PM Yashasvi 11th Class Maths Model Paper 1 | Yashasvi Important Bits

by

PM Yashasvi Scholarship 11th Class Maths Model Paper 1 | Yashasvi Important Bits

 

Inter 1st Year(11th) Students Practice This Bits{10th class Syllabus}

1. The decimal expansion of 22/7 is
(a) Terminating
(b) Non-terminating and repeating
(c) Non-terminating and Non-repeating
(d) None of the above
Answer: (b) Non-terminating and repeating

2. For some integer n, the odd integer is represented in the form of:
(a) n (b) n + 1
(c) 2n + 1 (d) 2n
Answer: (c) 2n + 1

3. HCF of 26 and 91 is:
(a) 15 (b) 13
(c) 19 (d) 11
Answer: (b) 13

4. Which of the following is not irrational?
(a) (3 + √7)
(b) (3 – √7)
(c) (3 + √7) (3 – √7)
(d) 3√7
Answer: (c) (3 + √7) (3 – √7)

5. The addition of a rational number and an irrational number is equal to:
(a) rational number
(b) Irrational number
(c) Both
(d) None of the above
Answer: (b) Irrational number

6. The multiplication of two irrational numbers is:
(a) irrational number
(b) rational number
(c) Maybe rational or irrational
(d) None
Answer: (c) Maybe rational or irrational

7. If set A = {1, 2, 3, 4, 5,…} is given, then it represents:
(a) Whole numbers
(b) Rational Numbers
(c) Natural numbers
(d) Complex numbers
Answer: (c) Natural numbers

8. If p and q are integers and is represented in the form of p/q, then it is a:
(a) Whole number
(b) Rational number
(c) Natural number
(d) Even number
Answer: (b) Rational number

9. The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is:
(a) 65
(b) 15
(c) 13
(d) 25
Answer: (c) 13

10. The least number that is divisible by all the numbers from 1 to 5 is:
(a) 70
(b) 60
(c) 80
(d) 90
Answer: (b) 60

11. The sum or difference of two irrational numbers is always
(a) rational
(b) irrational
(c) rational or irrational
(d) not determined
Answer: (b) irrational

12. The decimal expansion of the rational number 23/(22 . 5) will terminate after
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) more than 3 decimal places
Answer: (b) two decimal places

All competitive exams most important Bits

13. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy
(a) 1 < r < b
(b) 0 < r ≤ b
(c) 0 ≤ r < b
(d) 0 < r < b
Correct option: (c) 0 ≤ r < b

14. For some integer m, every even integer is of the form
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1
Answer: (c) 2m

15. Using Euclid’s division algorithm, the HCF of 231 and 396 is
(a) 32
(b) 21
(c) 13
(d) 33
Answer: (d) 33

16. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is
(a) 4
(b) 2
(c) 1
(d) 3
Answer: (b) 2

17. The prime factorisation of 96 is
(a) 25 × 3
(b) 26
(c) 24 × 3
(d) 24 × 32
Answer: (a) 25 × 3

18. n² – 1 is divisible by 8, if n is
(a) an integer
(b) a natural number
(c) an odd integer
(d) an even integer
Answer: (c) an odd integer

19. For any two positive integers a and b, HCF (a, b) × LCM (a, b) =
(a) 1
(b) (a × b)/2
(c) a/b
(d) a × b
Answer: (d) a × b

20. The values of the remainder r, when a positive integer a is divided by 3 are
(a) 0, 1, 2
(b) Only 1
(c) Only 0 or 1
(d) 1, 2
Answer: (a) 0, 1, 2

21. The zeroes of x2–2x –8 are:
(a) (2,-4)
(b) (4,-2)
(c) (-2,-2)
(d) (-4,-4)
Answer: (b) (4,-2)

22. What is the quadratic polynomial whose sum and the product of zeroes is √2, ⅓ respectively?
(a) 3×2-3√2x+1
(b) 3×2+3√2x+1
(c) 3×2+3√2x-1
(d) None of the above
Answer: (a) 3×2-3√2x+1

23. If the zeroes of the quadratic polynomial ax2+bx+c, c≠0 are equal, then
(a) c and b have opposite signs
(b) c and a have opposite signs
(c) c and b have same signs
(d) c and a have same signs
Answer: (d) c and a have same signs

