections – Section A, B and C.
(iii) Section – A contains of 20 questions. Attempt any 16 questions from Q. No. 01 to 20.
(iv) Section – B also contains of 20 questions. Attempt any 16 questions from Q. No. 21 to 40.
(v) Section – C contains of two Case Studies containing 5 questions in each case. Attempt any 4 questions from Q. No. 41 to 45 and another 4 from Q. No. 46 to 50.
(vi) There is only one correct option for every Multiple Choice Question (MCQ). Marks will not be awarded for answering more than one option.
(vii) There is no negative mark.

• Question 1
The exponent of 5 in the prime factorisation of 3750 is
(a) 3
(b) 4
(c) 5
(d) 6 VIEW SOLUTION

• 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
(a) 1
(b) 2
(c) 3
(d) 5 VIEW SOLUTION

• Question 3
The values of x and y satisfying the two equations 32x + 33y = 34, 33x + 32y = 31 respectively are :
(a) –1, 2
(b) –1, 4
(c) 1, –2
(d) –1, –4 VIEW SOLUTION

• Question 4
If A(3, $\sqrt{3}$), B(0, 0) and C(3, k) are the three vertices of an equilateral triangle ABC, then the value of k is
(a) 2
(b) –3
(c) $-\sqrt{3}$
(d) $-\sqrt{2}$ VIEW SOLUTION

• Question 5
In figure, DE || BC, AD = 2 cm and BD = 3 cm, then ar (∆ABC) : ar (∆ADE) is equal to

(a) 4 : 25
(b) 2 : 3
(c) 9 : 4
(d) 25 : 4 VIEW SOLUTION

• Question 6
If $\mathrm{cot\theta }=\frac{1}{\sqrt{3}},$ the value of sec2θ + cosec2θ is
(a) 1

(b) $\frac{40}{9}$

(c) $\frac{38}{9}$

(d) $5\frac{1}{3}$ VIEW SOLUTION

• Question 7
The area of a quadrant of a circle where the circumference of circle is 176 m, is
(a) 2464 m2
(b) 1232 m2
(c) 616 m2
(d) 308 m2 VIEW SOLUTION

• Question 8
For an event E, P(E) + $\mathrm{P}\left(\overline{\mathrm{E}}\right)$ = x, then the value of x3 – 3 is
(a) –2
(b) 2
(c) 1
(d) –1 VIEW SOLUTION

• 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?
(a) 17 m/min
(b) 19 m/min
(c) 23 m/min
(d) 13 m/min VIEW SOLUTION

• Question 10
In figure, the graph of a polynomial P(x) is shown. The number of zeroes of P(x) is

(a) 1
(b) 2
(c) 3
(d) 4 VIEW SOLUTION

• 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
(a) 9x + 8y = 7
(b) –12x – 8y = 7
(c) –12x + 8y = 7
(d) 12x + 8y = 7 VIEW SOLUTION

• 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
(a) 8
(b) 9
(c) 7
(d) 6  VIEW SOLUTION

• Question 13
In ∆ABC and ∆DEF, ∠F = ∠C, ∠B = ∠E and AB = $\frac{1}{2}$ DE. Then, the two triangles are
(a) Congruent, but not similar.
(b) Similar, but not congruent.
(c) Neither congruent nor similar.
(d) Congruent as well as similar. VIEW SOLUTION

• Question 14
In ∆ABC right angled at B, sinA = $\frac{7}{25}$ then the value of cosC is
(a) $\frac{7}{25}$
(b) $\frac{24}{25}$
(c) $\frac{7}{24}$
(d) $\frac{24}{7}$ VIEW SOLUTION

• Question 15
The minute hand of a clock is 84 cm long. The distance covered by the tip of minute hand from 10:10 am to 10:25 am is
(a) 44 cm
(b) 88 cm
(c) 132 cm
(d) 176 cm VIEW SOLUTION

• Question 16
The probability that the drawn card from a pack of 52 cards is neither an ace nor a spade is
(a) $\frac{9}{13}$
(b) $\frac{35}{52}$
(c) $\frac{10}{13}$
(d) $\frac{19}{26}$ VIEW SOLUTION

