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1. CLASS : XI (J1 & J2) TIME : 40 to 50 Min. DPP. NO.-1 Q.1 State whether the followingstatements are True or False. (i) If x, y, z are all different real numbers, then 1 1 1 2 2 2 ( ) ( ) ( ) x y y z z x      = 1 1 1 2 x y y z z x            (ii) tan2 · sin2 = tan2 – sin2. (iii) 101 · 99 1 102 1   = 101. (iv) sin(1) – cos(1) < 0 (v) There exist natural numbers, m & n such that m2 = n2 + 2002. Fill in the blanks. Q.2 The expression                               90 tan 90 cot 90 sin 90 tan 180 cos 180 tan whereverit is defined, is equal to ______. Q.3 If 2 cos2 (+x)+ 3 sin(+x)vanishes then the values ofx lying in theinterval from0 to 2are_____. Q.4 If tan 25º = a then the value of tan tan tan tan 205 115 245 335       in terms of ‘a’ is _____. Select the correct alternative : (Only one is correct) Q.5 The number of real solution(s) of the equation, sin (2x) = x + x is : (A) 0 (B) 1 (C) 2 (D) none of these Q.6 The expression                                          x 2 3 tan . 2 x cos x 2 7 sin x 2 3 cos . 2 x tan 3 simplifies to (A) (1 + cos2x) (B)sin2x (C) – (1 + cos2x) (D) cos2x Q.7 Number of values of ‘x’  (–2,2) satisfying the equation 6 2 . 4 2 x 2 cos x 2 sin   is (A) 8 (B) 6 (C) 4 (D) 2 Q.8 Let m = tan 3 and n = sec 6, then which one of the following statement holds good? (A) m & n both are positive (B) m & n both are negative (C) m is positive and n is negative (D) m is negative and n is positive. Q.9 Let y = ..... 3 1 2 1 3 1 2 1     , then the value of y is (A) 2 3 13  (B) 2 3 13  (C) 2 3 15  (D) 2 3 15  Q.10 If tan = a b where a, b are positive reals and   1st quadrant then the value of sin sec7 + cos cosec7 is (A) 2 / 7 4 4 3 ) ab ( ) b a ( ) b a (   (B) 2 / 7 4 4 3 ) ab ( ) b a ( ) b a (   (C) 2 / 7 4 4 3 ) ab ( ) a b ( ) b a (   (D) 2 / 7 4 4 3 ) ab ( ) b a ( ) b a (   
2. Fill in the blanks. Q.1 If tan = 2 and    , 3 2       then the value of the expression     3 3 cos sin cos is equal to _______. Select the correct alternative : (Only one is correct) Q.2 The numberof values ofkforwhichthesystem ofequations (k + 1)x + 8y = 4k ; kx + (k + 3)y = 3k – 1 hasinfinitelymanysolutionsis (A) 0 (B) 1 (C) 2 (D)infinite Q.3 116peopleparticipatedinaknockouttennistournament.Theplayersarepaired upin thefirst round, the winners ofthefirstroundarepairedupinthesecondround,andso ontillthefinal isplayedbetweentwo players.Ifafteranyround,thereisoddnumberofplayers,oneplayerisgivenabye,i.e.heskipsthatround andplaysthenextroundwiththewinners.Thetotalnumberofmatchesplayedinthetournamentis (A) 115 (B) 53 (C) 232 (D) 116 Q.4 PQRS is asquare. SR is atangent (at point S) tothecircle with centre O and TR = OS. Then, the ratio of area of the circle to the area of the square is (A) 3  (B) 7 11 (C)  3 (D) 11 7 Q.5 The two legs of a right triangle are sin + sin 3 2          and cos – cos 3 2          . The length of its hypotenuseis (A)1 (B) 2 (C) 2 (D)somefunction of Q.6 If f(x) =                  ) x 3 ( sin x 2 3 sin 3 4 4 –                  ) x 5 ( sin x 2 sin 2 6 6 then, forall permissible values ofx,f(x)is (A) – 1 (B) 0 (C) 1 (D)notaconstant function Subjective : Q.7 Ifanequilateraltriangleandaregularhexagonhavethesameperimeterthenfindtheratiooftheirareas. Q.8 Prove the identity,              cos sin cos sin 2 1 cot 1 cot tan 1 tan 2 2 2 3 2 3 . Q.9 Apolynomial inxof degreethreewhichvanishes when x =1 &x =–2,andhas thevalues 4&28 when x = –1 and x = 2 respectivelyis ______. Q.10 The length of a common internal tangent to two circles is 7 and a common external tangent is 11. Compute the product of the radii ofthe two circles. Q.11 Prove that x4 + 4 is prime onlyfor one value of x  N. CLASS : XI (J1 & J2) TIME : 45 to 55 Min. DPP. NO.-2