24. The degree of the polynomial, x4 – x2 +2 is
(a) 2
(b) 4
(c) 1
(d) 0
Answer: (b) 4

25. If one of the zeroes of cubic polynomial is x3+ax2+bx+c is -1, then product of other two zeroes is:
(a) b-a-1
(b) b-a+1
(c) a-b+1
(d) a-b-1
Answer: (b) b-a+1

26. If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be:
(a) Zero of p(x)
(b) Value of p(x)
(c) Constant of p(x)
(d) None of the above
Answer: (a) Zero of p(x)

27. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial is:
(a) Intersects x-axis
(b) Intersects y-axis
(c) Intersects y-axis or x-axis
(d) None of the above
Answer: (a) Intersects x-axis

8. A polynomial of degree n has:
(a) Only one zero
(b) At least n zeroes
(c) More than n zeroes
(d) At most n zeroes
Answer: (d) At most n zeroes

29. The number of polynomials having zeroes as -2 and 5 is:
(a) 1
(b) 2
(c) 3
(d) More than 3
Answer: (d) More than 3

30. Zeroes of p(x) = x2-27 are:
(a) ±9√3
(b) ±3√3
(c) ±7√3
(d) None of the above
Answer: (b) ±3√3

31. Given that two of the zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0, the third zero is
(a) -b/a
(b) b/a
(c) c/a
(d) -d/a
Answer: (a) -b/a

32. If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is
(a) 10
(b) –10
(c) 5
(d) –5
Answer: (b) -10

33. A quadratic polynomial, whose zeroes are –3 and 4, is
(a) x² – x + 12
(b) x² + x + 12
(c) (x²/2) – (x/2) – 6
(d) 2x² + 2x – 24
Answer: (c) (x²/2) – (x/2) – 6

34. The zeroes of the quadratic polynomial x2 + 99x + 127 are
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal
Answer: (b) both negative

35. The zeroes of the quadratic polynomial x2 + 7x + 10 are
(a) -4, -3
(b) 2, 5
(c) -2, -5
(d) -2, 5
Answer: (c) -2, -5

36. If the discriminant of a quadratic polynomial, D > 0, then the polynomial has
(a) two real and equal roots
(b) two real and unequal roots
(c) imaginary roots
(d) no roots
Answer: (b) two real and unequal roots

37. If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, then the relation between the degrees of p(x) and g(x) is
(a) degree of p(x) < degree of g(x)
(b) degree of p(x) = degree of g(x)
(c) degree of p(x) > degree of g(x)
(d) nothing can be said about degrees of p(x) and g(x)
Answer: (a) degree of p(x) < degree of g(x)

38. By division algorithm of polynomials, p(x) =
(a) g(x) × q(x) + r(x)
(b) g(x) × q(x) – r(x)
(c) g(x) × q(x) × r(x)
(d) g(x) + q(x) + r(x)
Answer: (a) g(x) × q(x) + r(x)

39. The product of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is
(a) -b/a
(b) c/a
(c) -d/a
(d) -c/a
Answer: (c) -d/a

40. If the graph of a polynomial intersects the x-axis at three points, then it contains ____ zeroes.
(a) Three
(b) Two
(c) Four
(d) More than three
Answer: (a) Three

41. The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have:
(a) Unique solution
(b) Exactly two solutions
(c) Infinitely many solutions
(d) No solution
Answer: (c) Infinitely many solutions

42. If a pair of linear equations is consistent, then the lines are:
(a) Parallel
(b) Always coincident
(c) Always intersecting
(d) Intersecting or coincident
Answer: (d) Intersecting or coincident

All competitive exams most important Bits

43. The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have
(a) Unique solution
(b) Exactly two solutions
(c) Infinitely many solutions
(d) No solution
Answer: (d) No solution

44. If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then what is the value of k?
(a) 4/15
(b) 15/4
(c) ⅘
(d) 5/4
Answer: (b) 15/4

45. If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:
(a) -6x+10y-4=0
(b) 6x-10y-4=0
(c) 6x+10y-4=0
(d) -6x+10y+4=0
Answer: (a) -6x+10y-4=0

