SINGLE CORRECT ANSWER TYPE QUESTIONS: TRIGONOMETRY 2 2

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Class-Jr.X_E-E SIMPLE HOLIDAY PACKAGE CLASS-IX MATHEMATICS SUB BATCH : E-E SINGLE CORRECT ANSWER TYPE QUESTIONS: TRIGONOMETRY. siθ+cosθ + siθ cosθ = ) ) ). If a cos q, y bsi q, the a y b ) ) ).

1 Class-Jr.X_E-E SIMPLE HOLIDAY PACKAGE CLASS-IX MATHEMATICS SUB BATCH : E-E SINGLE CORRECT ANSWER TYPE QUESTIONS: TRIGONOMETRY. siθ+cosθ + siθ cosθ = ) ) ). If a cos q, y bsi q, the a y b ) ) ). The value of π π 5π 7π 9π cot cot cot cot cot is ) ) ). If sia : cosa = :, the seca + coseca is ) 5 ) 5 ) p 5p si A si A = 6 6 ) ) si A cos A ) ta A ta ta ta ta ) ) ) 7. If A + B = 5, the the value of (+Ta A) (+Ta B) is ) ) ) 8. If cosa = 5 5 taa + tab ad sib =, the the value of - taatab is 9. ) 6 6 ) 6 6 π π π π 5π cos cos cos cos cos 6 6 ) NARAYANA GROUP OF SCHOOLS Page

2 Class-Jr.X_E-E. cos 5 + cos 95 + cos 5 = ) ) ). si a si b a, cos a cos b b si a b ab ) ab ) a+b a b ab ) a b. A B C 8 cos cos cos A B C ) si A si B si C ) si Asi B si C cos A cos B cosc ) cos Acos B cos C. p a b p, ) 6 65 si a si b, 65 ) 7 a b cosa cos b cos 65 = ) If y = si θ + cos θ, the for all real values of ) y, ) y, 6 y, 6 ) y, 5. cos A cosa si A si A cos A si A ) ) ) 6. The value of si θ - cosθ lies i the iterval ), 5 ), 5, 5, ) Noe 7. If Ta+Ta+Ta+8Cot8= the the geeral solutio of = ) π π, Z ) π π, Z 6 8. The value of satisfyig Si7θ Siθ Siθ i ) π π, 9 ) π π, 9 9. The solutio set of cosq si q is π π, Z ) π, Z π π, 6 π θ are ), ) p p : Z ) p p : Z p p : Z 6 ) p p : Z 6 NARAYANA GROUP OF SCHOOLS Page

3 Class-Jr.X_E-E. If Si ta Si cos.the 5 ) : Z ) : Z or : Z 6 : Z ) No solutio. If Sec Cos the 5 ) : Z ) : Z or : Z 6 : Z or : Z ) : Z or ; Z. The geeral solutio of Si=Cos is π ) ( ), Z ) π, Z No Solutio ) π,. If Z Ta(θ 5 ) Ta(θ 5 ), θ π the θ ) π ) π π 6 ) π. If Si. Si6. Si6, the = 8 π π π 6 8 π π 9 5. I ABC, a si C c si A ) π π ) π ) ) ) ) 6. The ratio of the sides of a triagle ABC is : :. The ratio of A : B : C is ) : 5 : ) : : : : ) : : si B C 7. I ABC, bc ) ) s ) s A C Si Si 8. I ABC, If a, b, c are i A.P. the = B Si ) ) ) 9. If A =, C = 9, c 7, the a = ) 7 ) 7 ). I ABC if A + C = B, the a c a ac c = A C A C A B A B ) cos ) si ta ) ta NARAYANA GROUP OF SCHOOLS Page

4 Class-Jr.X_E-E A B C. I ABC, If a, b, c are i A.P., the Cot, Cot, Cot are i ) A.P. ) G.P. H.P. ) A.G.P A B. I ay triagle ABC, ta ta ) a a b c. I ABC ) = r r r r b a b c c a b c ) a+b ) a b c ) a b c Rr )R. I a triagle ABC r r cos C ) ab / c ) ( a b) / c abc / ) abc / 5. I ABC r(r +r +r = ) ab bc ca s ) ab bc ca s ) 6. I ABC (r -r)(r -r)(r r) ) Rs ) ab bc ca s ab bc ca s Rr R ) 7. If the circumcetre of a triagle lies iside the triagle the the triagle is ) right agled ) acute agled obtuse agled ) scalee 8. I triagle ABC, the legth of the altitude draw from A to BC is ) asi Bsi C si A ) 9. cos A +cos B + cos C = bsi C si A si B csi Asi B si C ) a cos B si C si A ) + r R ) - r R - R r ) + R r. I triagle ABC, AD is altitude from A. If the B abc b c, c, AD b c, ) 7 ) 97 7 ) NARAYANA GROUP OF SCHOOLS Page

