# Quiz (1-11) WA PQRS.pdf

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### Quiz (1-11) WA PQRS.pdf

• 1. BULLS EYE QUIZ-1 Q.1 In thediagram,ABCD is a parallelogram, and BFDE is a square. If AB = 20 cm and CF = 16 cm, what is the perimeter of the parallelogramABCD? (A) 86 cm (B) 92 cm (C) 96 cm (D) 106 cm Q.2 Giventhreesegmentsoflengthx,11–x,andx –4,respectively.Which ofthefollowingindicatestheset of all numbers x such that thethree segments couldbethelengths ofthe sides of atriangle? (A) x > 4 (B) 5 < x < 7 (C) 4 < x < 11 (D) 0 < x < 11 Q.3 Arhombus is formed bytworadiiand two chords ofa circlewhoseradius is16 cm. Find thearea of the rhombus. (A) 3 128 cm2 (B) 128 cm2 (C) 256 cm2 (D) 3 256 cm2 Q.4 Two congruent 30° – 60° – 90° triangles are placed, as shown, so that theyoverlappartlyandtheirhypotenuses coincide.Ifthehypotenuseis 12cm, findthearea common toboth triangles. (A) 3 6 cm2 (B) 3 8 cm2 (C) 3 9 cm2 (D) 3 12 cm2 Q.5 Acirculararchhaving width24m andheight 9m isto be constructed. Whatis the radius ofthecircleof which the archis an arc? (A)10m (B) 12.5 m (C) 13.5m (D)14m QUIZ-2 Q.1 The minute hand of a clock travels k radians from 1 pm to 2.35pm. The value of k is ________. Q.2 The number palindrome 1 2 3 4 3 2 1 is a perfect square. Its positive root is _____. Q.3 Thereal number 2 3 12 75         whenexpressed in thesimplest form is equal to (A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 Q.4 The sum ofthe solutions on theinterval (0, 2] to the equation: 0 = –             x cos x sin x sin x cos 2 x sin 2 3 2 2 , is (cos x  0 ) (A) 3 (B) 4 (C) 5 (D) 6 Q.5 Twicethemeasureofthesupplement ofan angleisadded tothreetimesthemeasureofthecomplement of the same angle. The sum is the measure of an interior angle of a regular nine-sided polygon. The measureofthesupplement oftheangle, is (A) 82° (B) 72° (C) 98° (D) 108° MATHEMATICS Quiz from 1 to 5
• 2. Q.6 Let XOY be a right triangle with XOY = 90°. Let M and N be the midpoints of legs OX and OY respectively. If XN = 19 andYM = 22, then XYequals (A) 26 (B) 5 13 (C) 32.5 (D) 41 QUIZ-3 Q.1 If (1, 2) is one of the points of intersection of the graphs of ax2 + by2 = 5 and bx2 + ay2 = 5, then find a + b. (A) 2 (B) 3 (C) 4 (D) 5 Q.2 Given parallelogramABCD, withAB = 10,AD = 12 and BD = 13 2 .The length of (AC) is (A) 10 (B) 13 2 (C) 3 12 (D) 109 2 Q.3 The continued fraction . .......... 2 1 2 1 2 1 2     , has the valueequal to (A) 1 (B) 5/4 (C) 3/2 (D) 7/4 Q.4 If x2 – xy + y2 = a and x3 + y3 = b then xy = (A) 2 2 a b – 1 (B) 3 b a 3 b 2 2  (C) 2 3 2 a 3 a b  (D) a 3 b 2 a 3 2  Q.5 Asquareandanequilateraltrianglehavethesameperimeter.LetAbetheareaofthecirclecircumscribed about the square and B be the area of the circle circumscribed about the triangle.The ratioA/B equals (A) 9 : 16 (B) 3 : 4 (C) 27 : 32 (D) 6 3 : 8 Q.6 ABC is arighttrianglewithhypotenuseABandAC =15cm.Altitude CH dividesABinto segmentsAH and HB, with HB =16cm.The area of ABC, is (A) 120 cm2 (B) 144cm2 (C) 150cm2 (D) 216cm2 QUIZ-4 Q.1 Threeidenticalsquaresareplaceside-by-sideasindicatedinthefigure. Linesarethendrawn from OtoAandfromOtoB. Findthemeasureof angleAOC plus angle BOC, is ________. Q.2 The number 308 18 can be written in the form b a  where a and b are whole numbers and a > b. The value of (a – b), is (A) 4 (B) 12 (C) 16 (D) 18 Q.3 Consider the eightdigit numberN =11115556.Which of the followingstatements are true? I. N isdivisible by11 II. N – 9 is a prime III N is a perfect square (A) I (B) II (C) III (D) I, II and III
