CBSE Class 10 Mathematics Previous Year Question Paper Term 1 2021 JSK-1-Set-4

Does the sound of Class 10 Maths intrigue you? Or, does it scare you away? All of these happen because it's not easy to handle the Board pressure for CBSE Class 10. But, we will surely help you to tackle the syllabus for Class 10 Maths by providing you with the Class 10 Revision NotesClass 10 Textbook SolutionsClass 10 Tests for all of the chapters available in CBSE Class 10 Maths. We know that scoring more marks in CBSE Class 10 Maths has never been this easy before. But, by referring to all of the study materials we provide at TopperLearning, you can easily score more marks in the Class 10 board examination.


The study materials are created by our subject experts that we offer for CBSE Class 10, very well know the syllabus and essential facts of CBSE Class 10. These study materials will help you understand all the CBSE Class 10 Maths concepts as we focus on providing solutions that simplify a subject's complex fundamentals. At TopperLearning, we believe in delivering quality solutions at a low cost, and we strictly follow the latest CBSE Class 10 syllabus. We make sure that these study materials are revised from time to time. Our TopperLearning packages involve all the study resources for CBSE Class 10, such as Solved question papersvideo lessons and revision notes to help you score high marks. We also provide you with the updated NCERT textbook Solutions and RD Sharma textbook solutions, which provide students with step-by-step explanations.


Our study materials have also introduced the Case Study Based Questions for CBSE Class 10 of all the chapters available in Class 10. These questions are designed based on the latest syllabus of CBSE Class 10.

So why wait when you can quickly get the CBSE class 10 plans.

Read  more

SECTION A

Question numbers 1 to 20 are multiple choice questions of 1 mark each.

Select the correct option.

Question 1.

If HCF (39, 91) = 13, then LCM (39, 91) is :

  1. 91
  2. 273
  3. 39
  4. 3549

 

Question 2.

begin mathsize 12px style 4 square root of 57 end style is a/an :

  1. integer 
  2. rational number
  3. natural number
  4. irrational number
 

Question 3.

The line represented by 4x - 3y = 9 intersects the y-axis at :

  1. (0, - 3) 
  2. begin mathsize 12px style open parentheses 9 over 4 comma 0 close parentheses end style
  3. (-3,0)
  4. begin mathsize 12px style open parentheses 0 comma 9 over 4 close parentheses end style
 

Question 4.

The point on x-axis equidistant from the points P(5, 0) and Q(- 1, 0) is :

  1. (2, 0) 
  2. (- 2, 0) 
  3. (3, 0) 
  4. (2, 2)  


Question 5.

If ΔABC and ΔPQR are similar triangles such that ∠A = 31° and ∠R = 69°, then ∠Q is: 

  1. 70° 
  2. 100° 
  3. 90° 
  4. 80°
 

Question 6. 

begin mathsize 12px style Given space that space cos space straight theta equals fraction numerator square root of 3 over denominator 2 end fraction comma space then space the space value space of space fraction numerator cosec squared straight theta minus sec squared straight theta over denominator coses squared straight theta plus sec squared straight theta end fraction is colon end style

  1. - 1 
  2. begin mathsize 12px style 1 half end style
  3. begin mathsize 12px style negative 1 half end style
 

Question 7.

The area swept by 7 cm long minute hand of a clock in 10 minutes is:

  1. 77 cm2
  2. begin mathsize 12px style 12 5 over 6 cm squared end style
  3. begin mathsize 12px style 7 1 over 12 cm squared end style
  4. begin mathsize 12px style 25 2 over 3 cm squared end style

 

Question 8.

The probability of getting two heads when two fair coins are tossed together, is:

  1. begin mathsize 12px style 1 third end style 
  2. begin mathsize 12px style 1 fourth end style
  3. begin mathsize 12px style 1 half end style
  4. 1
 

Question 9.

Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers, is :

  1. 2
  2. 4
 

Question 10.

The pair of equations y = 2 and y = -3 has 

  1. one solution 
  2. Two solutions
  3. infinitely many solutions 
  4. no solutions
 

Question 11.

In the figure given below, what value of x will make PQ || AB?

