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3(a). In English  Prove that cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8 = 0 Solution: cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8               =  cos π/8 +cos 7π/8+ cos 3π/8 +cos 5π/8               =  cos(π − 7π/8) +cos 7π/8+ cos 3π/8 +cos (π − 3π/8)               = − cos 7π/8 +cos 7π/8 + cos 3π/8 −  cos 3π/8               = 0 3(a). In Hindi   fl) dhft, fd   cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8 = 0 Solution: cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8               =  cos π/8 +cos 7π/8+ cos 3π/8 +cos 5π/8               =  cos(π − 7π/8) +cos 7π/8+ cos 3π/8 +cos (π − 3π/8)               = − cos 7π/8 +cos 7π/8 + cos 3π/8 −  cos 3π/8               = 0                   

In English 2.(d) In the figure, if chord AC = 8 cm and chord BC = 6 cm find the radius of the circle with centre            O . Solution:                 In Hindi 2 (d).  Fp= esa]  O  dsUnz okys o`Rr dh thok  AC = 8  lseh rFkk thok  BC = 6  lseh gks] rks o`Rr dh f=T;k Kkr dhft,A Solution:               

2 (c) If 14 is the median of numbers 7, 8, (2 x - 3), (2 x - 1), 15 17, 20, and 22 arranged in ascending order then find the value of x. Solution: In English       In Hindi ;fn vkjksgh dze esa la[;kvksa  7, 8, (2 x - 3), (2 x - 1), 15 17, 20  vkSj  22  dh ekf/;dk 14 gS] rks   x.  dk eku Kkr dhft,S Solution:

2(ii) In English             A purchaser gets a rebate of 12.5% on television of the value Rs. 9000. After rebate, 10% commercial tax is charged on remaining amount, Then find the amount of commercial tax. Solution: Given                 Market price of a television = Rs. 9000                                               Discount = 12.5%                   Cost price of a television   = MP[1 − (D/100)]                                                            = 9000 ✖ [1 − (12.5/100)]                                                            = 9000 ✖ [ 1 − 0.125]                                                            = 9000 ✖ 0.825                                                            = Rs. 7875                               Rate of sales Tax = 10%                                           Sales Tax = 10 % of 7875                                                           = Rs 787.5  In Hindi    ,d dzsrk  dks 9]000  : ewY; ds Vsyhfotu ij  12.5%   dh NwV feyrh g

 2) Do all the parts:   a) In triangle ABC, if AB = BC   ∠90° then find value of the following :  (i) sin A     (ii) cos A Solution:  In English lHkh [k.M dhft, % f=Hkqt  ABC  esa ;fn  AB = BC   ∠90°  gS] rks fuEu ds eku Kkr dhft, % (i) sin A       (ii) cos A Solution: In Hindi

1. (e) In figure, O is the centre of circle. If  ∠  BAO = 25°  and ∠ BCO = 20°    then the measure of             ∠ADC  will be (i). 20° (ii) 25° (iii) 45° (iv) 90° Solution: Answer (iii)   45° In English                   In the given ∠BAO = 25°                                   and  ∠OCB = 20°                                   Let   ∠AOC = x°                              ∠ABC = 1/2 ✕  ∠  AOC (angle is the remaining part of the circle)                                         = 1/2    ✕ x =(1/2)x ext  ∠AOC = 360°−   ∠AOC ( angle at a point )                    =( 360−  x)° In Quadrilateral AOCB       We know that Sum of angles of a quadrilateral is 360°     ∠BAO + ∠ABC  +ext  ∠AOC  +  ∠OCB =  360° 25° +   (1/2) x +  ( 360−  x)°+  20°=  360°                         405° −  (1/2) x =  360°                                         (1/2) x  =  405° −  360°                                                    x =  90°                                  

1. (d) If mode of data 2, 3, 4, 5, 5, 5, 6, 7, 7, 7, x and 2 be 7 then value of x will be (i) 2    (ii) 5     (iii) 7     (iv) None of these. Answer (iii) 7 Solution:                 Given data in ascending order –                     2, 3, 4, 5, 5, 5, 6, 7, 7, 7, x                        Mode of data is 7             The most frequent numbers is 7                         Then,       x = 7 In Hindi        दिए गए डेटा को आरोही क्रम में लिखने पर                  2, 3, 4, 5, 5, 5, 6, 7, 7, 7,  x                        डेटा का बहुलक =  7             सबसे अधिक आवृत्ति 7 की ह                         अतः     x = 7