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WBSSC Math(Pass) Mock Test 1

  Q1. Prove that

 

  Q2.  Show that the equation will have a pair of equal roots, if .

 

  Q3. Given the equations , , where    are not all zero, prove that .

 

  Q4. Show that the set G of all numbers of the form 2n , where n is an integer, is an abelian group with respect to ordinary

         multiplication.

 

  Q5. Prove that the pair of straight line joining the origin to the other two points of the intersection of the curves

        and will be at right angles if .

 

   Q6. Perpendiculars PL, PM, PN are drawn from the point Pto the co-ordinate planes. Show that the equation of

         the plane LMN is

 

  Q7. Prove that .

 

  Q8. If , then applying Roll’s Theorem show that the equation  ( real, )has at least

         one root in (0,1).

 

  Q9. Examine the convergence of the series .

 

  Q10. Show that .

 

  Q11. Solve the equation .

 

  Q12. Find graphically the feasible space, if any, for the following equations: , , .

 

  Q13. In numerical for a polynomial prove that the operation    .

 

  Q14. The law of motion in a straight line being , show that the acceleration is constant, being the displacement of

           the particle in time when its velocity is .

 

   Q15. Find the probability of getting the product of faces a perfect square, when two dice are thrown together.

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