46.The solution of the equations x-y=2 and x+y=4 is:
(a) 3 and 1
(b) 4 and 3
(c) 5 and 1
(d) -1 and -3
Answer: (a) 3 and 1

47. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:
(a) 3/12
(b) 4/12
(c) 5/12
(d) 7/12
Answer: (c) 5/12

48. The solution of 4/x+3y=14 and 3/x-4y=23 is:
(a) ⅕ and -2
(b) ⅓ and ½
(c) 3 and ½
(d) 2 and ⅓
Answer: (a) ⅕ and -2

49. Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Her speed of rowing in still water and the speed of the current is:
(a) 6km/hr and 3km/hr
(b) 7km/hr and 4km/hr
(c) 6km/hr and 4km/hr
(d) 10km/hr and 6km/hr
Answer: (c) 6km/hr and 4km/hr

50. The angles of cyclic quadrilaterals ABCD are: A = (6x+10), B=(5x)°, C = (x+y)° and D=(3y-10)°. The value of x and y is:
(a) x=20° and y = 10°
(b) x=20° and y = 30°
(c) x=44° and y=15°
(d) x=15° and y=15°
Answer: (b) x=20° and y = 30°

51. The pair of equations x = a and y = b graphically represents lines which are
(a) parallel
(b) intersecting at (b, a)
(c) coincident
(d) intersecting at (a, b)
Answer: (d) intersecting at (a, b)

52. The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has
(a) one solution
(b) two solutions
(c) infinitely many solutions
(d) no solution
Answer: (c) infinitely many solutions

53. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(a) a unique solution
(b) exactly two solutions
(c) infinitely many solutions
(d) no solution
Answer: (d) no solution

54. The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(a) 3
(b) -3
(c) -12
(d) no value
Answer: (d) no value

55. If the lines representing the pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are coincident, then
(a) a1/a2 = b1/b2
(b) a1/a2 = b1/b2 = c1/c2
(c) a1/a2 ≠ b1/b2
(d) a1/a2 = b1/b2 ≠ c1/c2
Answer: (b) a1/a2 = b1/b2 = c1/c2

56. A pair of linear equations which has a unique solution x = 2, y = -3 is
(a) x + y = -1; 2x – 3y = -5
(b) 2x + 5y = -11; 4x + 10y = -22
(c) 2x – y = 1; 3x + 2y = 0
(d) x – 4y – 14 = 0; 5x – y – 13 = 0
Answer: (b) 2x + 5y = -11; 4x + 10y = -22

57. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively
(a) 4 and 24 (b) 5 and 30
(c) 6 and 36 (d) 3 and 24
Answer: (c) 6 and 36

58. If the pair of linear equations has a unique solution, then the lines representing these equations will
(a) coincide
(b) intersect at one point
(c) parallel to each other
(d) parallel to x-axis
Answer: (b) intersect at one point

59. Which of the following method(s) is/are used to find the solution of a pair of linear equations algebraically?
(a) Substitution Method
(b) Elimination Method
(c) Cross- multiplication Method
(d) All the above
Answer: (d) All the above

60. The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15 will be
(a) parallel lines
(b) coincident lines
(c) intersecting lines
(d) perpendicular lines
Answer: (a) parallel lines

61. The points (-1, –2), (1, 0), (-1, 2), (-3, 0) form a quadrilateral of type:
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus
Answer: (a) Square

62. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 2
(b) -2
(c) 1
(d) -1
Answer: (a) 2

63. The midpoint of a line segment joining two points A(2, 4) and B(-2, -4) is
(a) (-2, 4)
(b) (2, -4)
(c) (0, 0)
(d) (-2, -4)
Answer: (c) (0, 0)

64. The distance of point A(2, 4) from the x-axis is
(a) 2 units
(b) 4 units
(c) -2 units
(d) -4 units
Answer: (b) 4 units

65. The distance between the points P(0, 2) and Q(6, 0) is
(a) 4√10
(b) 2√10
(c) √10
(d) 20
Answer: (b) 2√10

66. If O(p/3, 4) is the midpoint of the line segment joining the points P(-6, 5) and Q(-2, 3), the the value of p is:
(a) 7/2
(b) -12
(c) 4
(d) -4
Answer: (b) -12

