1. In a ΔABC, length of the side BC is six times the tangent of its opposite angle with other sides being equal and having an inclination of 30° . Find the area of the triangle ( Sin(C/5)=0.40 ).

2. How many pairs of positive integers p,q satisfy

(1/p)+(1/q)=(1/12) where q is an odd integer less than 60 ?

3. Find the simplified value of

(√3+1)(10+√12)(√12-2)(5-√3).

4. The monthly incomes of A and B are in the ratio 3:4 and their monthly expenses in 7:11 . If each saves ₹10,000 per month ,find the monthly income of A .

5. A right circular cone of volume x ,a right circular cylinder of volume y and a sphere of volume z all have the same radius ,and the common height of cone and cylinder is equal to diameter of the sphere ,find the relation among x,y and z

6. Find the remainder ,if x^{2019}+1 is divided by (x+1).

7. If **0°≤ x ≤90°** and ( **81 ^{sin2x }+ 81^{cos2x}=30** ) then find the value of x .

and the values of ‘**k**‘ & ‘**k ^{2}**‘ are the roots(provided all the roots are positive) of the equation

**x**

^{3}-px^{2}+(p^{2}-181)x-(7p-4) ,^{n. }

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