Question

Section-C
Each 3 Marks
Q-27. PQR is a triangle right angled at P and M is a point on Q R Such
that PM is perpendicular to QR. Show that PM QMX MR
M
Q-28. Prove that
sin - 2 sin 0/2 cos' - Cos 8 = tan 0.
Q-29. Check whether - 150 is a term of the A.P. 11,8,5.....​

Answer 1

Answer 27:-

In ΔQMP and ΔQPR

     <QMP = <QPR                       (EACH = 90 degree)

          <Q = <Q                                 (COMMON)

⇒     ΔQMP SIMILAR ΔQPR   ....(1)  (AA similarity)

     Again in ΔPMR and ΔQPR,

         <PMR = <QPR                     (EACH = 90 degree)

          <R = < R                              (COMMON)

⇒    ΔRMP similar ΔQPR     .......(2) (AA similarity)

From (1) and (2) we get

                   ΔQMP similar ΔPMR

Therefore,  

             The corresponding sides are proportional  

                                    QM/PM = PM/RM

⇒              QM.RM = PM. PM          (BY CROSS-MULTIPLICATION)  

⇒               PM² = QM.RM

Answer 29:-

a = 11

d = 8 - 11 = - 3

Let - 150 be the nth term of the given A.P.

We know that,

an = a + (n - 1)d

⇒ - 150 = 11 + (n - 1) - 3

⇒ - 150 = 11 - 3n + 3

⇒ (- 150) + (- 14) = - 3n

⇒ - 3n = - 164

⇒ 3n = 164

⇒ n = 164/3

So, it is clear that n is not an integer.

Therefore, - 150 is not a term of the given A.P.

Answer 2

Answer:

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Step-by-step explanation: