प्रिय छात्रों,
यदिआप सभी इस मॉडल पेपर को पूरी तरह से हल कर लेते हैं और हर एक टॉपिक को अच्छे से समझ लेते हैं, तो आपका MPTET VARG 2 (मध्य प्रदेश शिक्षक पात्रता परीक्षा वर्ग 2) में सिलेक्शन पक्का है। यह पेपर विशेष रूप से परीक्षा में पूछे जाने वाले महत्वपूर्ण टॉपिक्स और पैटर्न को ध्यान में रखकर तैयार किया गया है। इसे ध्यानपूर्वक हल करके आप:
1. **आत्मविश्वास बढ़ाएं**: परीक्षा के पैटर्न और प्रश्नों के प्रकार से परिचित होंगे।
2. **कमजोरियों को पहचानें**: जिन टॉपिक्स में आपको और अभ्यास की जरूरत है, उन्हें समझ पाएंगे।
3. **समय प्रबंधन सुधारें**: निर्धारित समय में प्रश्नों को हल करने की क्षमता विकसित करेंगे।
4. **सटीकता बढ़ाएं**: बार-बार अभ्यास करके गलतियों को कम करेंगे।
याद रखें, मेहनत और लगन से ही सफलता मिलती है। यदि आप पूरी मेहनत करेंगे, तो सफलता जरूर मिलेगी। शुभकामनाएं!
**ध्यान केंद्रित रहें, दृढ़ निश्चयी बनें!**
- आपका हितैषी
Sanjeev khare
1. Which of the following is an irrational number?
A) 3/4 B) √2 C) 0.75 D) -1
Ans: B) √2
2. The decimal expansion of 7/8 is:
A) Non-terminating repeating B) Non-terminating non-repeating
C) Terminating D) Irrational
Ans: C) Terminating
3. The product of a rational and irrational number is:
A) Rational B) Irrational C) Integer D) Even number
Ans: B) Irrational
4. Euclid’s Division Lemma is used to find:
A) LCM B) HCF C) Square D) Cube
Ans: B) HCF
5. The Fundamental Theorem of Arithmetic deals with:
A) Primes B) Surds C) Integers D) Natural Numbers
Ans: A) Primes
6. 0.232323... is:
A) Rational B) Irrational C) Integer D) Natural
Ans: A) Rational
7. √49 is:
A) Irrational B) Prime C) Rational D) Composite
Ans: C) Rational
8. If x² = 5, then x is:
A) Rational B) Irrational C) Integer D) Even
Ans: B) Irrational
9. Which number has a non-terminating, non-repeating decimal expansion?
A) 4/5 B) 22/7 C) √3 D) 0.8
Ans: C) √3
10. According to laws of exponents, (a^m)*(a^n) = ?
A) a^(m-n) B) a^(m+n) C) a^(mn) D) a^(m/n)
Ans: B) a^(m+n)
11. Which of the following is a polynomial?
A) 3x² + 2/x B) x² - √x C) x³ - 2x + 1 D) √x + 5
Ans: C) x³ - 2x + 1
12. The degree of 3x⁴ - 5x² + 6 is:
A) 2 B) 3 C) 4 D) 5
Ans: C) 4
13. Zeroes of the polynomial x² - 9 are:
A) 3, -3 B) 0, 9 C) -3, -9 D) 1, -9
Ans: A) 3, -3
14. Which algebraic identity is used in (a + b)²?
A) a² - b² B) a² + 2ab + b² C) a² + b² D) a³ + b³
Ans: B) a² + 2ab + b²
15. If a + b = 0, then a³ + b³ = ?
A) 0 B) ab C) a² + b² D) 3ab
Ans: A) 0
16. x² + 5x + 6 = 0 has zeroes:
A) -2, -3 B) 2, 3 C) 1, 6 D) -1, -6
Ans: A) -2, -3
17. If one zero of a polynomial is 2 and the sum of zeroes is 5, the other zero is:
A) 3 B) -3 C) 7 D) 2
Ans: A) 3
18. The graph of a linear equation in two variables is a:
A) Circle B) Line C) Parabola D) Hyperbola
Ans: B) Line
19. A pair of linear equations can have:
A) No solution B) One solution C) Infinite solutions D) All of these
Ans: D) All of these
20. Which method is not used to solve a pair of linear equations?
A) Substitution B) Elimination C) Division D) Graphical
Ans: C) Division
21. x² - 4x + 4 = 0 has:
A) Two distinct roots B) One root C) No real root D) Three roots
Ans: B) One root
22. The roots of x² + 2x - 15 = 0 are:
A) -5, 3 B) 5, -3 C) -5, -3 D) 5, 3
Ans: A) -5, 3
23. The quadratic formula is:
A) (-b ± √b² - 4ac)/2a B) (b ± √a² - 4bc)/2c
Ans: A) (-b ± √b² - 4ac)/2a
24. Discriminant (D) = 0 implies:
A) No roots B) Equal roots C) Real and distinct roots D) Imaginary roots
Ans: B) Equal roots
25. x² - 7x + 10 = 0; product of roots = ?
