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प्रश्न पत्र · यूपी पीजीटी

UP PGT 2016 — Mathematics (Series A)

1 or 2 February 2019125 प्रश्नसही उत्तर पर +3.4, गलत उत्तर पर −0

पीडीएफ डाउनलोड करेंप्रैक्टिस टेस्ट शुरू करें

प्रश्न उत्तर प्रदेश माध्यमिक शिक्षा सेवा चयन बोर्ड के 1 or 2 February 2019 के पेपर से। हर प्रश्न का उत्तर उसके नीचे है, खोलने पर ही दिखता है, और पूरी उत्तर कुंजी अंत में है। स्कोर पाने के लिए पेपर को समयबद्ध प्रैक्टिस टेस्ट के रूप में दें।

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बोर्ड ने अपनी अंतिम उत्तर कुंजी में प्रश्न 102 हटा दिया: यहाँ दिखाया गया है, बिना उत्तर के, और स्कोर में नहीं गिना जाता।

प्रश्न अंग्रेज़ी में हैं, जैसे मूल पेपर में थे।

Mathematics

1. If A and B are symmetric matrices, then AB is symmetric matrix if and only if
- (a) AB = BA
- (b) AB = – BA
- (c) AB⁻¹ = B⁻¹A
- (d) None of the above
उत्तर देखें
उत्तर: (a)
2. If the roots of the equation x² + x + a = 0, a > 0 are real and distinct, then the roots of the equation x² – 4√a x + 1 = 0 are
- (a) rational
- (b) irrational
- (c) imaginary
- (d) none of the above
उत्तर देखें
उत्तर: (c)
3. The matrix A = is
- (a) Symmetric
- (b) Skew-symmetric
- (c) Orthogonal
- (d) Singular
उत्तर देखें
उत्तर: (c)
4. If 1, ω, ω² are the cube roots of unity, then value of the determinant is
- (a) ω²
- (b) ω
- (c) 1
- (d) 0
उत्तर देखें
उत्तर: (d)
5. Number of terms in the expansion of (2x – y + 3z)²⁰ is
- (a) 228
- (b) 230
- (c) 231
- (d) 236
उत्तर देखें
उत्तर: (c)
6. The sum of two distinct roots of the equation = 0 is
- (a) 3
- (b) 12
- (c) 15
- (d) 9
उत्तर देखें
उत्तर: (c)
7. What is equal to ?
- (a) –1/2
- (b) –1/4
- (c) –1/12
- (d) does not exist
उत्तर देखें
उत्तर: (c)
8. If Q is a non-singular matrix and P is a square matrix such that det(Q⁻¹P²Q) = 4, then det P is equal to
- (a) 0
- (b) 1
- (c) 2
- (d) 4
उत्तर देखें
उत्तर: (c)
9. If A = , then A³ is equal to
- (a) A
- (b) 4A
- (c) 3A
- (d) 2A
उत्तर देखें
उत्तर: (b)
10. If a, b, c are rational numbers and ax² + bx + c = 0 and 2x² + x – 2 = 0 have a common root, then 4a – 2b + 3c is equal to
- (a) –1
- (b) –2
- (c) 0
- (d) 4
उत्तर देखें
उत्तर: (c)
11. If H and K are subgroups of a group G and O(H) = 3, O(K) = 5, O(G) = 30 then O(H ∩ K) is
- (a) 1
- (b) 2
- (c) 3
- (d) 5
उत्तर देखें
उत्तर: (a)
12. If A⁻¹ = , then 2A is equal to
- (a)
- (b)
- (c)
- (d)
उत्तर देखें
उत्तर: (c)
13. If x, y are elements of a group G and O(y) = 3, then O(xyx⁻¹) is
- (a) 1
- (b) 2
- (c) 3
- (d) 6
उत्तर देखें
उत्तर: (c)
14. If f : G → G′ is a group isomorphism then which of the following is true ?
- (a) O(a) < O(f(a))
- (b) O(a) = O(f(a))
- (c) O(a) > O(f(a))
- (d) None of the above
उत्तर देखें
उत्तर: (b)