3. Fill in the blanks. Q.1 The smallest natural number of the form 1 2 3 X 4 3Y, which is exactlydivisible by 6 where 0  X, Y 9, is ______ . Q.2 The lineAB is 6 meters in length and is tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. Theradius of the outer circle is _______ Q.3 The positive integers p, q & r are all primes. If p2  q2 = r then the set of all possible values of r is ______ . Select the correct alternative : (Only one is correct) Q.4 Solution set ofthe equation 3 2 3 3 0 2x 6 2( 6 2 2       . ) x x x is (A) {–3, 2} (B) {6, –1} (C) {–2, 3} (D) {1, – 6} Q.5 Exact value of cos2 73º + cos2 47º  sin2 43º + sin2 107º is equal to : (A) 1/2 (B) 3/4 (C) 1 (D) none Q.6 If           4 cos 3 cos 2 cos 4 sin 3 sin 2 sin = tan k is an identitythen the value k is equal to : (A) 2 (B) 3 (C) 4 (D) 6 Select the correct alternative : (More than one are correct) Q.7 Theexpression           97 cos 157 cos 7 cos 23 sin 98 cos 158 cos 8 cos 22 sin when simplifiedreduces to : (A) sec(–100) (B) cosec         2 3 (C) sin        2 7 (D) cot        4 5 Q.8 If 1 1 1     sin sin sin cos cos A A A A A , for all permissible values ofA, thenAbelongs to (A) First Quadrant (B) Second Quadrant (C) Third Quadrant (D) Fourth Quadrant CLASS : XI (J1 & J2) TIME : 45 to 55 Min. DPP. NO.-3
4. Q.9 The sines oftwo angles of a triangle are equal to 13 5 & 101 99 . The cosine of the thirdangle is : (A) 245 1313 (B) 255 1313 (C) 735 1313 (D) 765 1313 Q.10 If secA = 8 17 and cosecB = 4 5 then sec(A + B) can have the value equal to (A) 36 85 (B) – 36 85 (C) 84 85  (D) 84 85 Match the Column. This question contains two columns. Column-Icontains four questions and column-IIcontains their answers written in random order. Each entryin column-Iis associatedwith some or theother entryof column-II. Some entriesin column-IImaynot be the answers of anyentryof column-I. Credit will begivenonlywhenall thematchingarecorrect. Column-I Column-II (i) Numberofright triangleon agiven hypotenuse, is (A) 2 (ii) In ascalenetriangle, centroid dividesthelinejoining orthocentreand circumcentrein aratio K whereK equals (B) 2 3 (iii) Three sides of a regular hexagon, no two of which share a vertex of the hexagon areextededtoform an equilateral triangle. The perimeter of the trianglethusformedisptimestheperimeteroftheoriginalhexagon where p equals (C) 5 1 3 (iv) In thefigureshown BC is tangent tothecircle with centre D and diameter 12. Length of FB is (D)infinite (E) 3 1 5