• 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?
(a) 4 : 00 pm
(b) 4 : 30 pm
(c) 5 : 00 pm
(d) 5 : 30 pm VIEW SOLUTION

• Question 18
A quadratic polynomial, the product and sum of whose zeroes are 5 and 8 respectively is
(a) $k\left[{x}^{2}-8x+5\right]$
(b) $k\left[{x}^{2}+8x+5\right]$
(c) $k\left[{x}^{2}-5x+8\right]$
(d) $k\left[{x}^{2}+5x+8\right]$ VIEW SOLUTION

• Question 19
Point A (–1, y) and B (5, 7) lie on a circle with centre O (2, –3y). The value of y are
(a) 1, –7
(b) –1, 7
(c) 2, 7
(d) –2, –7 VIEW SOLUTION

• Question 20
Given that $\mathrm{sec\theta }=\sqrt{2}$, the value of $\frac{1+\mathrm{tan\theta }}{\mathrm{sin\theta }}$ is
(a) $2\sqrt{2}$
(b) $\sqrt{2}$
(c) $3\sqrt{2}$
(d) 2 VIEW SOLUTION

• Question 21
The greatest number which when divides 1251, 9377 and 15628 leaves remainder 1, 2 and 3 respectively is
(a) 575
(b) 450
(c) 750
(d) 625 VIEW SOLUTION

• Question 22
Which of the following cannot be the probability of an event?

(a) 0.01

(b) 3%

(c) $\frac{16}{17}$

(d) $\frac{17}{16}$ VIEW SOLUTION

• Question 23
The diameter of a car wheel is 42 cm. The number of complete revolutions it will make in moving 132 km is
(a) 104
(b) 105
(c) 106
(d) 103 VIEW SOLUTION

• Question 24
If θ is an acute angle and tan θ + cot θ = 2, then the value of sin3θ + cos3θ is

(a) 1

(b) $\frac{1}{2}$

(c) $\frac{\sqrt{2}}{2}$

(d) $\sqrt{2}$
VIEW SOLUTION

• 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
(a) 3 : 2
(b) 2 : 3
(c) 3 : 4
(d) 4 : 3 VIEW SOLUTION

• Question 26
If x – 1 is a factor of the polynomial p(x) = x3 + ax2 + 2b and a + b = 4, then
(a) a = 5, b = –1
(b) a = 9, b = –5
(c) a = 7, b = –3
(d) a = 3, b =1 VIEW SOLUTION

• Question 27
If a and b are two coprime numbers, then a3 and b3 are
(a) Coprime
(b) Not coprime
(c) Even
(d) Odd VIEW SOLUTION

• Question 28
The area of a square that can be inscribed in a circle of area $\frac{1408}{7}$ cm2 is
(a) 321 cm2
(b) 642 cm2
(c) 128 cm2
(d) 256 cm2 VIEW SOLUTION

• Question 29
If A(4, –2), B(7, –2) and C(7, 9) are the vertices of a ΔABC, then ΔABC is
(a) equilateral triangle
(b) isosceles triangle
(c) right angled triangle
(d) isosceles right angled triangle VIEW SOLUTION

• Question 30
If α, β are the zeros of the quadratic polynomial p(x) = x2 – (k + 6)x + 2(2k – 1), then the value of k, if α + β = $\frac{1}{2}$αβ, is
(a) –7
(b) 7
(c) –3
(d) 3 VIEW SOLUTION

• Question 31
If n is a natural number, then 2(5n + 6n) always ends with
(a) 1
(b) 4
(c) 3
(d) 2 VIEW SOLUTION

• Question 32
The line segment joining the points P(–3, 2) and Q(5, 7) is divided by the y-axis in the ratio
(a) 3 : 1
(b) 3 : 4
(c) 3 : 2
(d) 3 : 5 VIEW SOLUTION