15. If A = {4ⁿ – 3n – 1, n ∈ N} and B = {9(n – 1), n ∈ N}, then which of the following is true ?
- (a) A ⊆ B
- (b) B ⊆ A
- (c) A ∪ B = A
- (d) None of the above
उत्तर देखें
उत्तर: (a)
16. In the additive group of integers the order of every element except zero is
- (a) finite
- (b) infinite
- (c) some times finite and some times infinite
- (d) none of the above
उत्तर देखें
उत्तर: (b)
17. If W is a subspace of R⁴ spanned by {(1, 0, –1, 0), (0, 1, 0, 1)}, then which of the following is in W ?
- (a) (1, 2, 1, 2)
- (b) (1, 2, –1, 2)
- (c) (2, 2, 3, 2)
- (d) (0, 1, 1, 1)
उत्तर देखें
उत्तर: (b)
18. Let V be a vector space over R consisting of solutions of d²y/dx² – 4y = 0. Dimension of V is
- (a) 0
- (b) 1
- (c) 2
- (d) 4
उत्तर देखें
उत्तर: (c)
19. For what value of m, the vector (m, 3, 1) is a linear combination of the vectors (3, 2, 1) and (2, 1, 0) ?
- (a) 2
- (b) 3
- (c) 5
- (d) 1
उत्तर देखें
उत्तर: (c)
20. Vectors x = (1, 0, 1), y = (–4, a, 4) and z = (a, –1, –a) are linearly dependent in R³, if a is equal to
- (a) 2 only
- (b) –2 only
- (c) ± 2 both
- (d) 0
उत्तर देखें
उत्तर: (c)
21. The equation r(6 – 4 cosθ) = 5 represents
- (a) a parabola
- (b) an ellipse
- (c) a hyperbola
- (d) a circle
उत्तर देखें
उत्तर: (b)
22. The focus of the parabola 4y² – 6x – 4y = 5 is
- (a) (–5/8, 1/2)
- (b) (–3/8, 1/2)
- (c) (–7/8, –1/2)
- (d) (–5/8, –1/2)
उत्तर देखें
उत्तर: (a)
23. Equation 9x² + 2hxy + 4y² + 6x + 2fy = 3 represents two parallel lines if (h + f) is equal to
- (a) 2
- (b) 6
- (c) 8
- (d) 0
उत्तर देखें
उत्तर: (c)
24. If the line y = x + 3 meets the circle x² + y² = 9 at A and B, then the equation of the circle whose diameter is AB, is
- (a) x² + y² + 3x – 3y = 0
- (b) x² + y² – 3x + 3y = 0
- (c) x² + y² + 3x + 3y = 0
- (d) x² + y² – 3x – 3y = 0
उत्तर देखें
उत्तर: (a)
25. Circles x² + y² – 2x – 4y = 0 and x² + y² – 8y – 4 = 0
- (a) touch externally
- (b) touch internally
- (c) do not touch
- (d) none of the above
उत्तर देखें
उत्तर: (b)
26. The centre of the conic 5x² – 6xy + 5y² + 22x – 26y + 29 = 0 is
- (a) (–1, 1)
- (b) (–1, 2)
- (c) (2, 2)
- (d) (0, 3)
उत्तर देखें
उत्तर: (b)
27. If e and e′ be the eccentricities of the hyperbola x²/a² – y²/b² = 1 and its conjugate hyperbola, then
- (a) e² + e′² = 1
- (b) e = e′
- (c) 1/e² + 1/e′² = 1
- (d) 1/e² – 1/e′² = 1
उत्तर देखें
उत्तर: (c)
28. Centre of circle passing through the points (2, 0), (0, 6) and (5, 1) is
- (a) (3/2, 1)
- (b) (2, 3)
- (c) (5/2, 2)
- (d) (5/2, 7/2)
उत्तर देखें
उत्तर: (d)
29. The vertices of a hyperbola are (1, 0) and (–1, 0) and the foci are (2, 0) and (–2, 0). The equation of the hyperbola is
- (a) 3x² – y² = 3
- (b) 2x² – 3y² = 3
- (c) x² – 3y² = 2
- (d) 3x² – 2y² = 6
उत्तर देखें
उत्तर: (a)
30. Equation of a cone, whose vertex is at origin and base is the curve z = k, f(x, y) = 0, is
- (a) f(xk/z, yk/z) = 0
- (b) f(k, xyz) = 0
- (c) f(ky, kxz) = 0
- (d) none of the above
उत्तर देखें
उत्तर: (a)
31. is equal to
- (a) 7/5
- (b) 5/7
- (c) 2/7
- (d) 2/5
उत्तर देखें
उत्तर: (b)
32. If f(x + 1/x) = x³ + 1/x³, then f(1) is equal to
- (a) –3
- (b) –2
- (c) –1
- (d) 0
उत्तर देखें
उत्तर: (b)
33. Number of points, where the function f(x) = |x + 3| + |x² – 4| is not differentiable, is
- (a) 0
- (b) 1
- (c) 2
- (d) 3
उत्तर देखें
उत्तर: (d)