5. Fill in the blanks : Q.1 The expression 1 t cos t sin 1 t cos t sin 6 6 4 4     when simplified reduces to ______ . Q.2 The exact value of           69 sin 51 cos 39 cos 21 sin 66 sin 6 sin 6 cos 24 sin is ______. Q.3 A rail road curve is to be laid out on a circle. If the track is to change direction by280 in a distance of 44 meters then the radius of the curve is ________. [use  = 22/7] Select the correct alternative : (Only one is correct) Q.4 If cos ( + ) = m cos(), then tan is equal to : (A) 1 1         m m tan (B) 1 1         m m tan (C) 1 1         m m cot  (D) 1 1         m m cot  Q.5 The side ofa regular dodecagon is 2 cm. The radius ofthe circumscribed circle in cms. is : (A) 4 6 2 ( )  (B) 6 2  (C) 2 2 3 1  (D) 6 2  Q.6 Whichofthefollowingconditionsimplythattherealnumberxisrational? I x1/2 is rational II x2 and x5 are rational III x2 and x4 are rational (A) I and II only (B) I and III only (C) II and III only (D) I, II and III Q.7 The number of all possible triplets (a1, a2, a3) such that a1 + a2cos2x + a3sin²x = 0 for all x is : (A) 0 (B) 1 (C) 3 (D) infinite Select the correct alternative : (More than one are correct) Q.8 Whichofthefollowingwhensimplifiedreducestounity? (A) 1 2 2 4 4 2 2                sin cot cos      (B)   sin sin cos tan        2 + cos ( – ) (C) 1 4 1 4 2 2 2 2 2 sin cos ( tan ) tan       (D) 1 2 2   sin (sin cos )    Subjective : Q.9 If [1  sin(+) + cos( + )]2 + 1 3 2 3 2 2                       sin cos     = a + b sin2 then find the value of a and b. Q.10 If secA – tanA = p, p  0, find the value of sinA. CLASS : XI (J1 & J2) TIME : 45 to 55 Min. DPP. NO.-4
6. Fill in the blanks : Q.1 Exact value of tan200º (cot10º  tan10º) is ______ . Q.2 The greatest valueoftheexpression sin2 15 8 4         x  sin2 17 8 4         x for 0  x   8 is ___________. Select the correct alternative : (Only one is correct) Q.3 The expression     1 2 2 2 3 4    sin cos . tan       1 4 sin 2 cot cot    2 3 2 2               when simplified reduces to : (A) 1 (B) 0 (C) sin2 (/2) (D) sin2  Q.4 Exact value of cos 20º + 2 sin2 55º  2 sin 65º is : (A) 1 (B) 1 2 (C) 2 (D) zero Q.5 Let sin cos 3 2   = p where     F H G I K J 18 48 23 48 , & sin cos 3 2   = q where     F H G I K J 13 48 14 48 , Then (A) p > 0 and q > 0 (B) p > 0 and q < 0 (C) p < 0 and q < 0 (D) p < 0 and q > 0 Q.6 1 290 cos  + 1 3 250 sin  = (A) 2 3 3 (B) 4 3 3 (C) 3 (D) none Subjective : Q.7 Prove the identity, cos 3 2 4          + sin (3 8)  sin(412) = 4 cos 2 cos4sin6. Q.8 Prove that: 1 x 3 cos 2 x 4 cos x 5 cos   = cos x + cos 2x. Q.9 Prove the identity, sin 2 (1 + tan 2 . tan) + 1 1   sin sin   = tan 2 + tan2   4 2        . Q.10 Prove that   tan 8 tan = (1 + sec2) (1 + sec4) (1 + sec8) CLASS : XI (J1 & J2) TIME : 45 to 55 Min. DPP. NO.-5
7. Q.1 If sin2 = 4 sin2, show that 5 tan( – ) = 3 tan( + ). Q.2 Findthedegreemeasureof allangles‘x’suchthat 0  x  180°and cos6x –sin6x + 4 x 2 cos · x 2 sin2 =0 Q.3 If 0 < x < 4  and cos x + sin x = 4 5 , find the numerical values of cos x – sin x. Q.4 Three real numbers a, b, c satisfy2b = a + c, show that c cos b cos a cos c sin b sin a sin     = tan b. Q.5 Prove the identity 2 2 cos 3 cos sin 3 sin                  = 8 cos2, wherever it is defined. Q.6 Findthevalueof  lyingin the interval [0, 2] andsatisfyingthe cubic, 2sin3 – 5sin2 + 2 sin = 0. Q.7 Find the exact value of cos236° + sin218°. CLASS : XI (ALL) TIME : 45 Min. DPP. NO.-6
