mathematics ONLINE TEST

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12th Maths One Mark Test – Full Portion

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1 / 90

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

2 / 90

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

3 / 90

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

4 / 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?

5 / 90

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

6 / 90

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

7 / 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?

8 / 90

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

9 / 90

Subtraction is not a binary operation in?

10 / 90

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

11 / 90

Which of the following is a tautology?

12 / 90

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

13 / 90

A zero of x³ + 64 is?

14 / 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?

15 / 90

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

16 / 90

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

17 / 90

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

18 / 90

If Aᵀ A¯¹ is symmetric, then A² =?

19 / 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?

20 / 90

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

21 / 90

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

22 / 90

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

23 / 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?

24 / 90

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

25 / 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?

26 / 90

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

27 / 90

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

28 / 90

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

29 / 90

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

30 / 90

iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³ is?

31 / 90

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

32 / 90

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

33 / 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?

34 / 90

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

35 / 90

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

36 / 90

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

37 / 90

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

38 / 90

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

39 / 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?

40 / 90

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

41 / 90

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

42 / 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

43 / 90

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

44 / 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)?

45 / 90

The polynomial x³ + 2x + 3 has?

46 / 90

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

47 / 90

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

48 / 90

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

49 / 90

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

50 / 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

51 / 90

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

52 / 90

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

53 / 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?

54 / 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

55 / 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?

56 / 90

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

57 / 90

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

58 / 90

The value of |a + b|² + |a – b|² is?

59 / 90

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

60 / 90

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

61 / 90

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

62 / 90

The proposition p (¬p ˅ q) is?

63 / 90

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

64 / 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?

65 / 90

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

66 / 90

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

67 / 90

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

68 / 90

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

69 / 90

Which of the following is a contradiction?

70 / 90

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

71 / 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?

72 / 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?

73 / 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?

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

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

76 / 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?

77 / 90

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

78 / 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?

79 / 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 = ?

80 / 90

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

81 / 90

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

82 / 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

83 / 90

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

84 / 90

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

85 / 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

86 / 90

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

87 / 90

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

88 / 90

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

89 / 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?

90 / 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?

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