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QUIZ-1 Q.1 In the diagram, ABCD is a parallelogram, and BFDE is a square. If AB = 20 cm and CF = 16 cm, what is the perimeter of the parallelogram ABCD? (A) 86 cm (B) 92 cm (C) 96 cm (D) 106 cm Q.2 Given three segments of length x, 11 – x, and x – 4, respectively. Which of the following indicates the set of all numbers x such that the three segments could be the lengths of the sides of a triangle? (A) x > 4 (B) 5 < x < 7 (C) 4 < x < 11 (D) 0 < x < 11 Q.3 A rhombus is formed by two radii and two chords of a circle whose radius is 16 cm. Find the area of the rhombus. (A) 128 cm2 (B) 128 cm2 (C) 256 cm2 (D) 256 cm2 Q.4 Two congruent 30° – 60° – 90° triangles are placed, as shown, so that they overlap partly and their hypotenuses coincide. If the hypotenuse is 12cm, find the area common to both triangles. (A) 6 cm2 (B) 8 cm2 (C) 9 cm2 (D) 12 cm2 Q.5 A circular arch having width 24m and height 9m is to be constructed. What is the radius of the circle of which the arch is 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 The real number 3 75 2 12 when expressed in the simplest form is equal to (A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 Q.4 The sum of the solutions on the interval (0, 2] to the equation: 0 = – (2 sin2 x + 2 cos2 x) , is (cos x 0 ) cos x (A) 3 (B) 4 (C) 5 (D) 6 Q.5 Twice the measure of the supplement of an angle is added to three times the measure of the complement of the same angle. The sum is the measure of an interior angle of a regular nine-sided polygon. The measure of the supplement of the angle, is (A) 82° (B) 72° (C) 98° (D) 108° BULLS EYE 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 and YM = 22, then XY equals (A) 26 (B) 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 parallelogram ABCD, with AB = 10, AD = 12 and BD = 2 . The length of (AC) is (A) 10 (B) 2 (C) 12 (D) 2 Q.3 The continued fraction 2 1 2 1 2 1 , has the value equal to 2 ........... (A) 1 (B) 5/4 (C) 3/2 (D) 7/4 Q.4 If x2 – xy + y2 = a and x3 + y3 = b then xy = b2 b2 b b2 a3 a 2 2b3 (A) a 2 – 1 (B) 3a 2 3 (C) 3a2 (D) 3a Q.5 Asquare and an equilateral triangle have the same perimeter. Let Abe the area of the circle circumscribed about the square and B be the area of the circle circumscribed about the triangle. The ratio A/B equals (A) 9 : 16 (B) 3 : 4 (C) 27 : 32 (D) 3 8 Q.6 ABC is a right triangle with hypotenuse AB and AC = 15 cm. Altitude CH divides AB into segments AH and HB, with HB = 16cm. The area of ABC, is (A) 120 cm2 (B) 144cm2 (C) 150cm2 (D) 216cm2 QUIZ-4 Q.1

- 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