34. What is the general solution of the differential equation ydx – (x + 2y²)dy = 0 ?
- (a) x = y² + cy
- (b) x = 2cy²
- (c) x = 2y² + cy
- (d) x = 2y + cy²
उत्तर देखें
उत्तर: (c)
35. dx is equal to
- (a) 1/2
- (b) 3/2
- (c) 5/2
- (d) 2
उत्तर देखें
उत्तर: (c)
36. If f(x) = √(4 – x²), then is equal to
- (a) 1/√3
- (b) √3
- (c) 0
- (d) 2/√3
उत्तर देखें
उत्तर: (a)
37. Value of dx is equal to
- (a) 0
- (b) 1/3
- (c) 2/3
- (d) 4/3
उत्तर देखें
उत्तर: (d)
38. Solution of the differential equation , y(0) = 1 is
- (a) y√(x² + y²) = 2x + y
- (b) x√(x² + y²) = x + y
- (c) y√(x² + y²) = x + y
- (d) x√(x² + y²) = 2x + y
उत्तर देखें
उत्तर: (c)
39. Maclaurin’s expansion of tan⁻¹x is
- (a)
- (b)
- (c)
- (d)
उत्तर देखें
उत्तर: (b)
40. Number of asymptotes of the curve x²y – 3x² – 5xy + 6y + 2 = 0 is
- (a) 0
- (b) 1
- (c) 2
- (d) 3
उत्तर देखें
उत्तर: (d)
41. If y = , then value of dy/dx at x = 2 is
- (a) 1
- (b) 2
- (c) 0
- (d) 3
उत्तर देखें
उत्तर: (c)
42. The differential equation for the family of curves y = Ae²ˣ + Be⁻²ˣ, where A and B are arbitrary constants, is
- (a) d²y/dx² + 4y = 0
- (b) d²y/dx² – 4y = 0
- (c) d²y/dx² + dy/dx – 4y = 0
- (d) d²y/dx² + 4 dy/dx – y = 0
उत्तर देखें
उत्तर: (b)
43. tan⁻¹x > cot⁻¹x is true for
- (a) x = 1
- (b) x > 1
- (c) x < 1
- (d) All values of x
उत्तर देखें
उत्तर: (b)
44. Which one of the following is correct ?
- (a) sinh⁻¹x = i sin⁻¹(ix)
- (b) cosh⁻¹x = log(x + √(1 – x²))
- (c) cosh⁻¹x = i cos⁻¹(ix)
- (d) tanh⁻¹x = –i tan⁻¹(ix)
उत्तर देखें
उत्तर: (d)
45. Value of is
- (a) π + 2 tan⁻¹x
- (b) π/2 + 2tan⁻¹x
- (c) π/2 – 2tan⁻¹x
- (d) π – 2 tan⁻¹x
उत्तर देखें
उत्तर: (d)
46. If |z + 5| ≤ 2, z = x + iy, then the greatest value of |z + 2| is
- (a) 2
- (b) 4
- (c) 5
- (d) 6
उत्तर देखें
उत्तर: (c)
47. If i = √–1, then the general value of iⁱ is equal to
- (a)
- (b)
- (c)
- (d) none of the above
उत्तर देखें
उत्तर: (b)
48. Sinh⁻¹(cot x) is equal to
- (a) log(cosx + sinx)
- (b) log(cosx – sinx)
- (c) log(cotx + cosecx)
- (d) log(tanx + cotx)
उत्तर देखें
उत्तर: (c)
49. If A + iB = , then value of A – B is
- (a) 1/5
- (b) 2/5
- (c) 3/5
- (d) –1/5
उत्तर देखें
उत्तर: (c)
50. If |a⃗| + |b⃗| = |c⃗| and a⃗ + b⃗ = c⃗, then angle between a⃗ and b⃗ is
- (a) 0°
- (b) 45°
- (c) 90°
- (d) 180°
उत्तर देखें
उत्तर: (a)
51. If vectors p⃗ = xî + 3ĵ + 2k̂, a⃗ = 2î + 2ĵ + 3k̂ and b⃗ = 2î + 3ĵ + 4k̂ are coplanars, then value of x is
- (a) 2
- (b) –2
- (c) 3
- (d) –3
उत्तर देखें
उत्तर: (b)
52. If â and b̂ are two unit vectors inclined at an angle 30° to each other, then |â + b̂| is equal to
- (a) √3 – 1
- (b) √3 + 1
- (c) (√3 – 1)/√2
- (d) (√3 + 1)/√2
उत्तर देखें
उत्तर: (d)
53. If F⃗ = grad (x³ + y³ + z³ – 3xyz), then F⃗ is
- (a) solenoidal
- (b) irrotational
- (c) solenoidal and irrotational both
- (d) none of the above
उत्तर देखें
उत्तर: (b)
54. A vector, which is normal to the surface x² – xy + yz = 5 at the point (1, 2, 3) is
- (a) î + 2ĵ
- (b) 2ĵ + 2k̂
- (c) 2î + k̂
- (d) ĵ + 2k̂
उत्तर देखें
उत्तर: (b)