• 3. BULLS EYE Q.4 If 0 < x < 2 and 2tan x = 4sin x then the number of value of x is ________. (A) 1 (B) 2 (C) 3 (D) 4 Q.5 The valueoftheseries 1 + 2 – 3 – 4 + 5 + 6 – 7 – 8 + 9 + ... – 99 – 100, is (A) –100 (B) 0 (C) 1 (D) 100 QUIZ-5 Q.1 Thesumofthedigits oftheintegral solution oftheequation 1 x 32 14    =4 is (A) 785 (B) 765 (C) 20 (D) 18 Q.2 Giventhefollowingsystemofequations 3 1 y 1 x 1   ; 5 1 z 1 x 1   ; 7 1 z 1 y 1   The value of the ratio y z is (A) 17 (B) 23 (C) 29 (D) 31 Q.3 The equation 2 x 2 = 162x – 3 has twosolutions. Their sum is (A) 0 (B) 2 (C) 6 (D) 8 Q.4 If sin2x + sin x cos x – 6cos2x = 0 and 0 x 2     , then the value of tan x, is (A) 0 (B) – 3 (C) 2 (D) –6 Q.5 If sin  = 13 5  and  is in Quadrant III, then the value of        2 cos , is (A) 13 6  (B) 26 1 (C) 12 5  (D) 26 26  ANSWERS QUIZ-1 Q.1 C Q.2 B Q.3 A Q.4 D Q.5 B QUIZ-2 Q.1 18 57 Q.2 1111 Q.3 B Q.4 A Q.5 A Q.6 A QUIZ-3 Q.1 A Q.2 D Q.3 A Q.4 C Q.5 C Q.6 C QUIZ-4 Q.1 45° Q.2 A Q.3 C Q.4 B Q.5 D QUIZ-5 Q.1 C Q.2 C Q.3 D Q.4 B Q.5 D
• 4. BULLS EYE MATHEMATICS Quiz from 6 to 9 QUIZ-6 (CLASS-XI) Q.1 The value of the expression x 3 sin x 5 sin x 3 cos x 5 cos   at x = /8, is _______. Q.2 If y= 2 sin          2 x 2 – 1 then the largest possible value of yfor all real x, is (A) 1 (B) 2 (C) 3 (D) 0 Q.3 Which of statements I, IIand III and IV below are true? I cos  = cos(–) for all angles . II sin =sin(–)forall angles . III cos  = cos(–) for some angles . IV sin  =sin(–)forsomeangles . (A) I, III, IV but not I (B) I and III but not II or IV (C) I and IV but not II or III (D) III and IV but not II or III Q.4 Numberofsides ina polygonifthe sum of its interiorangles is2520°, is (A) 14 (B) 16 (C) 18 (D) 20 Q.5 SupposeABCDisaquadrilateralinscribedinacircle.Thenamongthefollowingidentitieshowmanyare always true. I sinA=sinC II sinA + sinC = 0 III cosB + cosD = 0 IV cosB = cosD (A) 0 (B) 1 (C) 2 (D) 3 Q.6 Valueofsin 705° is (A) 4 2 6  (B) 4 6 2  (C) 4 2 3  (D) 2 3 1 QUIZ-7 (CLASS-XI) Q.1 If the base of a triangle is increased % 6 . 66 and the altitude to this base is decreased 40% then the change inthearea ofthetriangle, is (A) 1% increase (B) 0% increase (C) 1/2% decrease (D) 1% decrease Q.2 The value of the parameter m for whichthe equation 1 x 3 2 x   = m x 6 1 x 2   has no solution for x, is (A) 12 (B) 18 (C) 14 (D) 13 Q.3 The value of x such that 4(1 + y)x2 – 4x + 1 – y = 0 is true for all real values of y, is (A) – 1/2 (B) – 2/3 (C) 2/3 (D) 1/2 Q.4 Knowing that 2 is a solution of the equation 6x3 – 25x2 + 32x – 12 = 0, the sum of the other two solutions,is (A) – 12/5 (B) 12/5 (C) – 13/6 (D) 13/6
