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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 − ...

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)]                                 ...

 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  ...

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     ...

IN ENGLISH 1. (c) When we purchase something from market then we have to pay certain additional amount than its fixed rate. This additional amount is called (i) income tax    (ii) excise duty   (iii) custom duty  (iv) commercial tax  Answer:   (iv) commercial tax  IN HINDI 1.(c)  जब हम बाजार से कोई वस्तु खरीदते है तो हमें निर्धारित दर  से अधिक धनराशि उस वास्तु पर देनी पड़ती हैं  यह  धनराशि   कही जाती हैं (i)   आयकर     (ii)  उत्पाद शुल्क    (iii) सीमा शुल्क (iv)   वाणिज्यिक कर   Answer:  (iv)   वाणिज्यिक कर  

1. (b) if    sin  θ    =  csc   θ    and 0 ≤  θ ≤ π  then value of    θ  will be         (i) π     (ii) π/2       (iii) π  /4       (iv) 0.            यदि   sin  θ    =  csc   θ       तथा  0 ≤  θ ≤ π  तो  θ  का मान होगा        (i) π        (ii) π/2         (iii) π  /4       (iv) 0.

1. a) Roots of the equation 4 + 5x + 2 x 2  = 0 will be      i) Rational and equal       ii) Rational and unequal      iii) Irrational       iv) Not real 1 . a)   lehdj.k    4 + 5x + 2 x 2  = 0 के मूल होंगे       i)  परिमेय और समान       ii)   परिमेय और समान       iii)  अपरिमेय       iv)  vokLrfod Solution: ( iv) Not real