Mathematics Tes...

If ⁿP_r = 1680 and ⁿC_r = 70, then 69 n + r! is equal to-

If for a ΔABC, cot A⋅cot B⋅cot C>0 then the triangle is-

The vertices of a triangle are A(x₁, x₁tan α), B (x₂, x₂tan β) and C(x₃, x₃ tan γ) . If the circumcentre of ΔABC coincides with the origin and H (a,b) be its orthocentre, then a/b is equal to: (Here α, β and γ are acute angles)-

The number of real values of k for which the lines  are intersecting, is-

If a³ + b⁶ = 2, then the maximum value of the term independent of x in the expansion of 

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r is equal to-

If ln(x + y) = 2xy, theny′ (0) is equal to-

If the tangent and the normal to x²- y² = 4 at a point cut off intercepts a1, a2on the x-axis respectively and  b₁, b₂ on the y-axis respectively then the value of  a₁a₂ + b₁b₂ is-

Two vertices of a triangle are (3, -2) and (-2, 3) and its orthocentre is (- 6, 1). The coordinates of its third vertex are-