55. Which one of the following is not correct for a common catenary ?
- (a)
- (b) ds/dψ = c sec²ψ
- (c)
- (d)
उत्तर देखें
उत्तर: (c)
56. A ball is thrown vertically upward with a given velocity. It reaches a maximum height 100 m. If on second time its initial velocity is doubled then the ball will reach a maximum height of
- (a) 100 m
- (b) 150 m
- (c) 200 m
- (d) 400 m
उत्तर देखें
उत्तर: (d)
57. A stone is projected horizontally with a velocity 9.8 m/s from a tower of height 100 m. Its speed after 1 sec. of projection is (g = 9.8 m/s²)
- (a) 9.8 m/s
- (b) 4.9 m/s
- (c) 9.8 √2 m/s
- (d) None of the above
उत्तर देखें
उत्तर: (c)
58. If a body is acted upon by three forces and body is in equilibrium, then
- (a) All of them are parallel
- (b) They meet at a point
- (c) Any two of them are parallel
- (d) Either they are all parallel or they meet in a point
उत्तर देखें
उत्तर: (d)
59. Two projectiles are projected with same velocity but with angles of projection (45° – θ) and (45° + θ). Ratio of their horizontal range is
- (a) 1 : 2
- (b) 1 : 3
- (c) 2 : 1
- (d) 1 : 1
उत्तर देखें
उत्तर: (d)
60. The Cartesian equation of a common catenary is
- (a)
- (b)
- (c)
- (d)
उत्तर देखें
उत्तर: (d)
61. Domain of the function f(x) = √(2ˣ – 5ˣ) is
- (a) x < 0
- (b) x ≤ 0
- (c) x > 0
- (d) x ≥ 0
उत्तर देखें
उत्तर: (b)
62. If f(x) = (x – 1)/(x + 2) and y = f⁻¹(x), then dy/dx is equal to
- (a) 3/(1 – x)
- (b) 3/(1 + x)
- (c) 3/(1 – x)²
- (d) 3/(1 + x)²
उत्तर देखें
उत्तर: (c)
63. The value of 1² + 3² + 5² + . . . + (2n – 1)² is
- (a) (1/3) n(4n² – 1)
- (b) (1/3) n(4n² + 1)
- (c) (1/6) n(4n² – 1)
- (d) (1/6) n(4n² + 1)
उत्तर देखें
उत्तर: (a)
64. The least value of ‘n’, for which 1 + 3 + 3² + . . . + 3ⁿ⁻¹ > 700, is equal to
- (a) 4
- (b) 5
- (c) 6
- (d) 7
उत्तर देखें
उत्तर: (d)
65. If = 3 : 5, then n is equal to
- (a) 2
- (b) 3
- (c) 4
- (d) 5
उत्तर देखें
उत्तर: (c)
66. The inverse of a skew-symmetric of order 3
- (a) is a skew-symmetric matrix
- (b) is a symmetric matrix
- (c) is a diagonal matrix
- (d) does not exist
उत्तर देखें
उत्तर: (d)
67. If the sum of the coefficients of powers of x in the expansion of (a²x³ – 8ax² + 16)⁴⁸ is zero, then a is equal to
- (a) –2
- (b) –1
- (c) 2
- (d) 4
उत्तर देखें
उत्तर: (d)
68. Value of is
- (a)
- (b)
- (c)
- (d)
उत्तर देखें
उत्तर: (c)
69. The system of linear equations x₁ + 2x₂ + x₃ = 3 2x₁ + 3x₂ + x₃ = 3 3x₁ + 5x₂ + 2x₃ = 1 has
- (a) infinitely many solutions
- (b) exactly 3 solutions
- (c) unique solution
- (d) no solution
उत्तर देखें
उत्तर: (d)
70. If 5ᵗʰ term of a harmonic progression is 7 and 7ᵗʰ term is 5, then 35ᵗʰ term is
- (a) 0
- (b) 1
- (c) 7/12
- (d) 1/35
उत्तर देखें
उत्तर: (b)
71. If log3, log(3ˣ – 2) and log(3ˣ + 4) are in arithmetical progression, then x is equal to