5 Class-Jr.X_E-E 5 6. COMPLEX NUMBERS ) ) ). If, the i i ), ) i, i i i,. If, are the comple cube roots of uity the )Noe. If )- ) W ) z z, the the value of z z z z z z )6 ) 8 )5 5. If is a comple cube root of uity, the the value of the epressio is ( )( ) ( )( )... ( )( )( ) is ) ) 6. cos isi cos i si ) ) cos ) i si cos ) si 7. The cube roots of i are ) i /, i /, i / ) i /, i /, i / i /, i /, i / ) oe 8. The mod- amplitude form of si i cos is ) cos ) cos cos 9.,, are the cube roots of uity the )oe 7 is NARAYANA GROUP OF SCHOOLS Page 5

6 Class-Jr.X_E-E )6 )7 9 ) Both ad 5. The cojugate of is ) ) ) Both ad 5. The fourth roots of uity are ) )- I ) All of these 5. The value/s of i is /are 9 ) cis ) cis Both ad ) cis Paragraph for Q Nos: 5 to 55: If or i i, i i i ( ). i i i, e i i i i I ad ( )( ) ( )( )( ),, are the cube roots of uity i.e ω ω ω I 5. The smallest positive iteger for which i i where i is ) ) ) 5. If z i the z z is )- ) ) 55. If is a cube root of uity the, 5 is equal to ) ) I ) 56. If, are the comple cube roots of uity the )- ) W ) If z z, the the value of z z z z z z )6 ) 8 )5 is QUADRATIC EQUATIONS are equal, the a, b, c 58. If the roots of a b ba c b c are i NARAYANA GROUP OF SCHOOLS Page 6

7 Class-Jr.X_E-E ) GP ) AP HP ) AGP 59. The coditio that a root of the equatio a b c may be reciprocal to a root of is a b c ) bb aa ab bc ba b c ) cb ba ac cd ab bc cc a a ab bc ba b c ) a + b + c = 6. The umber of real solutios of the equatios 7 is ) ) ) 6. The roots of the equatio ) ad ) ad ad ), ad 6. If the equatios p + q = ad a + b = have a commo root ad the secod equatio has equal roots the ) aq = (b + p) ) aq = b + p ap = (b + q) ) ap = b + q 6. The solutio of is ), ), ), are 6. If, are the roots of the equatio a b c the b c a a is ) ) ) 65. If the the value of 5 is ) Zero ) positive Negative ) ot determied 66. The roots of the equatio are ),, ),, -,-, ),i 67. If,, are the roots of -5-7+=, the the equatio whose roots are,, is ) 5 7 ) ) The roots of the equatio is ),, ),,,, ),, 69. If,-, are roots of a 6 the a = ) ) 7 ) 5 7. If,,, are the roots of 8 5, the the equatio whose roots are,,, is NARAYANA GROUP OF SCHOOLS Page 7

8 Class-Jr.X_E-E ) 8 5 ) ) If,, are the roots of the equatio +q +r = the equatio whose roots are,, is ) r q ) r q ) r q r q 7. If the roots of k are i H.P, the k = ) 5 9 ) ) The root of the equatio is. ) ) - ) 7. If,, are the roots of the equatio 5, the is ) - ) -5 5 ) 75. Each of the roots of the equatio are icreased by k so that the ew trasformed equatio does ot cotai term. The k = ) ) 76. If the roots of ),, If,-, are roots of - ) - 6 are i A.P, the the roots are ) ) ),,,, 6 5 ),, a 6 the a = 7 ) If,,, are the roots of 8 5, the the equatio whose roots are,,, is ) 8 5 ) ) If,, are the roots of the equatio +q +r = the equatio whose roots are,, is ) r q ) r q ) r q r q 8. If the roots of - +8 = are i H.P. the the roots are ),, ),,,, ),, NARAYANA GROUP OF SCHOOLS Page 8