All competitive exams most important Bits

67. The point which divides the line segment of points P(-1, 7) and (4, -3) in the ratio of 2:3 is:
(a) (-1, 3)
(b) (-1, -3)
(c) (1, -3)
(d) (1, 3)
Answer: (d) (1, 3)

68. The ratio in which the line segment joining the points P(-3, 10) and Q(6, –8) is divided by O(-1, 6) is:
(a) 1:3
(b) 3:4
(c) 2:7
(d) 2:5
Answer: (c) 2:7

69. The coordinates of a point P, where PQ is the diameter of a circle whose centre is (2, – 3) and Q is (1, 4) is:
(a) (3, -10)
(b) (2, -10)
(c) (-3, 10)
(d) (-2, 10)
Answer: (a) (3, -10)

70. The area of a rhombus whose vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:
(a) 12 sq.unit
(b) 24 sq.units
(c) 30 sq.units
(d) 32 sq.units
Answer: (b) 24 sq.units

71. The distance of the point P(–6, 8) from the origin is
(a) 8 units
(b) 2√7 units
(c) 10 units
(d) 6 units
Answer: (c) 10 units

72. The distance between the points (0, 5) and (–5, 0) is
(a) 5 units
(b) 5√2 units
(c) 2√5 units
(d) 10 units
Answer: (b) 5√2 unit

73. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5
(b) 12
(c) 11
(d) 7 + √5
Answer: (b) 12

74. The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is
(A) (a + b + c)2
(B) 0
(C) a + b + c
(D) ab
Answer: (b) 0

75. The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is
(a) (0, 0)
(b) (0, 2)
(c) (2, 0)
(d) (–2, 0)
Answer: (a) (0, 0)

76. If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then
(a) a = b
(b) a = 2b
(c) 2a = b
(d) a = –b
Answer: (c) 2a = b

77. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, then the value of p is
(a) 4
(b) -6
(c) 7
(d) -2
Answer: (c) 7

78. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, -5) is the midpoint of PQ, then the coordinates of P and Q are, respectively
(a) (0, -5) and (2, 0)
(b) (0, 10) and (-4, 0)
(c) (0, 4) and (-10, 0)
(d) (0, -10) and (4, 0)
Answer: (d) (0, -10) and (4, 0)

79. The perpendicular bisector of the line segment joining the points A(1, 5) and B(4, 6) cuts the y-axis at
(a) (0, 13)
(b) (0, –13)
(c) (0, 12)
(d) (13, 0)
Answer: (a) (0, 13)

80. The fourth vertex D of a parallelogram ABCD whose three vertices are A(–2, 3), B(6, 7) and C(8, 3) is
(a) (0, 1)
(b) (0, –1)
(c) (–1, 0)
(d) (1, 0)
Answer: (b) (0, –1)

81. Which of the following triangles have the same side lengths?
(a) Scalene
(b) Isosceles
(c) Equilateral
(d) None of these
Answer: (c) Equilateral

82. Area of an equilateral triangle with side length a is equal to:
(a) (√3/2)a
(b) (√3/2)a2
(c) (√3/4) a2
(d) (√3/4) a
Answer: (c) (√3/4) a2

83. D and E are the midpoints of side AB and AC of a triangle ABC, respectively and BC = 6 cm. If DE || BC, then the length (in cm) of DE is:
(a) 2.5
(b) 3
(c) 5
(d) 6
Answer: (b) 3

84. The diagonals of a rhombus are 16 cm and 12 cm, in length. The side of the rhombus in length is:
(a) 20 cm (b) 8 cm
(c) 10 cm (d) 9 cm
Answer: (c) 10 cm

85. Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of the small triangle is 48 sq.cm, then the area of large triangle is:
(a) 230 sq.cm.
(b) 106 sq.cm
(c) 107 sq.cm.
(d) 108 sq.cm
Answer: (d) 108 sq. cm

86. If perimeter of a triangle is 100 cm and the length of two sides are 30 cm and 40 cm, the length of third side will be:
(a) 30 cm
(b) 40 cm
(c) 50 cm
(d) 60 cm
Answer: (a) 30 cm

