mathematics ONLINE TEST

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12th Maths One Mark Test – Full Portion

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1 / 90

Which of the following is a contradiction?

2 / 90

If α, β, γ are the roots of the equation x³ – 3x + 11 = 0, then α+ β + γ is______?

3 / 90

The radius of the circle passing through the point (6, 2) two of whose diameter are x + y = 6 and x + 2y = 4 is?

4 / 90

Let a, b and c be three non-coplanar vectors and let p, q, r be the vectors defined by the relations p =( b x c / [a b c]) q = (c x a / [a b c ]), r = (a x b / [a b c]) Then the value of (a + b).p + (b + c).q + (c + a).r = ?

5 / 90

The solution of (dy/dx) + p(x) y = 0 is?

6 / 90

The number of vectors of unit length perpendicular to the vectors (i + j) and (j + k) is?

7 / 90

If a = 2i + 3j – k, b = i + 2j – 5k, c = 3i + 5j – k, then a vector perpendicular to a and lies in the plane containing b and c is?

8 / 90

The volume of a sphere is increasing in volume at the rate of 3п cubic cm/ sec. The rate of change of its radius when radius is 1/2 cm

9 / 90

If ρ (A) =  ρ ([A| B]) , then the system AX = B of linear equations is?

10 / 90

If x + y = k is a normal to the parabola y² =12x , then the value of k is?

11 / 90

If A is a 3×3 non-singular matrix such that AAᵀ = Aᵀ A and B = A¯¹ Aᵀ, then BBᵀ =?

12 / 90

The slope at any point of a curve y = f (x) is given by (dy/dx) = 3x² and it passes through (-1,1). Then the equation of the curve is?

13 / 90

The Percentage error of fifth root of 31is appx how many times the percentage error in 31?

14 / 90

If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents to the circle (x − 3)² + ( y + 2)² = r² , then the value of r² is?

15 / 90

If a.b = b.c = c.a = 0, then the value of [a,b,c] is?

16 / 90

The identity element in the group {R – {1}, x} where a*b = a+ b-ab is?

17 / 90

Which one of the following is a binary operation on ℕ ?

18 / 90

Given ρ(A) = ρ(A,B) = number of unknowns, then the system has_____?

19 / 90

The eccentricity of the ellipse (x – 3)² + (y – 4)² = y²/9 is?

20 / 90

The number of arbitrary constants in the particular solution of a differential equation of third order is?

21 / 90

If |z – 3 / 2| = 2 , then the least value of |z| is?

22 / 90

If θ is the angle between the vectors a and b, then sinθ is?

23 / 90

A stone is thrown up vertically. The height it reaches at time t seconds is given by x = 80t – 16t². The stone reaches the maximum height in time t seconds is given by

24 / 90

Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with Probability 0.5. Assume that the results of the flips are independent, and let X equal the total number of heads that result. The value of E(X) is?

25 / 90

A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

26 / 90

Define * on ℤ by a*b = a+b + 1Ɐa, b Ɛ ℤ. Then the identity element if z is?

27 / 90

If Aᵀ A¯¹ is symmetric, then A² =?

28 / 90

The equation of the normal to the circle x² + y² − 2x − 2y +1 = 0 which is parallel to the line 2x + 4y = 3 is

29 / 90

If sin⁻¹ x + sin⁻¹ y = 2π / 3; then cos ⁻¹ x + cos ⁻¹ y is equal to?

30 / 90

The equation of the circle passing through (1,5) and (4,1) and touching y -axis is x² + y² − 5x − 6y + 9 + (4x + 3y −19) = 0 whereλ is equal to?

31 / 90

The angle between the vector 3i + 4j + 5k and the z – axis is?

32 / 90

A zero of x³ + 64 is?

33 / 90

If the two tangents drawn from a point P to the parabola y² = 4x are at right angles then the locus of P is?

34 / 90

sin⁻¹ (cos x) = (π / 2) – x is valid for?

35 / 90

A circular template has a radius of 10cm. The measurement of radius has an appx error of 0.02cm. Then the percentage error in calculating area of this template is

36 / 90

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is?

37 / 90

If |a| = |b| = 1 such that a + 2b and 5a – 4b are perpendicular to each other, then the angle between a and b is?

38 / 90

The solution of the differential equation 2x(dy/dx) – y = 3 represents?

39 / 90

The conjugate of a complex number is1 / i – 2. Then, the complex number is?

40 / 90

The volume of the parallelepiped with its edges represented by the vectors i + j, i + 2j, i + j + пk is?

41 / 90

Which of the following is a tautology?

42 / 90

If a and b are two unit vectors, then the vectors (a + b) x (a x b) is parallel to the vector?

43 / 90

The value of |a + b|² + |a – b|² is?

44 / 90

The circle passing through (1,-2) and touching the axis of x at (3,0) passing through the point?

