mathematics ONLINE TEST 0% 12th Maths One Mark Test – Full Portion Wish you all the Best ! 1 / 90 If |z₁| = 1, |z₂| = 2, |z₃| = 3, and |9z₁z₂ + 4z₁z₃ + z₂z₃| then the value of |z₁ + z₂ + z₃|is ? 4 2 1 3 2 / 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? cos ‾ ˡ (1/3) cos ‾ ˡ (2/7) 45° 60° 3 / 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? Perpendicular Parallel Inclined at an angle п/6 Inclined at an angle п/3 4 / 90 If a and b are parallel vectors, then | a b c| is equal to? 2 zero -1 1 5 / 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 2√5 10 6 6 / 90 If α, β, γ are the roots of the equation x³ – 3x + 11 = 0, then α+ β + γ is______? -11 zero -3 3 7 / 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, 4 2, 6 8 / 90 If ρ (A) = ρ ([A| B]) , then the system AX = B of linear equations is? Consistent and has a unique solution Consistent Inconsistent Consistent and has infinitely many solution 9 / 90 The identity element in the group {R – {1}, x} where a*b = a+ b-ab is? zero 1/a-1 a/a-1 1 10 / 90 The area of the parallelogram having diagonals a = 3i + j – 2k and b = i -3j + 4k is? 4 2√3 4√3 5√3 11 / 90 sin⁻¹ (cos x) = (π / 2) – x is valid for? – π ≤ x ≤ 0 0 ≤ x ≤ π -(π / 2) ≤ x ≤ (π / 2) -(π / 4) ≤ x ≤ (3π / 4) 12 / 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) 13 / 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 3cm/s 2cm/s 1cm/s 1/2 cm/s 14 / 90 The radius of the circle3x² + by² + 4bx − 6by + b²= 0 is? √11 √10 3 1 15 / 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 16 / 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? 16 and 24 7 and 19 5 and 17 0 and 12 17 / 90 Given ρ(A) = ρ(A,B) = number of unknowns, then the system has_____? No solution Unique solution Infinitely many solutions Inconsistent 18 / 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 Zero b a 19 / 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 1 2 4 3 20 / 90 If a and b are two unit vectors, then the vectors (a + b) x (a x b) is parallel to the vector? a + b 2a + b a – b 2a – b 21 / 90 z₁, z₂, and z₃ are complex numbers such that z₁ + z₂ + z₃ = 0 and |z₁| = |z₂| = |z₃| = 1 than z₁² + z₂² + z₃² is? 1 3 2 zero 22 / 90 The Percentage error of fifth root of 31is appx how many times the percentage error in 31? 5 1/31 1/5 31 23 / 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? 5π / 6 2π / 3 3π / 4 π / 4 24 / 90 The differential equation of the family of curves y = A eˣ + Be⁻ˣ , where A and B are arbitrary constants is? d² y/dx² – y = 0 dy/dx + y = 0 d² y/dx² + y = 0 dy/dx – y = 0 25 / 90 The centre of the circle inscribed in a square formed by the lines x² −8x −12 = 0 and y² −14y + 45 = 0 is? (7, 4) (9,4) (4,7) (4,9) 26 / 90 The general solution of the differential equation dy / dx = y/x is? y = k log x xy = k log y = kx y = kx 27 / 90 Subtraction is not a binary operation in? ℕ ℚ ℝ ℤ 28 / 90 The proposition p (¬p ˅ q) is? a contradiction logically equivalent to p ˄ q a tautology logically equivalent to p ˅ q 29 / 90 If a.b = b.c = c.a = 0, then the value of [a,b,c] is? |a| |b| |c| 1/3 |a| |b| |c| 1 -1 30 / 90 If A,B and C are invertible matrices of some order, then which one of the following is not true? adj (AB) = (adj A) (adj B) det A¯¹ = (det A)¯¹ (ABC)¯¹ = C¯¹ B¯¹ A¯¹ adj A = |A| A¯¹ 31 / 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 6 12 10 32 / 90 Which one is the contrapositive of the statement ( p ˅ q) → r ? ¬r → (¬p ˄ ¬q) ¬r → (¬p ˅ ¬q) p→ (q ˄ r) r → (p ˄ q) 33 / 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? (-5,2) (2,-5) (5,-2) (-2,5) 34 / 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 35 / 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? 0.11 1 1.1 11 36 / 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 = ? 2 zero 1 3 37 / 90 If |z – 3 / 2| = 2 , then the least value of |z| is? 2 3 5 1 38 / 90 If sin⁻¹ x + sin⁻¹ y = 2π / 3; then cos ⁻¹ x + cos ⁻¹ y is equal to? π / 6 2π / 3 π / 3 π 39 / 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 0.2% 0.0% 0.4% 0.1% 40 / 90 The volume of the parallelepiped whose sides are given by OA = 2i – 3j, OB = i + j – k and OC = 3i – k is? 4 4/9 2/7 4/13 41 / 90 The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is? 3 4 2 1 42 / 90 The polynomial x³ + 2x + 3 has? no zeros one negative and two imaginary zeros one positive and two imaginary zeros three real zeros 43 / 90 Which of the following is a contradiction? p ˅ q p ˄ q q ˅ ~q q ˄ ~q 44 / 90 If x + y = k is a