  1. 2
  2. 3
  3. 4
  4. 5
 

Question 12.

begin mathsize 12px style Given space that space sin space straight alpha space equals space fraction numerator square root of 3 over denominator 2 end fraction space and space tan space straight beta space equals fraction numerator 1 over denominator square root of 3 end fraction comma space then space the space value space of space cos space left parenthesis straight alpha minus straight beta right parenthesis space is colon end style

  1. begin mathsize 12px style fraction numerator square root of 3 over denominator 2 end fraction end style
  2. begin mathsize 12px style 1 half end style
  3. 0
  4. begin mathsize 12px style fraction numerator 1 over denominator square root of 2 end fraction end style
 

Question 13.

In a single throw of a die, the probability of getting a composite number is :

  1. begin mathsize 12px style 1 third end style
  2. begin mathsize 12px style 1 half end style
  3. begin mathsize 12px style 2 over 3 end style
  4. begin mathsize 12px style 5 over 6 end style

 

 

Question 14.

The decimal expansion of the rational number begin mathsize 12px style 3177 over 250 end style will terminate after

  1. One decimal place
  2. two decimal places
  3. three decimal places
  4. four decimal places

 

Question 15.

The pair of lines represented by the linear equations 3x + 2y = 7 and 4x + 8y - 11 = 0 are

  1. perpendicular
  2. parallel
  3. intersecting
  4. coincident

  

Question 16.

In an equilateral triangle with length of side p, the length of the altitude is :

  1. begin mathsize 12px style fraction numerator square root of 3 over denominator 2 end fraction straight P end style
  2. begin mathsize 12px style fraction numerator square root of 3 over denominator 4 end fraction straight P end style
  3. begin mathsize 12px style fraction numerator square root of 3 over denominator 2 end fraction straight p squared end style
  4. begin mathsize 12px style fraction numerator square root of 3 over denominator 4 end fraction straight P squared end style
 

Question 17.

Given that sin θ = begin mathsize 12px style straight p over straight q end style , tan θ is equal to :

  1. begin mathsize 12px style fraction numerator straight P over denominator square root of straight p squared minus straight q squared end root end fraction end style
  2. begin mathsize 12px style fraction numerator straight q over denominator square root of straight p squared minus straight q squared end root end fraction end style
  3. begin mathsize 12px style fraction numerator straight p over denominator square root of straight q squared minus straight p squared end root end fraction end style
  4. begin mathsize 12px style fraction numerator straight q over denominator square root of straight q squared minus straight p squared end root end fraction end style
 

Question 18.

A vertical pole of length 19 m casts a shadow 57 m long on the ground and at the same time a tower casts a shadow 51 m long. The a height of the tower is:

  1. 171m
  2. 13 m
  3. 17 m
  4. 117 m

 

Question 19.

The simplest form of begin mathsize 12px style square root of left parenthesis 1 minus cos squared straight theta right parenthesis left parenthesis 1 plus tan squared straight theta right parenthesis end root end style is 

  1. cos θ
  2. sin θ 
  3. cot θ
  4. tan θ
 

Question 20.

In the given figure, ∠ABC and ∠ ACB are complementary to each other and AD ⊥ BC. Then,

  1. BD.CD = BC2
  2. AB.BC = BC2
  3. BD.CD= AD2
  4. AB.AC = AD2
 

SECTION B

Questions no. 21 to 40 are of 1 mark each. Answer any 16 questions from Q. No. 21 - 40.

 

Question 21.

If one of the zeroes of a quadratic polynomial (k - 1) x2 + kx + 1 is -3, then the value of k is:

  1. begin mathsize 12px style 4 over 3 end style
  2. begin mathsize 12px style negative 4 over 3 end style
  3. begin mathsize 12px style 2 over 3 end style
  4. begin mathsize 12px style negative 2 over 3 end style
 

Question 22.

If the lengths of diagonals of a rhombus are 10 cm and 24 cm, then the perimeter of the rhombus is:

  1. 13 cm
  2. 26 cm
  3. 39 cm
  4. 52 cm
 

Question 23.

In the given figure, x expressed in terms of a, b, c, is :

  1. begin mathsize 12px style straight x equals fraction numerator ab over denominator straight a plus straight b end fraction end style
  2. begin mathsize 12px style straight x equals fraction numerator ac over denominator straight b plus straight c end fraction end style
  3. begin mathsize 12px style straight x equals fraction numerator bc over denominator straight b plus straight c end fraction end style
  4. begin mathsize 12px style straight x equals fraction numerator ac over denominator straight a plus straight c end fraction end style
 

Question 24.

begin mathsize 12px style fraction numerator 1 over denominator cosec space straight theta left parenthesis 1 minus cot space straight theta right parenthesis end fraction plus fraction numerator 1 over denominator secθ left parenthesis 1 minus tan space straight theta right parenthesis end fraction space is space equal space to end style

  1. 0
  2. 1
  3. sin θ + cos θ
  4. sin θ – cos θ
 

Question 25.