• 5. BULLS EYE Q.5 Suppose that x&yarenumberssuchthat sin(x+y)=3/10andsin (x – y)=1/2. Thevalueofsinx·cosy is (A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 Q.6 A circle of area 20 is centered at the point indicated bya solid dot in the accompanying figure. Suppose that ABC is inscribed in that circle and has area 8. The central angles ,  and  are as shown. What is the value of sin  + sin  + sin ? (A) 5 4 (B) 4 3 (C) 3 2 (D) 2  QUIZ-8 (CLASS-XI) Q.1 Solve for x, given that 3x + 2 = 3x + 216. Q.2 A rectangular closed box (shown) with dimensionsa, 2aand 1 hasasurfaceareaof 54, whereaisan integer. Determinethe volumeof thebox. Q.3 Compute the sum of the first 99 terms of the series (a > 0, a  1) logaa – logaa2 + logaa3 – logaa4 + logaa5 – logaa6 + ........... Q.4 In the figure, each region T represents an equilateral triangle andeachregionSasemicircle.Thecompletefigureisasemicircle ofradius6withitscentreO.Thethreesmallersemicirclestouch the large semicircleat pointsA, Band C.What is the radius of asemicircleS? Q.5 The lengths of the sides of triangleABC are 60, 80 and 100 with A=90°.The lineAD divides triangleABC into two triangles ofequal perimeter. Calculatethelength ofAD. QUIZ-9 (CLASS-XI) Q.1 If a + b = 1 and a2 + b2 = 85, then the value of (a3 + b3), is (A) 127 (B) 173 (C) 154 (D) 321 Q.2 Theset ofvalues ofkforwhichthesum of theroots ofP(x)=4x2 +k2x +k is equal totwice theproduct of theroots is (A) {–2} (B) {–2, 0} (C) {0} (D) {2} Q.3 If b a = 4 3 and c b = 9 8 and d c = 3 2 , then 2 b ad is equal to (A) 81 64 (B) 84 61 (C) 64 81 (D) 61 84 Q.4 Numberofdiagonalsin a regularpolygon with 20 sides, is (A) 170 (B) 180 (C) 190 (D) 200 Q.5 If two real numbers x and y satisfythe equation y x = x – y, then which of thefollowingis true? (A) Bothx and ymust be rational. (B) It is possible that y= 1. (C) Bothx and ymust be irrational. (D) x  4 or x  0 Q.6 Solve 3 3 28 x 6 28 x 6    = 2.
• 6. BULLS EYE QUIZ-10 (CLASS-XI) Q.1 Johnhas takenn tests.If hereceives71 onthenext test, hisaveragewill beexactly83. Ifhereceives 99, then the averagewill be exactly87 then the the value of n, is (A) 6 (B) 5 (C) 8 (D) thereis not enoughinformation providedto answerthequestion Q.2 If x + y = 1 and x2 + y2 = 4, then what x3 + y3 equal? (A) 2 11 or 2 5 (B) 10 (C) 2 5 (D) 2 11 Q.3 Findthenumberoftriangles withsides of integerlength whoseperimeteris 10. (A) 4 (B) 3 (C) 2 (D) 0 Q.4 If a and b are positive real numbers such that b > a, and c and d are negative real numbers such that d>c, then whichofthefollowingstatements must betrue? I d b > c a II b – d > a – c III (a + d)(b + c) > (a + c)(b + d) (A) onlyI (B) onlyII (C) onlyIII (D) onlyII and II Q.5 Aand B are points on the circumferenceof a circle of radius r and centre O. If the distance betweenA and B is r, findthe measureof angleAOBin radian. Q.6 Threemutuallytangent circles of equal radius two, are shownin the figure. Find thearea of the shadedportion between the three circles. QUIZ-11 (CLASS-XI) Q.1 If x > 0 such that x + x 1 = 4 then the value of x3 + 3 x 1 is (A) 60 (B) 52 (C) 64 (D) 12 (E)none Q.2 Simplify:  1 3 1 2 1 3 1 2     . (A) 1 + 3 3 2 (B) 2 1 29  (C) 3 14 1 (D) 1 + 3 15 Q.3 A marble of diameter 2 is dropped into a conical cup of height 4 and radius 3. When it gets stuck, how high is the bottom of themarble above the vertex of the cone? (A) 1/3 (B) 3 2 (C) 3 2 (D) 3 3 Q.4 Evaluate: 33 16 8 4 2 2 1 ) 1 2 )( 1 2 )( 1 2 )( 1 2 )( 1 2 (       (A) 1/4 (B) 1/2 (C) 1 (D) 2 x 1 x 8 4      2
• 7. BULLS EYE Q.6 Solvesystem ofequations x + 2y – z = 5 3x + 2y + z = 11 (x + 2y)2 – z2 = 15 ANSWERS KEY Quiz-10 (Class-XI) Q.1 A Q.2 D Q.3 C Q.4 C Q.5 /3 Q.6   2 3 4 Quiz-11 (Class-XI) Q.1 B Q.2 D Q.3 C Q.4 B Q.5 2 Q.6 x = 4; y = 0; z = – 1