A) -7 B) 17 C) 10 D) -10
26. Sum of angles in a triangle is:
A) 90° B) 180° C) 360° D) 270°
Ans: B) 180°
27. Alternate interior angles are:
A) Equal B) Unequal C) 90° D) 180°
Ans: A) Equal
28. Two triangles are congruent if:
A) Sides are equal B) Angles are equal C) One side and two angles match D) All of these
Ans: D) All of these
29. Which is not a property of a parallelogram?
A) Opposite sides are equal B) Diagonals are equal C) Opposite angles are equal D) Adjacent angles are supplementary
Ans: B) Diagonals are equal
30. A rhombus has:
A) Equal angles B) Equal diagonals C) Equal sides D) All sides and angles equal
Ans: C) Equal sides
31. Midpoint theorem states:
A) Midpoint connects two triangles B) Line joining midpoints is parallel to third side
Ans: B) Line joining midpoints is parallel to third side
32. Two circles intersect in:
A) 1 point B) 2 points C) 3 points D) No point
Ans: B) 2 points
33. Number of tangents from a point outside the circle:
A) 1 B) 2 C) 3 D) Infinite
Ans: B) 2
34. Angle subtended by a diameter at circle =
A) 45° B) 90° C) 60° D) 180°
Ans: B) 90°
35. Area of triangle with sides 5, 6, 7 using Heron’s Formula is:
A) 15 B) 18 C) 13.5 D) 10
Ans: C) 13.5
36. Area of circle =
A) 2πr B) πr² C) πd D) r²
Ans: B) πr²
37. Surface area of cube =
A) 6a² B) a³ C) 4a² D) a²
Ans: A) 6a²
38. Volume of a cone =
A) (1/3)πr²h B) πr²h C) (2/3)πr²h D) (1/2)πr²h
Ans: A) (1/3)πr²h
39. Total surface area of sphere =
A) 2πr² B) 4πr² C) πr² D) πr³
Ans: B) 4πr²
40. Frustum is obtained by:
A) Rotating a line B) Cutting a cone horizontally
Ans: B) Cutting a cone horizontally
41. sin 30° =
A) 1 B) √3/2 C) 1/2 D) 0
Ans: C) 1/2
42. cos 60° =
A) 0 B) 1/2 C) √3/2 D) 1
Ans: B) 1/2
43. tan 45° =
A) 1 B) 0 C) ∞ D) 2
Ans: A) 1
44. sin²θ + cos²θ =
A) 1 B) 2 C) 0 D) sinθ
Ans: A) 1
45. sec θ =
A) 1/sinθ B) 1/cosθ C) tanθ D) sinθ/cosθ
Ans: B) 1/cosθ
46. tanθ = sinθ / ?
A) cosθ B) secθ C) cotθ D) tanθ
Ans: A) cosθ
47. If θ = 0°, sinθ =
A) 1 B) 0 C) ∞ D) -1
Ans: B) 0
48. Complementary angle of 30° =
A) 90° B) 60° C) 30° D) 0°
Ans: B) 60°
49. Angle of elevation means:
A) Line of sight upward B) Horizontal line C) Downward vision
Ans: A) Line of sight upward
50. Height & Distance concept uses:
A) Similar triangles B) Congruent triangles C) Trapezium D) Circle
Ans: A) Similar triang
51. √(-4) =
A) 2 B) -2 C) 2i D) i
Ans: C) 2i
52. i² =
A) -1 B) 1 C) 0 D) i
Ans: A) -1
53. Modulus of 3 + 4i =
A) 7 B) 5 C) √13 D) 1
Ans: B) 5
54. Conjugate of 2 + 3i =
A) -2 + 3i B) 2 - 3i C) -2 - 3i D) 2 + 3i
Ans: B) 2 - 3i
55. First term of A.P. 3, 7, 11... is:
A) 4 B) 3 C) 11 D) 7
Ans: B) 3
56. Common difference of A.P. 2, 5, 8... =
A) 1 B) 3 C) 5 D) 2
Ans: B) 3
57. Sum of first n terms of A.P. =
A) n/2[2a + (n – 1)d]
Ans: A) n/2[2a + (n – 1)d]
58. nth term of G.P. =
A) ar^n B) ar^(n-1) C) ar^(n+1) D) a(n-1)
Ans: B) ar^(n-1)
59. Which of the following is a G.P.?
A) 2, 4, 6, 8
B) 3, 6, 12, 24
C) 1, 2, 3
D) 5, 10, 16
Ans: B) 3, 6, 12, 24
60. Quadratic equation with roots 3, -4 =
A) x² + x - 12 = 0 B) x² + x + 12 = 0 C) x² - x - 12 = 0
Ans: A) x² + x - 12 = 0
. Mean of first 10 natural numbers is:
A) 5
B) 5.5
C) 6
D) 4.5
Ans: B
2. If the mode of a data is 60 and the median is 50, then the mean is approximately:
A) 40
B) 50
C) 46.66
D) 56.66
Ans: C (Using Mode = 3Median - 2Mean)