8. Fill in the blanks : Q.1 The value of log cos 11 6 64 27  is equal to _________. Q.2 The solution set of the system of equations , x + y= 2 3  , cosx + cosy = 3 2 , where x & y are real , is _______. Q.3 If a  sinx . sin  3        x . sin  3        x  b then the ordered pair (a, b) is ______. Q.4 The value of b satisfying 3 1 3 b log 8  is _______. Q.5 The number of integral pair(s) (x, y) whosesum is equal to their product is ______. Q.6 Amixture of wine and water is made in the ratio of wine : total = k : m.Adding x units of water or removing x units of wine(x 0), eachproducesthesamenewratioofwine:total.Thenumericalvalue of the new ratio is ______. Q.7 If x2  5x + 6 = 0 and log2 (x + y) = log4 25, then the set of ordered pair(s) of (x, y) is ______. Select the correct alternative : (Only one is correct) Q.8 If A + B + C =  & sin A C        2 = k sin C 2 , then tan A 2 tan B 2 = (A) k k   1 1 (B) k k   1 1 (C) k k  1 (D) k k  1 Q.9 The equation ) 2 x 4 x ( log 2 7 7   = x – 2 has (A)twonaturalsolution (B)oneprimesolution (C)nocompositesolution (D)oneintegral solution Q.10 The number of real solution of the equation log10 (7x  9)2 + log10 (3x  4)2 = 2 is (A) 1 (B) 2 (C) 3 (D) 4 CLASS : XI (ALL) TIME : 45 Min. DPP. NO.-7
9. Fill in the blanks : Q.1 If x = 7 5 2 3   1 7 5 2 3  , then the value of x3 + 3x  14 is equal to ______. Select the correct alternatives : (More than one are correct) Q.2 If p, q  N satisfy the equation   x x x x  then p & q are : (A) relativelyprime (B) twin prime (C) coprime (D) if logq p is defined then logp q is not& vice versa Q.3 The expression, logp logp ...... p p p p p n radical sign        where p  2, p  N, when simplified is : (A) independent of p, but dependent on n (B) independent of n, but dependent on p (C) dependent on both p & n (D) negative . Q.4 Whichofthefollowingwhensimplified,reducestounity? (A) log105 . log1020 + 2 log2 10 (B) 2 2 3 48 4 log log log log   (C)  log5 log3 9 5 (D) 6 1       27 64 log 2 3 Q.5 The number N =   1 2 2 1 2 2 3 3 6 2 2    log log log when simplified reduces to : (A) a prime number (B) anirrational number (C) a real which is less than log3 (D) a real which is greater than log7 6 Subjective : Q.6 If tanA& tan B are the roots of the quadratic equation, ax2 + bx + c = 0 then evaluate a sin2 (A + B) + b sin (A + B). cos (A + B) + c cos2 (A + B). Q.7 If cos + cos = a and sin + sin= b then prove that, cos2 + cos2 =      a b a b a b 2 2 2 2 2 2 2     Q.8 Establishtricotomyineachofthisfollowingpairsofnumbers (i) 2 log 3 log 4 27 2 and 3 (ii) log log ( / ) / 4 1 16 5 1 25 and (iii) 4 and log log 3 10 10 81  (iv) log ( / ) log ( / ) / / 1 5 1 7 1 7 1 5 and Q.9 Compute the value of 81 27 3 1 3 36 4 9 5 9 7 log log log   Q.10 Given, log712 = a & log1224 = b . Show that, log54168 = 1 8 5   ab a b ( ) . CLASS : XI (ALL) TIME : 45 Min. DPP. NO.-8
10. Fill in the blanks : Q.1 If logx log18   2 8  = 1 3 . Then the value of 1000 x is equal to _____. Q.2 The expression log .5 0 2 8 has the value equal to ______. Q.3 Solution set of the equation 1 1 6  log x + 2 = 3 1 6  log x is _______. Q.4 The solution set of the equation 27 log 2 log x log 3 9 9 2 x . 6 4   = 0 is ______. Select the correct alternative : (Only one is correct) Q.5 Whichoneof thefollowingwhensimplifieddoes not reduceto an integer? (A) 2 6 12 3 log log log  (B) 243 log 32 log 3 2 (C) log log log 5 5 5 16 4 128  (D) log1/4 1 16 2        Q.6 Let u = (log2x)2 – 6 log2x + 12 where x is a real number. Then the equation xu = 256 has (A) no solution for x (B) exactlyone solution for x (C)exactlytwodistinct solutions for x (D)exactlythreedistinct solutions forx Q.7 The equation, log2 (2x2) + log2 x .   