If ‘n' is any natural number, then (12)n cannot end with the digit:

  1. 2
  2. 4
  3. 8
  4. 0
 

Question 26.

A wire can be bent in the form of a circle of radius 56 cm. If the same wire is bent in the form of square, then the area of the square will be:

  1. 8800 cm2
  2. 7744 cm2
  3. 6400 cm2
  4. 3520 cm2
 

Question 27.

The probability that a non-leap year has 53 Wednesday, is :

  1. begin mathsize 12px style 1 over 7 end style
  2. begin mathsize 12px style 2 over 7 end style
  3. begin mathsize 12px style 5 over 7 end style
  4. begin mathsize 12px style 6 over 7 end style
 

Question 28.

If the given figure, points A, B, C and D are concyclic and ∠CBE = 130°. Then ∠FDC is :

  1. 130°
  2. 80°
  3. 50°
  4. 30°
 
Question 29.
The x – coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, -5) and R(-3, 6), then the coordinates of P are :
  1. (8, 16)
  2. (10, 20)
  3. (20, 10)
  4. (16, 8)
 

Question 30.

If the point (x, 4) lies on a circle whose centre is at origin and radius is 5 cm, then the value of x is :

  1. 0
  2. ±4
  3. ±5
  4. ±3
 

Question 31.

The value of θ for which 2 sin 2θ = 1, is :

  1. 15°
  2. 30°
  3. 45°
  4. 60°
 

Question 32.

The number 385 can be expressed as the product of prime factors as 

  1. 5×11×13
  2. 5×7×11
  3. 5×7×13
  4. 5×11×17
 

Question 33.

The difference between circumference and radius of a circle is 111 cm. The area of the circle is  

  1. 1366 cm2
  2. 1386 cm2
  3. 1376 cm2
  4. 1396 cm2
 

Question 34.

From the letters of word ‘MANGO’, a letter is selected at random. The probability that the letter is a vowel, is :

  1. begin mathsize 12px style 1 fifth end style
  2. begin mathsize 12px style 3 over 5 end style
  3. begin mathsize 12px style 2 over 5 end style
  4. begin mathsize 12px style 4 over 5 end style 
 

Question 35.

If 17x – 19y = 53 and 19x – 17y = 55, then the value of (x + y) is :

  1. 1
  2. -1
  3. 3
  4. -3
 

Question 36.

The ratio in which the point ( -4, 6) divides the line segment joining the points A (-6, 10) and B(3, -8) is :

  1. 2:5
  2. 7:2
  3. 2:7
  4. 5:2
 

Question 37.

If sin2θ + sinθ = 1, then the value of cos2θ + cos4θ is :

  1. -1
  2. 1
  3. 0
  4. 2
 

Question 38.

38.The decimal expression of begin mathsize 12px style 43 over 162 end style:

  1. is terminating
  2. is non-terminating and non-recurring
  3. is non-terminating and recurring
  4. does not exist
 

Question 39.

If the circumference of a circle is tripled, then its area becomes:

  1. three times
  2. nine times
  3. eight times
  4. two times
 

Question 40.

A father is three times as old as his son. In 12 years time, he will be twice as old as his son. The sum of the present ages of the father and the son is:

  1. 36 years
  2. 48 years
  3. 60 years
  4. 42 years
 
SECTION C
(Case Study Based Questions)
Section C consists of 10 questions of 1 mark each. Attempt any 8 questions from Q. No. 4150.                8 × 1 = 8
 
 (Case Study – I)

A car moves on a highway. The path it traces is given below:

Based on the above information, answer the following questions:


Question 41.

What is the shape of the curve EFG?

  1. Parabola
  2. Ellipse
  3. Straight line
  4. Circle
 

Question 42.

If the curve ABC is represented by the polynomial –(x2 + 4x + 3), then its zeroes are:

  1. 1 and -3
  2. -1 and 3
  3. 1 and 3
  4. -1 and -3
 

Question 43.

If the path traced by the car has zeroes at -1 and 2, then it is given by:

  1. x2 + x + 2
  2. x2 - x + 2
  3. x2- x – 2
  4. x2 + x – 2
 

Question 44.