- (a) log₃4
- (b) log₂3
- (c) log₃8
- (d) log₈3
उत्तर देखें
उत्तर: (c)
72. There are 15 points in a plane such that no three of them are collinear. The number of triangles formed by joining them is
- (a) 455
- (b) 2730
- (c) 355
- (d) 454
उत्तर देखें
उत्तर: (a)
73. If G is a cyclic group of order 30, then total number of subgroups of G is
- (a) 6
- (b) 7
- (c) 8
- (d) 9
उत्तर देखें
उत्तर: (c)
74. If every element of a group G is its own inverse, then G is
- (a) finite
- (b) infinite
- (c) abelian
- (d) non-abelian
उत्तर देखें
उत्तर: (c)
75. 1³ – 2³ + 3³ – 4³ + ... –10³ + 11³ is equal to
- (a) 512
- (b) 756
- (c) 848
- (d) 954
उत्तर देखें
उत्तर: (b)
76. In the group G = {{2, 4, 6, 8}, ·₁₀} the identity element is
- (a) 2
- (b) 4
- (c) 6
- (d) 8
उत्तर देखें
उत्तर: (c)
77. Let G be a group with binary operation ∗ defined by a ∗ b = a + b + 1, ∀ a, b ∈ G. Inverse of element C of G is
- (a) 2 + C
- (b) 2 – C
- (c) –2 + C
- (d) –2 – C
उत्तर देखें
उत्तर: (d)
78. Number of all onto functions from the set {1, 2, 3, 4, 5} to itself is
- (a) 2⁵
- (b) 2⁵ – 1
- (c)
- (d)
उत्तर देखें
उत्तर: (c)
79. Every subgroup of a cyclic group is
- (a) normal
- (b) normal only when order of subgroup is prime
- (c) non-normal
- (d) normal when order of group is prime
उत्तर देखें
उत्तर: (a)
80. Which one of the following is a subspace of vector space R³ ?
- (a) {(a, b, c) ∈ R³ : a + b = 0}
- (b) {(a, b, c) ∈ R³ : a – b = 2}
- (c) {(a, b, c) ∈ R³ : a + b = 1}
- (d) {(a, b, c) ∈ R³ : a – b = 1}
उत्तर देखें
उत्तर: (a)
81. If T : U → V be a linear transformation then Kernel T is a subspace of
- (a) U ∩ V
- (b) U
- (c) V
- (d) U/V
उत्तर देखें
उत्तर: (b)
82. If T : V₂(R) → V₃(R) be defined as T(a, b) = (a + b, a – b, b) is a linear transformation, then nullity T is
- (a) 0
- (b) 1
- (c) 2
- (d) 3
उत्तर देखें
उत्तर: (a)
83. If V = R³, W = {(a, 0, 0) ∈ R³}, then dimension of vector space V/W is
- (a) 1
- (b) 2
- (c) 3
- (d) 4
उत्तर देखें
उत्तर: (b)
84. Let α, β be the roots of the equation x² + ax + a³ = 0, a ≠ 0. If (α, β) lies on the parabola y² = x, then the roots of the equation are
- (a) 2, 3
- (b) 4, –2
- (c) 4, 2
- (d) 2, – 3
उत्तर देखें
उत्तर: (b)
85. If 2x – y + z + 4 = 0 is a tangent plane to the sphere whose centre is (1, 0, 1), then radius of sphere is
- (a) 7
- (b) 7/√6
- (c) 5/√6
- (d) 5
उत्तर देखें
उत्तर: (b)
86. If the slope of one of lines represented by ax² – 6xy + y² = 0 is square of the slope of the other line, then the value of a are
- (a) 8, – 27
- (b) – 8, 27
- (c) 6, – 24
- (d) – 6, 24
उत्तर देखें
उत्तर: (a)
87. Distance of the point P(1, –2) from the centre of the circle x = 2 + 3cosθ, y = –4 + 3sinθ is
- (a) √7
- (b) √5
- (c) √3
- (d) √2
उत्तर देखें
उत्तर: (b)