3. The probability of an impossible event is:
A) 0
B) 1
C) 0.5
D) None
Ans: A
4. Variance is defined as:
A) Mean
B) Mean of squared deviations
C) Standard deviation
D) Range
Ans: B
5. A die is rolled once. The probability of getting a number less than 4 is:
A) 1/2
B) 1/3
C) 3/6
D) 1/6
Ans: C
6. Bernoulli trial has how many outcomes?
A) One
B) Two
C) Three
D) Infinite
Ans: B
7. In a binomial distribution, the mean is 4 and variance is 2. Then n = ?
A) 8
B) 4
C) 2
D) 6
Ans: A
8. Bayes' theorem is used for:
A) Finding area
B) Finding conditional probability
C) Derivatives
D) Limits
Ans: B
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Calculus (Limits, Derivatives, Integration)
9. The derivative of sin(x) is:
A) cos(x)
B) -cos(x)
C) -sin(x)
D) tan(x)
Ans: A
10. lim(x→0) (sin x)/x =
A) 0
B) 1
C) ∞
D) -1
Ans: B
11. If f(x) is differentiable, then f(x) is:
A) Discontinuous
B) Always constant
C) Continuous
D) Linear
Ans: C
12. d/dx (log x) = ?
A) x
B) 1/x
C) log x
D) 0
Ans: B
13. Integration of 1/x is:
A) x
B) ln|x| + C
C) 1/x
D) log x
Ans: B
14. Definite integral of x from 0 to 1 is:
A) 1
B) 0
C) 1/2
D) 2
Ans: C
15. The area under the curve y = x^2 from x=0 to x=1 is:
A) 1
B) 1/3
C) 1/2
D) 2/3
Ans: B
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Vector Analysis & Geometry
16. The dot product of two perpendicular vectors is:
A) 1
B) 0
C) -1
D) 2
Ans: B
17. If two vectors are parallel, then their cross product is:
A) Zero vector
B) Unit vector
C) Infinite
D) Equal
Ans: A
18. Curl of a gradient is always:
A) Zero
B) One
C) Negative
D) None
Ans: A
19. Gradient of a scalar function gives:
A) Vector field
B) Scalar field
C) Constant
D) None
Ans: A
20. Stoke’s theorem relates line integral to:
A) Surface integral
B) Volume integral
C) Triple integral
D) None
Ans: A
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Physics: Mechanics, Properties of Matter, Thermodynamics
21. SI unit of force is:
A) kg
B) N
C) m/s
D) Pascal
Ans: B
22. Rate of change of velocity is:
A) Speed
B) Displacement
C) Acceleration
D) Work
Ans: C
23. Unit of power is:
A) Watt
B) Joule
C) Newton
D) Ampere
Ans: A
24. Which law defines F = ma?
A) Newton’s 1st law
B) Newton’s 2nd law
C) Newton’s 3rd law
D) Law of Gravitation
Ans: B
25. Escape velocity depends on:
A) Mass of body
B) Radius of earth
C) Shape of object
D) Volume of object
Ans: B
26. Friction acts in the direction:
A) Motion
B) Opposite to motion
C) Perpendicular to motion
D) Along force
Ans: B
27. SI unit of pressure is:
A) Newton
B) Pascal
C) Joule
D) Watt
Ans: B
28. Archimedes principle relates to:
A) Friction
B) Buoyancy
C) Magnetism
D) Gravity
Ans: B
29. Viscosity is property of:
A) Solid
B) Liquid
C) Gas only
D) Vacuum
Ans: B
30. Which process transfers heat without a medium?
A) Conduction
B) Convection
C) Radiation
D) All
Ans: C
---
Electricity & Magnetism
31. SI unit of electric charge is:
A) Ampere
B) Volt
C) Coulomb
D) Ohm
Ans: C
32. Ohm’s law is given by:
A) V = IR
B) V = I/R
C) V = R/I
D) I = VR
Ans: A
33. Electric field due to a point charge varies as:
A) 1/r
B) 1/r²
C) r²
D) r
Ans: B
34. Electric dipole consists of:
A) Two like charges
B) Two opposite charges
C) One charge
D) No charge
Ans: B
35. Magnetic field lines never:
A) Cross
B) Start
C) Form loops
D) Pass through vacuum
Ans: A
36. Capacitance is measured in:
A) Volt
B) Ampere
C) Farad
D) Ohm
Ans: C
37. A device that stores electric charge:
A) Resistor
B) Capacitor
C) Transformer
D) Diode
Ans: B
38. Electric potential at a point is work done per unit charge in:
A) Moving it from infinity
B) Bringing from origin
C) Taking it away
D) Rotating it
Ans: A
39. Magnetic field is measured in:
A) Tesla
B) Coulomb
C) Weber
D) Ampere
Ans: A
40. Current is flow of:
A) Neutrons
B) Protons
C) Electrons
D) Atoms
Ans: C
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