The number of zeroes of the polynomial representing the whole curve, is:

  1. 4
  2. 3
  3. 2
  4. 1
 

Question 45.

The distance between C and G is:

  1. 4 units
  2. 6 units
  3. 8 units
  4. 7 units
 
(Case Study – II)

Shivani is an interior decorator. To design her own living room, she designed wall shelves. The graph of intersecting wall shelves is given below:
Based on the above information, answer the following questions:


Question 46.

If O is the origin, then what are the coordinates of S?

  1. (-6, -4)
  2. (6, 4)
  3. (-6, 4)
  4. (6, -4)
 

Question 47.

The coordinates of the mid-point of the line-segment joining D and H is:

  1. begin mathsize 12px style open parentheses negative 3 comma space 2 over 3 close parentheses end style 
  2. (3, -1)
  3. (3, 1)
  4. begin mathsize 12px style open parentheses negative 3 comma negative 2 over 3 close parentheses end style 
 

Question 48.

The ratio in which the x-axis divides the line-segment joining the points A and C, is:

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

Question 49.

The distance between the points P and G is

  1. 16 units
  2. 3√74 units
  3. 2√74 units
  4. √74 units
 

Question 50.

The coordinates of the vertices of rectangle IJKL are:

  1. I(2, 0), J(2, 6), K(8, 6), L(8, 2)
  2. I(2,-2), J(2, -6), K(8, -6), L(8, -2)
  3. I(-2, 0), J(-2, 6), K(-8, 6), L(-8, 2)
  4. I(-2, 0), J(-2, -6), K(-8, -6), L(-8, -2)

SECTION A


Ans 1. Correct Option: B

Product of numbers = LCM×HCF

∴ 39×91=LCM×13

∴ LCM=273

 

Ans 2. Correct Option: D

The product of any rational number and any irrational number will always be an irrational number. Here begin mathsize 12px style square root of 57 end style  is irrational, hence is begin mathsize 12px style 4 square root of 57 end style an irrational number.

 

Ans 3. Correct Option: A

Substituting x = 0 in 4x - 3y = 9, we get y = -3, hence the point is (0,-3).

 

Ans 4. Correct Option: A

A point on x-axis will have coordinates (x,0).

Now let A(x,0) is equidistant from the points P(5, 0) and Q(- 1, 0), all of which lie on the x-axis, thus we can say that PA = QA and A is the midpoint.

Hence,

begin mathsize 12px style therefore straight x fraction numerator 5 minus 1 over denominator 2 end fraction equals 2 space
therefore point space equals space left parenthesis 2 comma space 0 right parenthesis end style


Ans 5. Correct Option: D

ΔABC and ΔPQR are similar triangles

Hence by c.p.c.t.

∠A = ∠P 

∠B = ∠Q

∠C = ∠R

Also in ΔABC

∠A + ∠B + ∠C =180o

∴ ∠A + ∠Q + ∠R =180o

∴ ∠Q = 80o

 

Ans 6. Correct Option: C

begin mathsize 12px style cos space straight theta space equals space fraction numerator square root of 3 over denominator 2 end fraction
therefore straight theta space equals space 30 to the power of straight o
therefore fraction numerator cos space ec squared minus sec squared straight theta over denominator cosec squared straight theta plus sec squared straight theta end fraction equals fraction numerator 4 minus begin display style 4 over 3 end style over denominator 4 plus begin display style 4 over 3 end style end fraction equals 8 over 16 equals 1 half end style 

 

Ans 7. Correct Option: D

60 mins of clock = 360o

10 mins of clock = 60o

Now for the sector,

Radius = 7cm

begin mathsize 12px style therefore space Area space of space sector space equals straight theta over 360 xπr squared
equals 60 over 360 space straight x space 7 squared space straight x space 22 over 7 equals 25 2 over 3 cm squared end style 

 

Ans 8. Correct Option: B

Two coins are tossed, hence sample space S is

S = {HH, TT, HT, TH}, n(S)=4

A: getting two heads

A = {HH}, n(A)=1

P(A) = n(A)/n(S) = 1/4

 

Ans 9. Correct Option: A

Let the numbers be 12x and 12y, where x and y are co-primes.

Product of the numbers = 144xy

144xy = 6336

xy = 44

Hence two numbers can be 1 and 44, or 11 and 4.