88. The equations of the lines bisecting the angles between the pair of lines 3x² + xy – 2y² = 0 is
- (a) x² – 10xy – y² = 0
- (b) x² + 10xy – y² = 0
- (c) x² + 10xy + y² = 0
- (d) x² + xy – y² = 0
उत्तर देखें
उत्तर: (a)
89. In three dimensional geometry equation x² + y² = r² represents a
- (a) circle
- (b) sphere
- (c) cylinder
- (d) cone
उत्तर देखें
उत्तर: (c)
90. The equation of a plane containing x-axis is
- (a) ax + by = 0
- (b) by + cz = 0
- (c) ax + cz = 0
- (d) x + y + z = 0
उत्तर देखें
उत्तर: (b)
91. Let S and S′ be the foci and BB′ be the minor axis of an ellipse. If ∠BSS′ = θ, then eccentricity of the ellipse is
- (a) cos θ
- (b) sin θ
- (c) tan θ
- (d) cot θ
उत्तर देखें
उत्तर: (a)
92. If line ax + by + c = 0 is a normal to the curve xy = 4, then
- (a) a < 0, b < 0
- (b) a > 0, b > 0
- (c) a > 0, b < 0
- (d) a < 0, b = 0
उत्तर देखें
उत्तर: (c)
93. Maximum value of the function f(x) = is equal to
- (a) 3
- (b) 9
- (c) 27
- (d) 81
उत्तर देखें
उत्तर: (b)
94. If xy = 1, then is equal to
- (a) 0
- (b) 1
- (c) y
- (d) not defined
उत्तर देखें
उत्तर: (a)
95. If z = , then is equal to
- (a) (1/5) sin z
- (b) (2/5) tan z
- (c) (2/5) sin z
- (d) tan z
उत्तर देखें
उत्तर: (b)
96. If dx = a sin⁻¹ 3ˣ + C, then a is equal to
- (a) log 3
- (b) 1/log3
- (c) 1/2
- (d) 1
उत्तर देखें
उत्तर: (b)
97. What is , a > – 1, equal to ?
- (a) 1/(a + 1)
- (b) 2/(a + 1)
- (c) a/(a + 1)
- (d) (a – 1)/(a + 1)
उत्तर देखें
उत्तर: (a)
98. If 2y = x + 3 is a tangent line to the curve y³ = ax² + b at the point (1, 2), then 3b – 5a is equal to
- (a) 0
- (b) 2
- (c) 3
- (d) 4
उत्तर देखें
उत्तर: (a)
99. The least possible value of ‘a’ for which the function f(x) = x² + ax + 1 may be increasing in the interval [1, 2] is
- (a) 2
- (b) 1
- (c) 0
- (d) –2
उत्तर देखें
उत्तर: (d)
100. The area bounded by the curve y = sinx + cosx and the co-ordinate axes in the first quadrant is
- (a) √2 – 1
- (b) √2
- (c) √2 + 1
- (d) 1
उत्तर देखें
उत्तर: (c)
101. If z = f(x – y, y – t, t – x), then ∂z/∂x + ∂z/∂y + ∂z/∂t is equal to
- (a) x + y + t
- (b) x + y + t + 1
- (c) 1
- (d) 0
उत्तर देखें
उत्तर: (d)
102. If y = , then dy/dx is equal to
- (a) 3x/(x² + a²)
- (b) 3a/(x² + a²)
- (c) 3/(x² + a²)
- (d) a/(x² + a²)
उत्तर देखें
उत्तर: —
103. If a and b are arbitrary constants, then the partial differential equation of z = ax + a²y² + b is
- (a) q = 2py
- (b) p = 2q²y
- (c) q = 2p²y
- (d) p = xq²
उत्तर देखें
उत्तर: (c)
104. Solution of the differential equation (y – px) (p – 1) = p, p = dy/dx is (Where c is an arbitrary constant)
- (a) y = cx + c/(c – 1)
- (b) y = x² + c
- (c) y = cx + 2
- (d) y² = cx + 3
उत्तर देखें
उत्तर: (a)
105. If , then
- (a) A = 1, B = 0
- (b) A = 0, B = 1
- (c) A = 1, B = ∞
- (d) A = ∞, B = 1
उत्तर देखें
उत्तर: (b)