1 x log log 2 x x  + 1 2 log4 2 (x4) +   x log log 3 2 2 / 1 2 = 1 has : (A) exactlyonereal solution (B) two real solutions (C) 3 real solutions (D) no solution . Select the correct alternative : (More than one are correct) Q.8 The equation    2 8 8 x log log 2 x 8 = 3 has : (A)nointegralsolution (B)onenaturalsolution (C) tworeal solutions (D)oneirrationalsolution Subjective Q.9 Find the exact value of tan2 16  + tan2 16 3 + tan2 16 5 + tan2 16 7 Q.10 In anytriangle,if (sinA+ sin B + sin C) (sinA+ sin B  sin C) = 3 sinAsin B, find the angle C. Q.11 Whichissmaller? 80 1 log 3 1 or        2 15 1 log 2 1 CLASS : XI (ALL) TIME : 45 Min. DPP. NO.-9
11. NOTE: Dpp-10 & 11 can be simultaneously done for a better test practice. Q.1 Simplifywheneverdefined )) 180 ( cos ) sin( ) 90 sin( ) 540 ( sin ) 270 sin( ) 720 ( cos ) 270 sin( 2 3 3                       + ) 450 ( ec cos ) 270 cot( 2       where  is taken such that thedenominator appearingin anyfraction in the expression does not vanish. Q.2 Given x2 + 4y2 =12xy, where x>0, y>0 then prove that, log(x + 2y) – 2log2 = 2 1 (log x + log y). Q.3 Solve the equation, 2 x log ) x log(   . Q.4 Let fn(x) = sinnx + cosnx. Find the number of values of x in [0, ] for which the relation 6f4(x) – 4f6(x) = 2f2(x) holds valid. Q.5 If 2cos =x + x 1 , find thevalues of the followingin terms of cosine of the multipleangle of . (i) x2 + 2 x 1 ; (ii) x3 + 3 x 1 and (ii) x4 + 4 x 1 Hence deduce the value of xn + n x 1 , n  N. Q.6 If a  b > 1, then find the largest possible value of the expression       b a loga +       a b logb . Q.7 Prove that solutionofthe equation, 3 x 27 x 9 4 4 1 log 1 2 1 2 log 2                                is an irrational number. . Q.1 Find the possible value(s) of           cot ec cos sec tan cos sin if tan = – 3 4 . Q.2 If b a c log a c b log c b a log      , show that aa . bb . cc = 1. Q.3 Find the value of sin 2  and cos 2  . If sin = – 325 323 and           2 3 , Q.5 Prove that the expression, cos2 8  + cos2 8 3 + cos2 8 5 + cos2 8 7 is not irrational. Q.5 Show that, tan          2 6 tan          2 6 = 1 cos 2 1 cos 2     Q.6 Let y = x 5 cos x 4 cos x 2 cos x cos x 5 sin x 4 sin x 2 sin x sin       . Find the value of y where x = 36  . Q.7 Solve theequation ) 1 x ( log ) 5 . 0 x ( log 5 . 0 x 1 x      . CLASS : XI (ALL) TIME : 50 Min. DPP. NO.-10,11
12. Q.1 Find the number of degree in the acute angle  satisfying cos  = 2 1 2 2  ? Q.2 If x satisfies log2x + logx2 = 4, then log2x can be (A) tan(/12) (B) tan(/8) (C) tan (5/12) (D) tan(3/8) Q.3(a) Solve (x + 2)(x – 2)(x – 13) = (x + 2)(x – 7)(x – 11) for x. (b) Solve (x – 3)(x – 2)(x – 13) = (x – 3)(x – 4)(x – 11) for x. Q.4 Find all real numbers such that 5 x  – 7 x  = 2. Q.5 Let Dbeanypoint on thebaseof anisosceles triangleABC.AC is extended to E so that CE = CD. ED is extended to meetAB at F. If angle CED = 10°, find the cosine of the angle BFD. Q.6 Inthefigure,EisthemidpointofABandFisthemidpointofAD. Ifthe area of FAEC is 13 sq. units, find the area of the quadrilateralABCD. Q.7 In the figure, 'O' is the centre of the circle and A, B and C are three points on the circle. Suppose that OA =AB = 2 units and angle OAC = 10°. Find the length of the arc BC. Q.8 Find all values of asuch thatthe three equations ax + y = 1 x + y = 2 x – y = a aresimultaneouslysatisfied bysame orderedpair (x,y). Q.9 In a triangleABC, BC = 8, CA= 6 andAB = 10.Aline dividing the triangleABC into two regions of equal area is perpendicular toAB at the point X. Find the length BX. Q.10 If m, n > 1 and for all x > 0 and x  1 lognx = 3 logmx. Writeanequationexpressingmexplicitlyin termsof n. CLASS : XI (ALL) TIME : 40 Min. DPP. NO.-12