 

Ans 10. Correct Option: D

The graph of y = 2 and y = -3 does not intersect, hence no solution.


Ans 11. Correct Option: A

By converse of Basic proportionality theorem,

PQ || AB if,

begin mathsize 12px style CP over PA equals CQ over QB
therefore fraction numerator straight x plus 3 over denominator 3 straight x plus 19 end fraction equals fraction numerator straight x over denominator 3 straight x plus 4 end fraction
therefore left parenthesis straight x plus 3 right parenthesis left parenthesis 3 straight x plus 4 right parenthesis equals straight x left parenthesis 3 straight x plus 19 right parenthesis
therefore 3 straight x squared plus 4 straight x plus 9 straight x plus 12 equals 3 straight x squared plus 19 straight x
therefore 12 equals 6 straight x
therefore straight x equals 2 end style

  

Ans 12. Correct Option: A

begin mathsize 12px style sin space 60 space equals space fraction numerator square root of 3 over denominator 2 end fraction
therefore straight alpha space equals space 60
tan space equals space fraction numerator 1 over denominator square root of 3 end fraction
therefore straight beta space equals space 30
therefore cos space left parenthesis straight alpha space minus space straight beta right parenthesis space equals space fraction numerator square root of 3 over denominator 2 end fraction end style

 

Ans 13. Correct Option: A

A die is thrown, hence sample space S is given by

S= {1, 2, 3, 4, 5, 6}, n(S) = 6

A: number is composite

A= {4,6}, n(A) = 2

P(A) = 2/6 = 1/3

 

Ans 14. Correct Option: C

The denominator 250 can be expressed as 2×53 (powers of 2 and 5 only), here highest power is 3, and thus decimal will terminate after 3 places.

 

Ans 15. Correct Option: C

For 3x + 2y = 7 and 4x + 8y = 11

3/4 ≠ 2/8

So, intersecting.

 

Ans 16. Correct Option: A

Let ∆ABC be equilateral, with AD altitude

begin mathsize 12px style sin space 60 space equals AD over AB
therefore fraction numerator square root of 3 over denominator 2 end fraction equals AD over straight P
therefore space AD equals fraction numerator square root of 3 over denominator 2 end fraction straight p end style 

 

Ans 17. Correct Option: C

begin mathsize 12px style sin space theta straight p over straight q
therefore cos space straight theta space equals square root of 1 minus straight P squared over straight q squared end root equals square root of fraction numerator straight q squared minus straight P squared over denominator straight q squared end fraction end root
therefore tan space straight theta space equals space fraction numerator begin display style straight p over straight q end style over denominator square root of begin display style fraction numerator straight q squared minus straight p squared over denominator straight q squared end fraction end style end root end fraction equals fraction numerator straight P over denominator square root of straight q squared minus straight p squared end root end fraction end style

 

Ans 18. Correct Option: C

begin mathsize 12px style In space increment ABC space and space increment XYZ
angle straight B space equals angle straight Y space equals space 90 to the power of straight o
angle straight A space equals space angle straight X.... left parenthesis sun apostrophe straight s space rays right parenthesis
therefore increment ABC space tilde increment XYZ space.... left parenthesis AA space test right parenthesis
therefore AB over XY equals BC over YZ
therefore 19 over 57 equals BC over 51
therefore BC space equals space 17 space straight m end style

 

Ans 19. Correct Option: D

begin mathsize 12px style square root of left parenthesis 1 minus cos squared straight theta right parenthesis left parenthesis 1 plus tan squared straight theta right parenthesis end root
equals square root of sin squared straight theta cross times sec squared straight theta end root
equals sin space straight theta space cross times fraction numerator 1 over denominator cos space straight theta end fraction
equals tan space straight theta end style

 

Ans 20. Correct Option: C

∠ABC and ∠ ACB are complementary

Hence, ∠ABC + ∠ ACB = 90o

In ∆ABC

∠ABC + ∠ ACB + ∠BAC = 180o …(sum of angles of triangle)

∴ ∠BAC = 90o

So in right angled triangle BAC, a perpendicular is drawn to the hypotenuse from the 90o vertex, hence we have 

begin mathsize 12px style increment BAC space tilde increment BDA tilde increment ADC
increment BDA tilde increment ADC
BD over AD equals AD over CD space..... left parenthesis straight c. straight p. straight c. straight t right parenthesis
BD. CD equals AD squared end style

 

SECTION B 

Questions no. 21 to 40 are of 1 mark each. Answer any 16 questions from Q. No. 21 - 40.