106. Which one of the following is not correct ?
- (a) tan iθ = i tanh θ
- (b) cos iθ = cosh θ
- (c) cot iθ = i coth θ
- (d) sin iθ = i sinh θ
उत्तर देखें
उत्तर: (c)
107. Sum of the series + . . . is
- (a) π/4
- (b) π/2
- (c) π/8
- (d) 3π/4
उत्तर देखें
उत्तर: (c)
108. Value of tan⁻¹(1/2) + tan⁻¹(1/5) + tan⁻¹(1/8) is
- (a) π/4
- (b) π/2
- (c) π
- (d) tan⁻¹2
उत्तर देखें
उत्तर: (a)
109. The equation sin⁴θ – 2 cos²θ + a² = 0 will have atleast one solution, if
- (a) |a| ≤ 1½
- (b) |a| ≤ 2
- (c) |a| ≤ √2
- (d) |a| ≥ 1
उत्तर देखें
उत्तर: (c)
110. If = A + iB, where A and B are real, then √(A² + B²) is equal to
- (a)
- (b)
- (c)
- (d)
उत्तर देखें
उत्तर: (a)
111. 2 sinh(x + y) cosh(x – y) is equal to
- (a) sin 2x + sin 2y
- (b) sin 2x + sinh 2y
- (c) sinh 2x + sinh 2y
- (d) sinh 2x + sin 2y
उत्तर देखें
उत्तर: (c)
112. In a triangle ABC, a = 5, b = 7 and sin A = 3/4. How many such triangles are possible ?
- (a) 0
- (b) 1
- (c) 2
- (d) 3
उत्तर देखें
उत्तर: (a)
113. If div (rⁿ r⃗) = 0, then n is equal to
- (a) –3
- (b) 1
- (c) 2
- (d) –1
उत्तर देखें
उत्तर: (a)
114. If A⃗ = î + ĵ + k̂, A⃗.B⃗ = 2 and A⃗ × B⃗ = ĵ – k̂, then |3B⃗| is equal to
- (a) 2√2
- (b) 3√2
- (c) 2√3
- (d) 3√3
उत्तर देखें
उत्तर: (b)
115. If (A⃗ × B⃗)² + (A⃗.B⃗)² = 81 and |B⃗| = 3, then |A⃗| is equal to
- (a) 9
- (b) 3
- (c) 27
- (d) 1
उत्तर देखें
उत्तर: (b)
116. Value of [î – ĵ, ĵ – k̂, k̂ – ĵ] is
- (a) 1
- (b) 2
- (c) 3
- (d) 0
उत्तर देखें
उत्तर: (d)
117. The directional derivative of ϕ = xy + yz + zx at (1, 1, 1) in the direction of the vector î – 2ĵ + 2k̂ is
- (a) 1/3
- (b) 2/3
- (c) 5/3
- (d) 7/3
उत्तर देखें
उत्तर: (b)
118. If u⃗ and v⃗ are vector point function and ϕ is a scalar function, then which statement of the following is meaningful ?
- (a) ∇⃗ u⃗
- (b) ∇⃗(u⃗ × v⃗)
- (c) ∇⃗(ϕu⃗)
- (d) ∇⃗(u⃗ · v⃗)
उत्तर देखें
उत्तर: (d)
119. The motion of a projectile is described by the equation y = ax – bx². Range of projectile is
- (a) a/b
- (b) a/2b
- (c) 2a/b
- (d) none of the above
उत्तर देखें
उत्तर: (a)
120. If two equal perfectly elastic bodies impinge directly, then after impinge
- (a) Both interchange their velocities
- (b) Both come to rest
- (c) Velocities of both do not change
- (d) None of the above
उत्तर देखें
उत्तर: (a)
121. The centre of gravity of a solid right circular cone of height h is
- (a) At distance h/4 from vertex
- (b) At distance 3h/4 from vertex
- (c) At distance h/2 from vertex
- (d) None of the above
उत्तर देखें
उत्तर: (b)
122. The resultant of P⃗ and Q⃗ is R⃗. If P⃗ is reversed and Q⃗ remaining the same the new resultant becomes R⃗′. If R⃗ is perpendicular to R⃗′, then |P⃗| : |Q⃗| is