13. Q.1 If logab+ logbc + logca vanishes where a, b andc are positivereals different than unitythen thevalue of (logab)3 + (logbc)3 + (logca)3 is (A) an odd prime (B) an even prime (C) an odd composite (D)anirrationalnumber Q.2 Each ofthe four statements givenbelow areeitherTrueor False. I. sin765° = – 2 1 II. cosec(–1410°) = 2 III. tan 3 13 = 3 1 IV. cot         4 15 = – 1 Indicate the correct order of sequence, where 'T' stands for true and 'F' stands for false. (A) F T F T (B) F F T T (C) T F F F (D) F T F F Q.3 The value of p which satisfies the equation 122p–1 = 5(3p ·7p)is (A) 12 n 21 n 12 n 5 n l l l l   (B) 21 n 12 n 5 n 12 n l l l l   (C) 21 n 144 n 12 n 5 n l l l l   (D) 21 n 5 12 n 12 n l l l  Q.4 Theexpression      20 sin · 20 tan 20 sin 20 tan 2 2 2 2 simplifiesto (A)arationalwhichis notintegral (B) a surd (C)anaturalwhichis prime (D)a natural which is not composite Q.5 If tan 2  = m, then the value of     sin 1 ) 2 / ( sin 2 1 2 is (A) m 1 m 2  (B) m 1 m 1   (C) m 1 m 1   (D) m 2 m 1 Q.6 The value of 3 76 16 76 16       cot cot cot cot is : (A) tan46º (B) tan44º (C) cot 46º (D) cot2º Q.7 An unknown polynomial yields a remainder of 2 upon division by x – 1, and a remainder of 1 upon division byx – 2. Ifthis polynomial is divided by(x – 1)(x – 2), then theremainderis (A) 2 (B) 3 (C) – x + 3 (D) x + 1 Q.8 If sec x + tan x = 7 22 , find the value of tan 2 x . Use it to deduce the value of cosec x + cot x. CLASS : XI (ALL) TIME : 45 Min. DPP. NO.-13
14. Q.1        x sin 3 4 x sin dx d 3 when x = 12° is (A) 0 (B) 4 2 6  (C) 4 1 5  (D) 4 1 5  Q.2 Number of real x satisfying the equation | x – 1 | = | x – 2 | + | x – 3 | is (A) 1 (B) 2 (C) 3 (D) more than 3 Q.3 A rectanglehas its sides oflength sin x and cos x for some x. Largest possible area which it can have, is (A) 4 1 (B) 1 (C) 2 1 (D) can not be determined Q.4 If logAB + logBA2 = 4 and B <A then the value of logAB equals (A) 1 2  (B) 2 2 2  (C) 3 2  (D) 2 2  Q.5 The sum of3 real numbers is zero. If the sum of theircubes is C then their product is (A) a rational greater than 1 (B) a rational less than 1 (C) an irrational greater than 1 (D) an irrationalless than 1 Q.6 The sides of a triangleABC are as shown in the given figure. Let D be any internal point of this triangle and let e, f, and g denote the distance between the point D and the sides of the triangle. The sum (5e + 12f + 13g) is equal to (A) 120 (B) 90 (C) 60 (D) 30 Q.7 The value of tan27° + tan18° + tan27° tan18°, is (A)anirrationalnumber (B)rationalwhichisnotinteger (C)integerwhichisprime (D)integerwhichis not aprime. Q.8 If cos( + ) + sin( – ) = 0 and tan  = 2006 1 . Find tan . CLASS : XI (ALL) TIME : 45 Min. DPP. NO.-14