 
Ans 21. Correct Option: A

(k - 1)x2 + kx + 1

One of the zeros is -3

∴ (k - 1)9 - 3k + 1 = 0

∴ 9k – 9 - 3k + 1 = 0

∴ k=4/3

 

Ans 22. Correct Option: D

Diagonals of rhombus bisect each other perpendicularly

Hence,
begin mathsize 12px style side space equals space square root of 5 squared plus 12 squared end root space equals space 13 cm
Perimeter space equals space 13 space cross times space 4 space equals space 52 cm end style
 

Ans 23. Correct Option: B

begin mathsize 12px style In space increment QRP space and space increment TRS
angle PQR space equals space angle STR space angle.... left parenthesis given right parenthesis
angle straight R.... left parenthesis common right parenthesis
increment QRP tilde increment TRS space.... left parenthesis AA space test right parenthesis
therefore QR over TR equals QP over TS.... left parenthesis straight c. straight p. straight c. straight t right parenthesis
therefore fraction numerator straight b plus straight c over denominator straight c end fraction equals straight a over straight x
therefore straight x equals fraction numerator ac over denominator straight b plus straight c end fraction end style


Ans 24. Correct Option: C

begin mathsize 12px style fraction numerator 1 over denominator cosec space straight theta left parenthesis 1 minus cot space straight theta right parenthesis end fraction plus fraction numerator 1 over denominator sec space straight theta left parenthesis 1 minus tan space straight theta right parenthesis end fraction
equals fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator sin space straight theta end fraction end style open parentheses 1 minus begin display style fraction numerator cos space straight theta over denominator sin space straight theta end fraction end style close parentheses end fraction plus fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator cos space straight theta end fraction end style open parentheses 1 minus begin display style fraction numerator sin space straight theta over denominator cos space straight theta end fraction end style close parentheses end fraction
equals fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator sin space straight theta end fraction end style open parentheses begin display style fraction numerator sin space straight theta space minus space cos space straight theta over denominator sin space straight theta end fraction end style close parentheses end fraction plus fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator cos space straight theta end fraction end style open parentheses begin display style fraction numerator cos space straight theta space minus sin space straight theta over denominator cos space straight theta end fraction end style close parentheses end fraction
equals fraction numerator sin squared space straight theta over denominator sin space straight theta space minus space cos space straight theta end fraction plus fraction numerator cos squared space straight theta over denominator cos space straight theta space minus space sin space straight theta end fraction
equals fraction numerator sin squared space straight theta over denominator sin space straight theta space minus cos space straight theta end fraction minus fraction numerator cos squared space straight theta over denominator sin space straight theta space minus space cos space straight theta end fraction
equals fraction numerator sin squared space straight theta space minus space cos squared space straight theta over denominator sin space straight theta space minus space cos space straight theta end fraction
equals fraction numerator open parentheses sin space straight theta space minus space cos space straight theta close parentheses left parenthesis sin space straight theta space plus space cos space straight theta right parenthesis over denominator sin space straight theta space minus space cos space straight theta end fraction
equals space sin space straight theta space plus cos space straight theta end style


Ans 25. Correct Option: D

(12)n = (22 × 3)n

Now, to get 0 in the unit’s place, you will need 2 as well as 5 in its prime factors.

Thus (12)n cannot end with 0.

 

Ans 26. Correct Option: B

Circumference of circle = perimeter of square

begin mathsize 12px style 2 πr space equals 4 space cross times space side
therefore side space equals fraction numerator 2 cross times begin display style 22 over 7 end style cross times 56 over denominator 4 end fraction equals 88 cm
therefore Area space equals space 88 squared space equals space 7744 cm squared end style

 

Ans 27. Correct Option: A

A non-leap year has 52 weeks and 1 day, hence the sample space S will be 

S = {M, T, W, Th, F, Sa, S}, n(A) =7

A: getting extra Wednesday

A = {W}, n(A)=1

P(A) = 1/7

 

Ans 28. Correct Option: C

∠ABC + ∠CBE = 180o…(linear pair)

∴ ∠ABC = 50o

Quadrilateral ABCD is cyclic, hence

∠ABC + ∠CDA = 180o…(opposite angles are supplementary)

∴ ∠CDA = 130o

∠CDA + ∠CDF = 180o…(linear pair)

∴ ∠ADC = 50o

 

Ans 29. Correct Option: D

Let the coordinates of P be (2t,t).