9 Class-Jr.X_E-E 5 8. The root of the equatio is. ) ) - ) 8. The umber of real solutios of the equatios 7 is ) ) ) 8. The roots of the equatio is ),, ),,,, 8. The solutio set of is ) /, ) R ), / ) 85. If, 6, 9 are the roots of p + q + r + s = the the roots of 7p +9q +r +s = are ),, ),,,, 6,, ),, 86. The perpedicular bisector of the lie segmet joiig P, ad QK, has Y itercept -. The a possible value of K is ) - ) ) oe 87. The equatio of the straight lie i the symmetric form havig the give slope ad passig through the poit (, ) is + y y ) ) y y CO-ORDINATE GEOMETRY 88. The foot of the perpedicular of the poit (, 5) i y + = is ) (, ) (, (,) ) (, 89. If the algebraic sum of the perpedicular distaces from the poits (, ), (, ) ad (, ) to a variable straight lie be zero, the the lie passes through the poit ) (, ) ) (, ) (, ) ) (, ) 9. The reflectio of the poit (6,8) i the lie = y is ) (,) ) (-6,-8) (-8,-) ) (8,6) 9. Perpedicular distace from the origi to the lie joiig the poits (acos, asi ) (acos, asi ) is ) a cos ( - ) ) a cos ) a si ) a cos 9. The ratio i which the lie joiig the poits A(, ) ad B(, ) divides the lie joiig C(, ) ad D(, ) is ) 7 : 5 eterally ) 7 : 5 iterally 5 : 7 eterally ) 5 : 7 iterally NARAYANA GROUP OF SCHOOLS Page 9

10 Class-Jr.X_E-E 9. The equatio of oe of the bisectors bisectig the agles betwee the lies y + 7 = ad + 5y = is ) + y + 9 = ) y + 9 = y 9 = ) Noe of these 9. Equatio of the lie passig through the poit of itersectio of the lies +y-=, +y-6= ad perpedicular to 5-y-7= is ) +5y-9= ) +5y+7= +5y-6= ) +5y-= 95. The mid poits of the sides of a triagle are (5, ), (5, ) ad (, ).The orthoceter of this triagle is ) (, ) ) (, ) (, ) ),8 96. The differece of the slopes of the lies y y is ) ) ) 97. If y fy represets a pair of lies the f = ) ) ) The agle betwee the straight lies + y + y = is ) ) 5 6 ) The equatio to the two lies represeted by the equatio y cosec y is ) y cos ec cot, y cos ec cot ) y cos ec, y cot y, si ) sec, cot. If the lies k y y are equally iclied to the coordiate aes, the k = ) ) ). If the equatio of the pair of bisectors of the agle betwee the pair of lies y by is y y, the b = ) ) 8 ) 8. If k + y + y 5 y + 8 = represets a pair of straight lies, the k = ) ) ). If the agle betwee the pair of lies joiig the origi to the poits of itersectio of the curve ad the lie i a h by is 9, the ) a + b > ) a + b < a + b = ) Noe of these. The distace betwee the poits A = (,, ), B=(, 5, ) is ) 65 ) 6 7 ) The poits (,,5), (,, ad (7,, ) are ) colliear poits ) Form a isosceles triagle form a right agled triagle ) Form a equilateral triagle 6. If the sum of the squares of the perpedicular distaces of P from the coordiate aes is the the locus of P is ) y z 6 ) y z 6 y z ) y z NARAYANA GROUP OF SCHOOLS Page

11 Class-Jr.X_E-E 7. If (,,p) is the cetroid of the tetrahedro formed by the poits (k,, ), (,,), (6,,5) ad (,, the k+p = ) 7 ) 5 ) 5 8. The directio cosies of the lie joiig the poits A( 6, 5, ), B( 5,, ) is ),,,, ),, ),, 9. The agle betwee the lies whose directio cosies are,,, is ) ) ),, ad y z y z. The agle betwee the lies ad is ) ) 5 ) 9. The value of k if the lies y z y 5 z 6 ad may be k k 7 perpedicular ) ) - ) NARAYANA GROUP OF SCHOOLS Page

VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM (A) 10th Standard Reg.No. : MATHEMATICS - MOD EXAM 1(A)

Time : 0:30:00 Hrs VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM 018-19(A) 10th Stadard Reg.No. : MATHEMATICS - MOD EXAM 1(A) Total Mark : 100 I. CHOOSE THE BEST ANSWER WITH CORRECT OPTION:-