15. Q.1 A diameter and a chord of a circle intersect at a point inside the circle. The two parts of the chord are length 3 and5 and one part of the diameter is lengthunity.The radius ofthe circle is (A) 8 (B) 9 (C) 12 (D) 16 Q.2 Smallest positive solution of the equation, 4       x sin2 16 =   x sin 6 2 , is (A) 2  (B) 3 2 (C) 6 5 (D) none Q.3 The difference (sin8 75° – cos8 75°) is equal to (A) 1 (B) 8 3 3 (C) 16 3 3 (D) 16 3 7 Q.4 Thereisanequilateraltrianglewithside4andacirclewiththecentreononeofthevertexofthattriangle. Thearcofthatcircledividesthetriangleintotwopartsofequalarea.Howlongistheradiusofthecircle? (A)  3 12 (B)  3 24 (C)  3 30 (D)  3 6 Q.5 If log3(x) =p and log7(x) =q, whichof thefollowing yields log21(x)? (A) pq (B) q p 1  (C) 1 1 q p 1    (D) 1 1 q p pq    Q.6 Thevalueoftheexpression 1 ) 44 cos ....... .......... 2 cos 1 (cos 2 ) 89 sin ....... 3 sin 2 sin 1 (sin 2                equals (A) 2 (B) 2 1 (C) 2 1 (D) 1 Q.7 In a triangleABC, the value of C sin B sin A cos + A sin C sin B cos + B sin A sin C cos (A)isprime (B)is composite (C)isrational whichis notaninteger (D)aninteger Q.8 ABC is aright angledtriangle.Show that sinA·sinB·sin(A–B)+sinB·sinC·sin(B–C)+sinC·sinA·sin(C–A)+sin(A–B)·sin(B–C)·sin(C–A)=0. CLASS : XI (ALL) TIME : 45 Min. DPP. NO.-15
16. Q.1 Given that log (2)= 0.3010....., number of digits inthe number 20002000 is (A) 6601 (B) 6602 (C) 6603 (D) 6604 Q.2 If logx(logyz) = 0 and logy(logzx) = 0, where x, y, z > 1, then 2z – x – y equals (A) 0 (B) 1 (C) xy (D)yz Q.3 Whichofthefollowingisthelargest? (A) 6 log5 2 (B) 5 log6 3 (C) 6 log5 3 (D) 3 Q.4 If sin and cos  are the roots of the equation ax2 – bx + c = 0, then (A) a2 – b2 = 2ac (B) a2 + b2 = 2ac (C) a2 + b2 + 2ac = 0 (D) b2 – a2 = 2ac Q.5 Let a =cos x + cos         3 2 x + cos         3 4 x and b= sin x + sin         3 2 x + sin         3 4 x then which oneofthe followingdoes not hold good? (A) a = 2b (B) b = 2a (C) a + b = 0 (D) a  b Q.6 Suppose that log10(x – 2) + log10y = 0 and y x 2 y x     Then the value of (x + y), is (A) 2 (B) 2 2 (C) 2 + 2 2 (D) 4 + 2 2 Q.7 If x, y,z arereal numbers greaterthan 1and 'w'is a positive real number. If logxw = 24, logyw = 40 and logxyzw = 12 then logwz has the value equal to (A) 120 1 (B) 120 2 (C) 120 3 (D) 120 5 Q.8 If  and  are the roots of the quadratic equation (sin 2a)x2 – 2(sin a + cos a)x + 2 = 0, find them and hence prove that 2 + 2 = 2 · 2. Q.9 Findallintegral solutionof theequation,       3 x 2 2 x 4 2 x x log 3 x log 2 x log 4   . CLASS : XI (ALL) TIME : 50 Min. DPP. NO.-16
17. Q.1 Let N = 2 2 12 22 2 12 22          then log2N equals (A) 2 (B) 3 (C) 4 (D) none Q.2 The sum of all values of x so that ) 2 x 3 x ( ) 1 x 3 x ( 2 2 8 16      ,is (A) 0 (B) 3 (C) – 3 (D) – 5 Q.3 The equation, | sin x | = sin x + 3 in [0, 2] has (A) no root (B) onlyone root (C) two roots (D) more than two roots Q.4 Given log2(log8x)= log8(log2x)then (log2x)2 has thevalueequal to (A) 9 (B) 12 (C) 27 (D) 3 3 Q.5 The reals xand ysatisfy log8x + log4(y2) = 5 and log8y+ log4(x2) = 7 thenthe valueofxyis (A) 1024 (B) 512 (C) 256 (D) 81 Q.6 If sin 2x = 2025 2024 , where 4 5 < x < 4 9 , the value of the sin x – cos x is equal to (A) – 45 1 (B) 45 1 (C) ± 2025 1 (D) none Q.7 The equation ln           ) 1 k ( 1 k 1 ) 1 k ( k = F(k) ·                k n k 1 1 k 1 1 n l l is true for all k wherever defined. F(100) has the value equal to (A) 100 (B) 101 1 (C) 5050 (D) 100 1 Q.8 Let aandbaretworealnumbers suchthat, sina+sinb= 2 2 andcos a+cosb = 2 6 .Findthevalueof (i) cos(a – b) and (ii) sin(a + b). Q.9 For any 3 angle ,  and , prove that sin  + sin  + sin  = sin( +  + ) + 4 sin          2 ·sin          2 ·sin          2 . CLASS : XI (ALL) TIME : 50 Min. DPP. NO.-17