If P is equidistant from Q(2, -5) and R(-3, 6), hence

PQ = PR

begin mathsize 12px style square root of left parenthesis 2 straight t space minus 2 right parenthesis squared plus left parenthesis straight t plus 5 right parenthesis squared end root equals square root of left parenthesis 2 straight t plus 3 right parenthesis squared plus left parenthesis straight t minus 6 right parenthesis squared end root end style

∴ (2t- 2)2 + (t + 5)2 = (2t + 3)2 + (t - 6)2

∴ 4t2 - 8t + 4 + t2 + 10t + 25 = 4t2 + 12t + 9 + t2 - 12t + 36 

∴ -8t + 4 + 10t + 25 = 9 + 36

∴ 2t = 16

∴ t = 8

 

∴ P(16, 8)

 

Ans 30. Correct Option: D

Radius of a circle is the distance between a point on its circumference and its center

begin mathsize 12px style Radius space equals square root of left parenthesis straight x minus 0 right parenthesis squared plus left parenthesis 4 minus 0 right parenthesis squared end root
therefore space 5 equals square root of straight x squared plus 4 squared end root
therefore 25 equals straight x 2 space plus 42
therefore straight x equals plus-or-minus 3 cm end style

 

Ans 31. Correct Option: A

2 sin 2θ = 1

∴ sin 2θ = 1/2

But sin 30 = 1/2

∴ 2θ = 30o

∴ θ = 15o

 

Ans 32. Correct Option: B

385 can be expressed as 5×7×11

 

Ans 33. Correct Option: B

begin mathsize 12px style circumference space minus space Radius space equals space 2 πr space minus space straight r
therefore 2 πr space minus space straight r space equals space 111
therefore space straight r equals fraction numerator 111 over denominator 2 straight pi minus 1 end fraction
therefore straight r space equals space fraction numerator 111 over denominator 2 cross times begin display style 22 over 7 end style minus 1 end fraction
therefore straight r space equals space 21 cm
therefore Area space equals space 22 over 7 cross times 21 squared equals 1386 cm squared end style


Ans 34. Correct Option: C

S: Selecting letters of word ‘MANGO’

S = {M, A, N, G, O}, n(S) = 5

A: Selecting a vowel from letters of word ‘MANGO’

A = {A, O}, n(A) = 2

P(A) = 2/5

 

Ans 35. Correct Option: A

17x – 19y = 53 …(1)

19x – 17y = 55 …(2)

Eqn.(2) – eqn.(1) gives

∴ 2x + 2y = 2

∴ x + y = 1

 

Ans 36. Correct Option: C

Let point T(-4, 6) divides the line segment joining the points A(-6, 10) and B(3, -8) in the ratio k:1

Hence by section formula

begin mathsize 12px style therefore space minus 4 equals fraction numerator straight k cross times 3 plus 1 cross times negative 6 over denominator straight k plus 1 end fraction
therefore space minus 4 straight k space minus space 4 space equals space 3 straight k space minus space 6
therefore space straight k space equals space 2 over 7 end style
 

Ans 37. Correct Option: B 

sin2 θ + sin θ = 1...(1) 

sin θ = 1 - sinθ 

sin θ = cos2 θ

Substitute in (1)

∴ cosθ + cos2 θ = 1


Ans 38. Correct Option: B

begin mathsize 12px style 43 over 162 equals 0.265432...... end style

Hence, non-terminating and non-recurring.

 

Ans 39. Correct Option: B
Circumference = 2𝜋r
New circumference = 2𝜋R
∴ 3 x 2𝜋r = 2𝜋R
∴ R = 3r
Area = 𝜋r2
∴ New area = 𝜋R2 = 9𝜋r2
 

Ans 40. Correct Option: B

Let father’s present age be x and son’s present age be y

Given,

x = 3y

After 12 years

x + 12 = 2(y + 12)

x – 2y = 12

∴ 3y – 2y = 12

∴ y = 12 and x = 36

∴ Sum = 48

 
SECTION C
(Case Study Based Questions)
Section C consists of 10 questions of 1 mark each. Attempt any 8 questions from Q. No. 4150.         8 × 1 = 8
 
(Case Study – I)
 

Ans 41. Correct Option: A