normal to the parabola y² =12x , then the value of k is? 3 -1 1 9 45 / 90 The solution of (dy/dx) + p(x) y = 0 is? x = ce ᶴᵖᵈˠ x = ce ⁻ᶴᵖᵈˠ y = ce ⁻ᶴᵖᵈ ˣ y = ceᶴᵖᵈ ˣ 46 / 90 The number of arbitrary constants in the particular solution of a differential equation of third order is? 1 3 2 zero 47 / 90 The circle passing through (1,-2) and touching the axis of x at (3,0) passing through the point? (-2,5) (-5,2) (5,-2) (2,-5) 48 / 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 3/2 4/√3 2/√3 49 / 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 = Ce⁻ᵏᵗ Pt = C P = Ceᵏᵗ P = Ckt 50 / 90 The number of vectors of unit length perpendicular to the vectors (i + j) and (j + k) is? ∞ 3 2 1 51 / 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? zero -40/9 40/9 0, -40/9 52 / 90 iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³ is? -1 i zero 1 53 / 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 x − 2y + 3 = 0 x + 2y = 3 x + 2y + 3 = 0 2x + 4y + 3 = 0 54 / 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 = 3x³ + 4 y = x³ + 2 y = x³ + 5 y = 3x² + 4 55 / 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) 56 / 90 If |adj(adjA)| = |A|⁹, then the order of the square matrix A is? 2 5 3 4 57 / 90 sin⁻¹ 3/5 – cos⁻¹ 12/13 + sec⁻¹ 5/3 – cose⁻¹ 13/12 is equal to? tan⁻¹ 12/65 π zero 2π 58 / 90 Define * on ℤ by a*b = a+b + 1Ɐa, b Ɛ ℤ. Then the identity element if z is? 1 2 -1 zero 59 / 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 – 123k -17i – 21j + 97k 60 / 90 A zero of x³ + 64 is? 4i -4 4 zero 61 / 90 Which of the following is a tautology? p ˄ q q ˄ ~q p ˅ q q ˅ ~q 62 / 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? 1 6 zero 3 63 / 90 If θ is the angle between the vectors a and b, then sinθ is? √(1-((a.b) / (|a| |b|))² (|a x b|) / (a.b) zero (a.b) / (|a| |b|) 64 / 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)] 65 / 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 = max (a,b) a * b = a a * b = aᵇ a * b =min (a . b) 66 / 90 If a * b = √(a² + b²) on the real numbers then * is? commutative but not associative both commutative and associative associative but not commutative neither commutative nor associative 67 / 90 The value of |a + b|² + |a – b|² is? 2(|a|² – |b|²) 4|a|² |b|² 4a.b 2(|a|² + |b²|) 68 / 90 The volume of the parallelepiped with its edges represented by the vectors i + j, i + 2j, i + j + пk is? п/4 п п/2 п/3 69 / 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? 64 cubic units 8 cubic units 512 cubic units 24 cubic units 70 / 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? x = −1 2x + 1 = 0 x =1 2x −1 = 0 71 / 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/6 п/2 п/4 п/3 72 / 90 If * is defined by a*b = a² + b² + ab + 1, then (2*3)*2 is? 40 20 445 400 73 / 90 The solution of the differential equation 2x(dy/dx) – y = 3 represents? straight lines parabola circles ellipse 74 / 90 If Aᵀ A¯¹ is symmetric, then A² =? A¯¹ Aᵀ (A¯¹)² (Aᵀ)² 75 / 90 Which one of the following is a binary operation on ℕ ? Multiplication All the above Subtraction Division 76 / 90 If |z – 2 + i| ≤ 2, then the greatest value of |z| is ? √5 + 2 √5 – 2 √3 – 2 √3 +2 77 / 90 The operation * defined by a * b = ab / 7 is not a binary operation on? ℚ⁺ ℂ ℤ ℝ 78 / 90 A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is? 6 3 4 2 79 / 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 3/5 6/5 80 / 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? 2 3 1 4 81 / 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 82 / 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 a and b are collinear b, c are collinear 83 / 90 The eccentricity of the ellipse (x – 3)² + (y – 4)² = y²/9 is? √3/2 1/3√2 1/√3 1/3 84 / 90 If A is a 3×3 non-singular matrix such that AAᵀ = Aᵀ A and B = A¯¹ Aᵀ, then BBᵀ =? B Bᵀ A I₃ 85 / 90 The order and degree of the differential equation √(sin x) (dx + dy) = √(cos x) (dx – dy) is? 2, 2, 2, 1 1, 1 1, 2 86 / 90 The area between y² = 4x and its latus rectum is 2/3 8/3 5/3 4/3 87 / 90 The angle between the vector 3i + 4j + 5k and the z – axis is? 90° 45° 60° 30° 88 / 90 If d = a x (b x c) + b x (c x a) + c x (a + b), then ? a, b, c are coplanar d = a + b + c |d| = 1 d = 0 89 / 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 = Ckt P = C P = Ce⁻ᵏᵗ P = Ceᵏᵗ 90 / 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 2.5 3.5 2 3 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. You can verify your answers at the result page.