87. If triangles ABC and DEF are similar and AB=4 cm, DE=6 cm, EF=9 cm and FD=12 cm, the perimeter of triangle ABC is:
(a) 22 cm
(b) 20 cm
(c) 21 cm
(d) 18 cm
Answer: (d) 18 cm

88. The height of an equilateral triangle of side 5 cm is:
(a) 4.33 cm
(b) 3.9 cm
(c) 5 cm
(d) 4 cm
Answer: (a) 4.33 cm

89. If ABC and DEF are two triangles and AB/DE=BC/FD, then the two triangles are similar if
(a) ∠A=∠F
(b) ∠B=∠D
(c) ∠A=∠D
(d) ∠B=∠E
Answer: (b) ∠B=∠D

90. Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio
(a) 2: 3 (b) 4: 9
(c) 81: 16 (d) 16: 81
Answer: (d) 16: 81

91. Which of the following are not similar figures?
(a) Circles
(b) Squares
(c) Equilateral triangles
(d) Isosceles triangles
Answer: (d) Isosceles triangles

92. In triangle ABC, ∠BAC = 90° and AD ⊥ BC. Then
(A) BD . CD = BC2
(B) AB . AC = BC2
(C) BD . CD = AD2
(D) AB . AC = AD2
Answer: (c) BD . CD = AD2

93. If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then
(a) ΔPQR ~ ΔCAB
(b) ΔPQR ~ ΔABC
(c) ΔCBA ~ ΔPQR
(d) ΔBCA ~ ΔPQR
Answer: (a) ΔPQR ~ ΔCAB

94. In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 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
Answer: (b) similar but not congruent

95. It is given that ΔABC ~ ΔPQR, with BC/QR = 1/4 then, ar(ΔPRQ)/ar(ABC) is equal to
(a) 16
(b) 4
(c) 1/4
(d) 1/16
Answer: (a) 16

96. It is given that ΔABC ~ ΔDFE, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true:
(a) DE = 12 cm, ∠F = 50°
(b) DE = 12 cm, ∠F = 100°
(c) EF = 12 cm, ∠D = 100°
(d) EF = 12 cm, ∠D = 30°
Answer: (b) DE = 12 cm, ∠F = 100°

All competitive exams most important Bits

97. If triangle ABC is similar to triangle DEF, then,
(a) AB/FD = BC/EF = CA/DE
(b) AB/DE = BC/DF = CA/EF
(c) AB/DE = BC/EF = CA/FD
(d) AB/BC = CA/DE = EF/FD
Answer: (c) AB/DE = BC/EF = CA/FD

98. Which of the following is not a similarity criterion for two triangles?
(a) AAA
(b) SAS
(c) SSS
(d) ASA
Answer: (d) ASA

99. The ratio of the areas of two similar triangles is equal to
(a) square of the ratio of their corresponding sides
(b) cube of the ratio of their corresponding sides
(c) square root of the ratio of their corresponding sides
(d) twice the ratio of their corresponding sides
Answer: (a) square of the ratio of their corresponding sides

100. In ∆ABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The angle B is
(a) 120° (b) 60°
(c) 90° (d) 45°
Answer: (c) 90°

Next Paper

Also Read This:

 

Tags:

pm yashasvi scholarship model paper 2023, pm scholarship 2023,#pm yashasvi entrance test 2023 gk model paper, pm yashasvi scholarship 2023 model paper, pm yasasvi model paper,#pm yashasvi, pm yashasvi model paper 2023,yasasvi model paper, pm yasasvi model paper 2023, pm yashasvi scholarship, pm yashasvi scholarship 2023, pm yasasvi model paper class 9, pm yashasvi solved paper,#pm yashasvi entrance test 2023 maths model paper, pm yashasvi model paper, pm yashasvi, pm yashasvi scholarship, pm yashasvi,yashasvi scholarship important bits, pm yashasvi scholarship 2023, pm yashasvi yojana, pm yashasvi scholarship 2023 syllabus,#pm yashasvi, pm yashasvi scholarship online form 2023, pm yashasvi scholarship 2023 eligibility, how to apply for pm yashasvi scholarship, pm yashasvi scholarship 2023 last date, pm yashasvi scholarship 2023 model paper, pm yashasvi scholarship previous year bits pdf

Home | About us | Sitemap | Contact Us

© BharatBadi | All rights reserved