45 / 90

If 0≤ θ ≤ π and the system of equations x + (sinθ) y -(cosθ) z =0, (cos θ) x – y + z =0, (sin θ) x + y – z =0, has a non-trivial solution then θ is?

46 / 90

Which one is the inverse of the statement ( p ˅ q) → ( p ˄ q) ?

47 / 90

In the set ℝ of real numbers ‘* ’ is defined as follows. Which one of the following is not a binary operation on ℝ ?

48 / 90

The area between y² = 4x and its latus rectum is

49 / 90

The dual of ¬ (p ˅ q) ˅ [ p ˅ (p ˄ ¬r)] is?

50 / 90

If d = a x (b x c) + b x (c x a) + c x (a + b), then ?

51 / 90

If |adj(adjA)| = |A|⁹, then the order of the square matrix A is?

52 / 90

The population P in any year t is such that the rate of increase in the population is proportional to the population. Then?

53 / 90

If a and b are parallel vectors, then | a b c| is equal to?

54 / 90

P is the amount of certain substance left in after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then?

55 / 90

If a, b, c are three unit vectors such that a is perpendicular to b, and is parallel to c then a x(bxc) is equal to?

56 / 90

The radius of the circle3x² + by² + 4bx − 6by + b²= 0 is?

57 / 90

If a x (b x c) = (a x b)x c , where a, b, c are any three vectors such that b.c ≠ 0 and a.b ≠ 0, then a and c are?

58 / 90

The operation * defined by a * b = ab / 7 is not a binary operation on?

59 / 90

If a, b and c are any three vectors, then a x(b x c) = a x (b x c) if and only if?

60 / 90

If |z₁| = 1, |z₂| = 2, |z₃| = 3, and |9z₁z₂ + 4z₁z₃ + z₂z₃| then the value of |z₁ + z₂ + z₃|is ?

61 / 90

If the function f (x) = 1/12 for a < x < b , represents a probability density function of a continuous random variable X, then which of the following cannot be the value of a and b?

62 / 90

The differential equation of the family of curves y = A eˣ + Be⁻ˣ , where A and B are arbitrary constants is?

63 / 90

If |z – 2 + i| ≤ 2, then the greatest value of |z| is ?

64 / 90

Subtraction is not a binary operation in?

65 / 90

sin⁻¹ 3/5 – cos⁻¹ 12/13 + sec⁻¹ 5/3 – cose⁻¹ 13/12 is equal to?

66 / 90

If the volume of the parallelepiped with a x b, b x c, c x a as coterminous edges is 8 cubic units, then the volume of the parallelepiped with (a x b)x (b x c), (b x c)x(c x a) and (c x a) x (a x b) as coterminous edges is?

67 / 90

The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point (2,3)?

68 / 90

The centre of the circle inscribed in a square formed by the lines x² −8x −12 = 0 and y² −14y + 45 = 0 is?

69 / 90

If a = i + j + k, b = i + j, c = i and (a x b)x c = λa + μb, then the value of λ + μ is?

70 / 90

iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³ is?

71 / 90

The polynomial x³ + 2x + 3 has?

72 / 90

The area of the parallelogram having diagonals a = 3i + j – 2k and b = i -3j + 4k is?

73 / 90

The volume of the parallelepiped whose sides are given by OA = 2i – 3j, OB = i + j – k and OC = 3i – k is?

74 / 90

If a and b are unit vectors such that [a, b, a x b] = п/4, then the angle between a and b is?

75 / 90

A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is?

76 / 90

z₁, z₂, and z₃ are complex numbers such that z₁ + z₂ + z₃ = 0 and |z₁| = |z₂| = |z₃| = 1 than z₁² + z₂² + z₃² is?

77 / 90

The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is?

78 / 90

The point on the curve 6y=x³ + 2 at which y-coordinate changes 8 times as fast as x coordinate is

79 / 90

Which one is the contrapositive of the statement ( p ˅ q) → r ?

80 / 90

If * is defined by a*b = a² + b² + ab + 1, then (2*3)*2 is?

81 / 90

The order and degree of the differential equation (d²y/dx²) + (dy/dx)¹/³ + x¹/⁴ = 0 are respectively?

82 / 90

If a * b = √(a² + b²) on the real numbers then * is?

83 / 90

The general solution of the differential equation dy / dx = y/x is?

84 / 90

If the coordinates at one end of a diameter of the circle x² + y² −8x − 4y + c = 0 are (11, 2) , the coordinates of the other end are?

85 / 90

The proposition p (¬p ˅ q) is?

86 / 90

The order and degree of the differential equation √(sin x) (dx + dy) = √(cos x) (dx – dy) is?

87 / 90

If A,B and C are invertible matrices of some order, then which one of the following is not true?

88 / 90

The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is?

89 / 90

The area of the triangle formed by the complex numbers z, iz, and z + iz in the Argand’s diagram is?

90 / 90

If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3,0) and F₂ (-3,0) then PF₁+ PF₂ is?

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