mathematics ONLINE TEST 0% 12th Maths One Mark Test – Full Portion Wish you all the Best ! 1 / 90 A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is? 3 4 2 6 2 / 90 Define * on ℤ by a*b = a+b + 1Ɐa, b Ɛ ℤ. Then the identity element if z is? -1 2 1 zero 3 / 90 The population P in any year t is such that the rate of increase in the population is proportional to the population. Then? P = Ce⁻ᵏᵗ P = Ckt P = C P = Ceᵏᵗ 4 / 90 If |adj(adjA)| = |A|⁹, then the order of the square matrix A is? 4 5 3 2 5 / 90 The number of arbitrary constants in the particular solution of a differential equation of third order is? zero 3 2 1 6 / 90 Subtraction is not a binary operation in? ℤ ℕ ℝ ℚ 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? 60° cos ‾ ˡ (2/7) cos ‾ ˡ (1/3) 45° 8 / 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? P = Ckt P = Ceᵏᵗ Pt = C P = Ce⁻ᵏᵗ 9 / 90 The area of the parallelogram having diagonals a = 3i + j – 2k and b = i -3j + 4k is? 5√3 4 2√3 4√3 10 / 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 2x + 4y + 3 = 0 x + 2y = 3 x − 2y + 3 = 0 x + 2y + 3 = 0 11 / 90 If α, β, γ are the roots of the equation x³ – 3x + 11 = 0, then α+ β + γ is______? -3 3 zero -11 12 / 90 If |z – 2 + i| ≤ 2, then the greatest value of |z| is ? √5 – 2 √3 +2 √5 + 2 √3 – 2 13 / 90 The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is? 4/√3 2/√3 3/2 4/3 14 / 90 The eccentricity of the ellipse (x – 3)² + (y – 4)² = y²/9 is? 1/3√2 1/3 1/√3 √3/2 15 / 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 3 4 1 2 16 / 90 If sin⁻¹ x + sin⁻¹ y = 2π / 3; then cos ⁻¹ x + cos ⁻¹ y is equal to? π / 6 π 2π / 3 π / 3 17 / 90 iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³ is? 1 -1 i zero 18 / 90 z₁, z₂, and z₃ are complex numbers such that z₁ + z₂ + z₃ = 0 and |z₁| = |z₂| = |z₃| = 1 than z₁² + z₂² + z₃² is? 2 1 zero 3 19 / 90 The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is? d² x/dy² = 0 d² y/dx² = 0 d² y/dx² – y = 0 d² y/dx² + y = 0 20 / 90 The differential equation of the family of curves y = A eˣ + Be⁻ˣ , where A and B are arbitrary constants is? dy/dx – y = 0 dy/dx + y = 0 d² y/dx² – y = 0 d² y/dx² + y = 0 21 / 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? 3π / 4 π / 4 5π / 6 2π / 3 22 / 90 If A is a 3×3 non-singular matrix such that AAᵀ = Aᵀ A and B = A¯¹ Aᵀ, then BBᵀ =? Bᵀ A I₃ B 23 / 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? 512 cubic units 64 cubic units 8 cubic units 24 cubic units 24 / 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? -40/9 zero 0, -40/9 40/9 25 / 90 If |z₁| = 1, |z₂| = 2, |z₃| = 3, and |9z₁z₂ + 4z₁z₃ + z₂z₃| then the value of |z₁ + z₂ + z₃|is ? 2 4 3 1 26 / 90 The identity element in the group {R – {1}, x} where a*b = a+ b-ab is? a/a-1 1/a-1 zero 1 27 / 90 The polynomial x³ + 2x + 3 has? three real zeros one positive and two imaginary zeros one negative and two imaginary zeros no zeros 28 / 90 The volume of the parallelepiped whose sides are given by OA = 2i – 3j, OB = i + j – k and OC = 3i – k is? 2/7 4 4/13 4/9 29 / 90 Which one is the inverse of the statement ( p ˅ q) → ( p ˄ q) ? ( p ˄ q) → ( p ˅ q) (¬p ˄ ¬q) → (¬p ˅ ¬q) (¬p ˅¬q) → (¬p ˄ ¬q) ¬( p ˅ q) → ( p ˄ q) 30 / 90 sin⁻¹ (cos x) = (π / 2) – x is valid for? -(π / 4) ≤ x ≤ (3π / 4) – π ≤ x ≤ 0 -(π / 2) ≤ x ≤ (π / 2) 0 ≤ x ≤ π 31 / 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? п/3 п/2 п/4 п/6 32 / 90 The conjugate of a complex number is1 / i – 2. Then, the complex number is? -1 / i + 2 1 / i + 2 – 1 / i – 2 1 / i -2 33 / 90 The solution of (dy/dx) + p(x) y = 0 is? y = ceᶴᵖᵈ ˣ x = ce ᶴᵖᵈˠ y = ce ⁻ᶴᵖᵈ ˣ x = ce ⁻ᶴᵖᵈˠ 34 / 90 The dual of ¬ (p ˅ q) ˅ [ p ˅ (p ˄ ¬r)] is? (p ˄ q)˄[ p˄(p ˅ ¬r)] ¬ (p ˄ q) ˄ [p ˄ (p ˄ r)] ¬ (p ˄ q) ˄ [p ˅ (p ˄ ¬r)] ¬ (p ˄q) ˄[p ˄ ( p ˅ ¬r)] 35 / 90 The order and degree of the differential equation √(sin x) (dx + dy) = √(cos x) (dx – dy) is? 2, 1 1, 1 2, 2, 1, 2 36 / 90 The operation * defined by a * b = ab / 7 is not a binary operation on? ℤ ℚ⁺ ℂ ℝ 37 / 90 If a * b = √(a² + b²) on the real numbers then * is? both commutative and associative associative but not commutative neither commutative nor associative commutative but not associative 38 / 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? Inclined at an angle п/3 Perpendicular Inclined at an angle п/6 Parallel 39 / 90 If a.b = b.c = c.a = 0, then the value of [a,b,c] is? 1 1/3 |a| |b| |c| -1 |a| |b| |c| 40 / 90 The Percentage error of fifth root of 31is appx how many times the percentage error in 31? 1/5 31 1/31 5 41 / 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 2 3.5 2.5 3 42 / 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? 10 6 2√5 4 43 / 90 The area between y² = 4x and its latus rectum is 2/3 8/3 4/3 5/3 44 / 90 If θ is the angle between the vectors a and b, then sinθ is? (|a x b|) / (a.b) zero √(1-((a.b) / (|a| |b|))² (a.b) / (|a| |b|) 45 / 90 The number of vectors of unit length perpendicular to the vectors (i + j) and (j + k) is? 1 ∞ 3 2 46 / 90 The area of the triangle formed by the complex numbers z, iz, and z + iz in the Argand’s diagram is? 2 |z|² |z|² 3 / 2 |z|² 1 / 2 |z|² 47 / 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? 4 2 1 3 48 / 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? 2x + 1 = 0 2x −1 = 0 x = −1 x =1 49 / 90 The value of |a + b|² + |a – b|² is? 4a.b 2(|a|² + |b²|) 2(|a|² – |b|²) 4|a|² |b|² 50 / 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 = ? 1 zero 2 3 51 / 90 The circle passing through (1,-2) and touching the axis of x at (3,0) passing through the point? (2,-5) (5,-2) (-2,5) (-5,2) 52 / 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? -17i – 21j + 97k -17i – 21j – 97k -17i + 21j – 97k 17i + 21j – 123k 53 / 90 The angle between the vector 3i + 4j + 5k and the z – axis is? 60° 45° 90° 30° 54 / 90 The proposition p (¬p ˅ q) is? a contradiction a tautology logically equivalent to p ˄ q logically equivalent to p ˅ q 55 / 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 2cm/s 3cm/s 1cm/s 1/2 cm/s 56 / 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? 6 3 zero 1 57 / 90 If a and b are two unit vectors, then the vectors (a + b) x (a x b) is parallel to the vector? 