• Question 33
If cotθ + cosecθ = p and cotθ + cosecθ = q, then p2q2 =
(a) a2b2
(b) b2 – a2
(c) a2 + b2
(d) ba VIEW SOLUTION

• 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
(a) 22 : 7
(b) 11 : 7
(c) 7 : 11
(d) 7 : 22 VIEW SOLUTION

• Question 35
A dice is rolled twice. The probability that 5 will not come up either time is

(a) $\frac{11}{36}$

(b) $\frac{1}{3}$

(c) $\frac{13}{36}$

(d) $\frac{25}{36}$ VIEW SOLUTION

• Question 36
The LCM of two numbers is 2400. Which of the following CANNOT be their HCF?
(a) 300
(b) 400
(c) 500
​(d) 600  VIEW SOLUTION

• 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

(a)

(b)

(c)

(d) ​ VIEW SOLUTION

• Question 38
In a ∆ABC, ∠A = x°, ∠B = (3x – 2)°, ∠C = y°, Also ∠C – ∠B = 9°. The sum of the greatest and the smallest angles of this triangle is
(a) 107°
(b) 135°
(c) 155°
(d) 145° VIEW SOLUTION

• Question 39
If secθ + tanθ = p, then tanθ is
(a) $\frac{{p}^{2}+1}{2p}$

(b) $\frac{{p}^{2}-1}{2p}$

(c) $\frac{{p}^{2}-1}{{p}^{2}+1}$

(d) $\frac{{p}^{2}+1}{{p}^{2}-1}$ VIEW SOLUTION

• Question 40
The base BC of an equilateral ∆ABC lies on the y-axis. The co-ordinates of C are (0, –3). If the origin is the mid-point of the base BC, what are the co-ordinates of A and B?
(a)
(b)
(c)
(d)  VIEW SOLUTION

• Question 41
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:
The situation of amount paid by Radhika, is algebraically represented by
(a) x – 4y = 16
(b) x + 4y = 16
(c) x – 2y = 16
(d) x + 2y = 16 VIEW SOLUTION

• Question 42
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:
The situation of amount paid by Amruta, is algebraically represented by
(a) x – 2y = 11
(b) x – 2y = 22
(c) x + 4y = 22
(d) x – 4y = 11 VIEW SOLUTION

• Question 43
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:
What are the fixed charges for a book?
(a) ₹9
(b) ₹10
(c) ₹13
(d) ₹15 VIEW SOLUTION

• Question 44
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:
What are the additional charges for each subsequent day for a book?
(a) ₹6
(b) ₹5
(c) ₹4
(d) ₹3 VIEW SOLUTION

• Question 45
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:
What is the total amount paid by both, if both of them have kept the book for 2 more days?
(a) ₹35
(b) ₹52
(c) ₹50
(d) ₹58​ VIEW SOLUTION

• Question 46
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
(a) Similar by AA criterion
(b) Similar by SAS criterion
(c) Similar by RHS criterion
(d) Not similar VIEW SOLUTION

• Question 47
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 ratio of the area of the ∆AOB to the area of ∆COD, is
(a) 4 : 1
(b) 1 : 4
(c) 1 : 2
(d) 2 : 1 VIEW SOLUTION

• Question 48
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:

If the ratio of the perimeter of ∆AOB to the perimeter of ∆COD would have been 1 : 4, then
(a) AB = 2 CD
(b) AB = 4 CD
(c) CD = 2 AB
(d) CD = 4 AB VIEW SOLUTION

• Question 49
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:

If in ∆AOD and BOC,
(a) ∆AOD ∼ ∆BOC
(b) ∆AOD ∼ ∆BCO
(d) ∆ODA ∼ ∆OBC VIEW SOLUTION

• Question 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:

If the ratio of areas of two similar triangles AOB and COD is 1 : 4, then
which of the following statements is true?
(a) The ratio of their perimeters is 3 : 4
(b) The corresponding altitudes have a ratio 1 : 2
(c) The medians have a ratio 1 : 4
(d) The angle bisectors have a ratio 1 : 16 VIEW SOLUTION
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