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WBSSC Math(Pass) Mock Test 4

   Q1. Show If  where  then prove that .

   Q2. Prove that every orthogonal matrix is nonsingular.

   Q3. If be a ring, and then prove that .

   Q4. If the pair of straight lines joining the origin to the point of intersection of the ellipse      and the line

          are perpendicular to each other, then show that .

   Q5. Show that the semi-latus rectum of a conic is harmonic mean between the segment of a focal chord.

   Q6. The plane is rotated about its line of intersection with the plane through an angle .  Prove that

          its equation in new position is .

   Q7. Show that where are any three vectors.

   Q8. Test the convergence of the series .

   Q9. Show that maximum rectangle inscribed in a circle is a square.

   Q10. Evaluate .

   Q11. Solve the differential equation .

   Q12. Show that the vectors  and form a basis for .

   Q13. What is the chance that a leap year selected at random will contain 53 Sundays?

   Q14. Prove that .

   Q15. A particle describes the parabola under a force which is always directed towards its focus. Find the law

            of force.

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