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

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 = ?

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

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?

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

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

Subtraction is not a binary operation in?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The proposition p (¬p ˅ q) is?

The value of |a + b|² + |a – b|² is?

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

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

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

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?

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

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?

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

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

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

If Aᵀ A¯¹ is symmetric, then A² =?

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?

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?

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

The polynomial x³ + 2x + 3 has?

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

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

Which of the following is a contradiction?

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

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

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

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

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)?

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

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

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

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

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

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

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?

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?

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

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

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

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

iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³ is?

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?

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?

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

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

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

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

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

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

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

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

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

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

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

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

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?

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?

A zero of x³ + 64 is?

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?

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

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

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

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

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?

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

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

Which of the following is a tautology?

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

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

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

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

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