- (a) 1 : 2
- (b) 1 : 1
- (c) 2 : 1
- (d) 2 : 3
उत्तर देखें
उत्तर: (b)
123. The number of numbers between 100 and 300 that are divisible by 5 but not by 15 is
- (a) 20
- (b) 26
- (c) 32
- (d) 35
उत्तर देखें
उत्तर: (b)
124. The coefficient of the middle term in the expansion of (1 + 3x + 3x² + x³)⁸ in powers of x is
- (a) ¹²C₆
- (b) ¹²C₈
- (c) ²⁴C₈
- (d) ²⁴C₁₂
उत्तर देखें
उत्तर: (d)
125. Two constant forces P⃗ = 2î – 5ĵ + 6k̂ and Q⃗ = –î + 2ĵ – k̂ act on a particle at the point A(4, –3, –2). Moment of the resultant force about O(0, 0, 0) is
- (a) 21î + 22ĵ + 9k̂
- (b) –21î – 22ĵ – 9k̂
- (c) 21î – 22ĵ + 9k̂
- (d) 21î – 22ĵ – 9k̂
उत्तर देखें
उत्तर: (b)

उत्तर देखें

उत्तर कुंजी

उत्तर कुंजी इस परीक्षा की उत्तर प्रदेश माध्यमिक शिक्षा सेवा चयन बोर्ड की आधिकारिक उत्तर कुंजी से है। “—” का अर्थ है कि कुंजी में उत्तर नहीं दिया गया: प्रश्न हटाया गया।

Mathematics

प्र. 1: (a)
प्र. 2: (c)
प्र. 3: (c)
प्र. 4: (d)
प्र. 5: (c)
प्र. 6: (c)
प्र. 7: (c)
प्र. 8: (c)
प्र. 9: (b)
प्र. 10: (c)
प्र. 11: (a)
प्र. 12: (c)
प्र. 13: (c)
प्र. 14: (b)
प्र. 15: (a)
प्र. 16: (b)
प्र. 17: (b)
प्र. 18: (c)
प्र. 19: (c)
प्र. 20: (c)
प्र. 21: (b)
प्र. 22: (a)
प्र. 23: (c)
प्र. 24: (a)
प्र. 25: (b)
प्र. 26: (b)
प्र. 27: (c)
प्र. 28: (d)
प्र. 29: (a)
प्र. 30: (a)
प्र. 31: (b)
प्र. 32: (b)
प्र. 33: (d)
प्र. 34: (c)
प्र. 35: (c)
प्र. 36: (a)
प्र. 37: (d)
प्र. 38: (c)
प्र. 39: (b)
प्र. 40: (d)
प्र. 41: (c)
प्र. 42: (b)
प्र. 43: (b)
प्र. 44: (d)
प्र. 45: (d)
प्र. 46: (c)
प्र. 47: (b)
प्र. 48: (c)
प्र. 49: (c)
प्र. 50: (a)
प्र. 51: (b)
प्र. 52: (d)
प्र. 53: (b)
प्र. 54: (b)
प्र. 55: (c)
प्र. 56: (d)
प्र. 57: (c)
प्र. 58: (d)
प्र. 59: (d)
प्र. 60: (d)
प्र. 61: (b)
प्र. 62: (c)
प्र. 63: (a)
प्र. 64: (d)
प्र. 65: (c)
प्र. 66: (d)
प्र. 67: (d)
प्र. 68: (c)
प्र. 69: (d)
प्र. 70: (b)
प्र. 71: (c)
प्र. 72: (a)
प्र. 73: (c)
प्र. 74: (c)
प्र. 75: (b)
प्र. 76: (c)
प्र. 77: (d)
प्र. 78: (c)
प्र. 79: (a)
प्र. 80: (a)
प्र. 81: (b)
प्र. 82: (a)
प्र. 83: (b)
प्र. 84: (b)
प्र. 85: (b)
प्र. 86: (a)
प्र. 87: (b)
प्र. 88: (a)
प्र. 89: (c)
प्र. 90: (b)
प्र. 91: (a)
प्र. 92: (c)
प्र. 93: (b)
प्र. 94: (a)
प्र. 95: (b)
प्र. 96: (b)
प्र. 97: (a)
प्र. 98: (a)
प्र. 99: (d)
प्र. 100: (c)
प्र. 101: (d)
प्र. 102: —
प्र. 103: (c)
प्र. 104: (a)
प्र. 105: (b)
प्र. 106: (c)
प्र. 107: (c)
प्र. 108: (a)
प्र. 109: (c)
प्र. 110: (a)
प्र. 111: (c)
प्र. 112: (a)
प्र. 113: (a)
प्र. 114: (b)
प्र. 115: (b)
प्र. 116: (d)
प्र. 117: (b)
प्र. 118: (d)
प्र. 119: (a)
प्र. 120: (a)
प्र. 121: (b)
प्र. 122: (b)
प्र. 123: (b)
प्र. 124: (d)
प्र. 125: (b)