Mathematics Tes...

The series of natural numbers is divided into groups as (1), (2, 3, 4), (3, 4, 5, 6, 7), (4, 5, 6, 7, 8, 9, 10) .......... . If sum of elements in the 20^th group is ℓ, then ℓ is equal to 

The lines L₁ : x = y = z, L₂ :   x = y/2 = z/3 and a  line L₃ is passing through (1, 1, 1) form a triangle of area  √6 units, (1, 1, 1) being one of the vertices of the triangle. Then the point of intersection of the L₃ with L₂ is

The combined equation of 2 altitudes of an equilateral triangle is x² – 3y² – 4x + 6√3 y–5 = 0. The third  altitude has equation.

The mean marks of students of a school is 56. The mean marks of girls is 60 and that of boys is 50. If number of boys and girls are n and m respectively, then 9n / m equals

C₁ and C₂ are two circles whose equations are given as x² + y² = 25 and x² + y² + 10x + 6y + 1 = 0. Now C₃ is a variable circle which cuts C₁ and C₂ orthogonally. Tangents are drawn from the center of C₃ to C₁, if the locus of the mid point of the chord of contact of tangents is (where a, b ∈ Z⁺, and a and b are relative prime), then b/a is 

A line is drawn from a point P(x, y) on curve y = f(x), making an angle in anti-clockwise with the +ve x-axis which is supplementary to the one made by the tangent to the curve at P(x, y). The line meets the x-axis at A. Another line perpendicular to the first, is drawn from P(x, y) meeting the y-axis at B. If OA = OB, where O is the origin, then the curve which passes through (1, 1). 

Let p : Sindhu plays to win 

q : Sindhu gets Bharath Ratna

Then the contrapositive of "~(~q^p)" is 

Let A and B are non-singular matrices of order 3 such that |A| = 5 and A^–1B² + AB = 0, then A² |A²| – adj (adjB) is equal to

Number of points of non-differentiability of f(x) = | | x | – 1 | + | cosπx |; –2 < x < 2 is 

If C₀, C₁, ....., C₂₀₁₂ are binomial coefficients in the expansion of (1 + x)²⁰¹² and a₀, a₁, ....., a₂₀₁₂ are real numbers in arithmetic progression then value of  a₀C₀ – a₁C₁ + a₂C₂ – a₃C₃ + ..... + a₂₀₁₂C₂₀₁₂ is a