2a + b a + b 2a – b a – b 58 / 90 The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is? 4 3 2 1 59 / 90 Given ρ(A) = ρ(A,B) = number of unknowns, then the system has_____? Unique solution No solution Inconsistent Infinitely many solutions 60 / 90 The point on the curve 6y=x³ + 2 at which y-coordinate changes 8 times as fast as x coordinate is (-4,-11) (4,11) (-4,11) (4,-11) 61 / 90 The volume of the parallelepiped with its edges represented by the vectors i + j, i + 2j, i + j + пk is? п п/4 п/2 п/3 62 / 90 sin⁻¹ 3/5 – cos⁻¹ 12/13 + sec⁻¹ 5/3 – cose⁻¹ 13/12 is equal to? π tan⁻¹ 12/65 zero 2π 63 / 90 If * is defined by a*b = a² + b² + ab + 1, then (2*3)*2 is? 445 20 400 40 64 / 90 If |z – 3 / 2| = 2 , then the least value of |z| is? 5 3 1 2 65 / 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 0.1% 0.4% 0.2% 0.0% 66 / 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? y = 3x² + 4 y = x³ + 5 y = x³ + 2 y = 3x³ + 4 67 / 90 The centre of the circle inscribed in a square formed by the lines x² −8x −12 = 0 and y² −14y + 45 = 0 is? (4,9) (9,4) (4,7) (7, 4) 68 / 90 In the set ℝ of real numbers ‘* ’ is defined as follows. Which one of the following is not a binary operation on ℝ ? a * b = a a * b = aᵇ a * b =min (a . b) a * b = max (a,b) 69 / 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? 5 and 17 7 and 19 16 and 24 0 and 12 70 / 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? (2,-5) (-5,2) (-2,5) (5,-2) 71 / 90 If Aᵀ A¯¹ is symmetric, then A² =? Aᵀ A¯¹ (A¯¹)² (Aᵀ)² 72 / 90 The general solution of the differential equation dy / dx = y/x is? log y = kx xy = k y = kx y = k log x 73 / 90 If ρ (A) = ρ ([A| B]) , then the system AX = B of linear equations is? Inconsistent Consistent and has a unique solution Consistent and has infinitely many solution Consistent 74 / 90 If a and b are parallel vectors, then | a b c| is equal to? 2 1 zero -1 75 / 90 If d = a x (b x c) + b x (c x a) + c x (a + b), then ? |d| = 1 d = 0 a, b, c are coplanar d = a + b + c 76 / 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? None a and c are collinear b, c are collinear a and b are collinear 77 / 90 Which of the following is a tautology? p ˄ q p ˅ q q ˅ ~q q ˄ ~q 78 / 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? c b Zero a 79 / 90 A zero of x³ + 64 is? 4 zero 4i -4 80 / 90 The radius of the circle3x² + by² + 4bx − 6by + b²= 0 is? √11 1 3 √10 81 / 90 The order and degree of the differential equation (d²y/dx²) + (dy/dx)¹/³ + x¹/⁴ = 0 are respectively? 3, 3 2, 3 2, 6 2, 4 82 / 90 The solution of the differential equation 2x(dy/dx) – y = 3 represents? circles parabola straight lines ellipse 83 / 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)? 10/3 5/3 6/5 3/5 84 / 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? 8 10 6 12 85 / 90 If A,B and C are invertible matrices of some order, then which one of the following is not true? (ABC)¯¹ = C¯¹ B¯¹ A¯¹ adj A = |A| A¯¹ det A¯¹ = (det A)¯¹ adj (AB) = (adj A) (adj B) 86 / 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? 1.1 0.11 1 11 87 / 90 Which one is the contrapositive of the statement ( p ˅ q) → r ? r → (p ˄ q) ¬r → (¬p ˅ ¬q) ¬r → (¬p ˄ ¬q) p→ (q ˄ r) 88 / 90 Which one of the following is a binary operation on ℕ ? Division Subtraction Multiplication All the above 89 / 90 If x + y = k is a normal to the parabola y² =12x , then the value of k is? 1 -1 9 3 90 / 90 Which of the following is a contradiction? q ˅ ~q p ˅ q p ˄ q q ˄ ~q Your score is Note: Once you start the test, you are not allowed to go back. Results won’t be generated if you quit the test. Complete the test within the given time. Once the time is over, the test will be submitted automatically. 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