1. Class : XI (ACME)
Time : 2 hour Max. Marks : 130
INSTRUCTIONS
1. The question paper contains 12 pages and 3-parts. Part-A contains 20 objective questions, Part-B contains
3 "Match the Column" questions and Part-C contains 4 "Subjective" questions.All questions are compulsory.
Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If
you found some mistake like missing questions or pages then contact immediately to the Invigilator.
PART
-A
(i) Q.1 to Q.15 have only one correct alternative and carry 3 marks each.
There is NEGATIVE marking and 1 mark will be deducted for each wrong answer.
(ii) Q.16 to Q.20 have more than one correct alternatives and carry 5 marks each.
There is NO NEGATIVE marking. Marks will be awarded only if all the correct alternatives are selected.
PART
-B
(iii) Q.1 to Q.3 are "Match the Column" type which may have one or more than one matching options and
carry 8 marks for each question. 2 marks will be awarded for each correct match within a question.
There is NEGATIVE marking. 0.5 Marks will be deducted for each wrong match. Marks will be awarded
only if all the correct alternative(s) is/are selected.
PART
-C
(iv) Q.1 to Q.4 are "Subjective" questions and carry 9 marks each. There is NO NEGATIVE marking.
Marks will be awarded only if all the correct bubbles are filled in your OMR answer sheet.
2. Indicate the correct answer for each question by filling appropriate bubble in your OMR answer sheet.
3. Use only HB pencil for darkening the bubble.
4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed.
5. The answer(s) of the questions must be marked by shading the circles against the question by dark HB pencil only.
REVIEW TEST-6
MATHEMATICS
PART-B
For example if correct match for
(A) is P, Q; for (B) is P, R;
for (C) is P and for (D) is S then the
correct method for filling the bubbles is
P Q R S
(A)
(B)
(C)
(D)
PART-C
Ensure that all columns
(4 beforedecimal and2afterdecimal)are
filled.Answer havingblank column will
be treated as incorrect. Insert leading
zero(s) if required after rounding the
result to 2 decimal places.
e.g. 86 should be filled as 0086.00
.
.
.
.
.
.
.
.
.
.
PART-A
For example if only 'B' choice is
correct then, the correct method for
filling the bubble is
A B C D
For example if only 'B & D' choices
are correct then, the correct method
for filling the bubbles is
A B C D
The answer of the question in any
other manner (such as putting ,
cross , or partial shading etc.)
will be treated as wrong.

2. ROUGHWORK
PART-A
Select the correct alternative. (Only one is correct) [15 × 3 = 45]
There is NEGATIVE marking and 1 mark will be deducted for each wrong answer.
Q.1 A triangle with sides a = 15, b = 28 andc = 41. The length of the altitude from the vertex Bon the side
AC is
(A) 6 (B) 7 (C) 9 (D) 16
Q.2 If sides a, b and c of triangleABC satisfy
c
b
a
c
b
a 3
3
3




= c2 then tan 





4
C
has the value equal to
(A) 2 – 1 (B) 2 – 3 (C) 1/ 3 (D) 2 + 3
Q.3 In a triangleABC, ABC = 45°, point D is onBC so that2BD =CD and DAB= 75°. ACBequals
(A) 15° (B) 60° (C) 30° (D) 75°
Q.4 The first term of an infinite geometricseries is 2 andits sum be denoted byS. If |S – 2 |<1/10 then the
true set of the range of common ratio of theseries is
(A) 





5
1
,
10
1
(B) 






2
1
,
2
1
– {0}
(C) 






20
1
,
19
1
– {0} (D) 






21
1
,
19
1
– {0}
Q.5 Number of solution satisfyingthe equation, tan22x = 2 tan 2x · tan 3x + 1 in [0, 2] is
(A) 0 (B) 1 (C) 2 (D) 4
Q.6 Numerical value of
12
cos






 


4
cos
12
5
sin +
12
sin






 


4
sin
12
5
cos , is
(A)
2
1
(B)
2
3
(C) 2 + 3 (D)
2
3
1

3. ROUGHWORK
Q.7 Two circles both touching the coordinate axes and pass through the point (6, 3). The radii of the two
circles are the roots of the equation
(A) t2 – 12t + 20 = 0 (B) t2 – 15t + 36 = 0 (C) t2 – 18t + 45 = 0 (D) t2 – 14t + 48 = 0
Q.8 Let 'a' and 'b' are the roots of the equation x2 – mx + 2 = 0. Suppose that 






b
1
a and 






a
1
b are the
roots of the equation x2 – px + q = 0. If p = 2q then the value of m is equal to
(A) 4 (B) 6 (C) 8 (D) 9
Q.9 The value of the determinant
y
x
1
x
y
x
1
1
x
1
0
1




depends on
(A)onlyx (B)onlyy (C) both x and y (D)neitherx nor y
Q.10 The sum of all the positive integers greater than 1 and less than 1000, which leave a remainderof one
when divided by2, 3, 4, 5 and 6, is
(A) 8176 (B) 7936 (C) 8167 (D) none
Direction forQ.11 and Q.12 (2 questions together)
Consider the digits 1, 2, 2, 3, 3, 3 and answer the following
Q.11 If all the 6 digit numbers using these digits only are formed and arranged in ascending order of their
magnitudethen29th numberwillbe
(A) 213332 (B) 233321 (C) 233312 (D) none
Q.12 LetMdenotesthenumberofsixdigitnumbersusingonlythegivendigitsifnotallthe2'saretogetherand
N denotes the corresponding figure if no 3's are together then M – N equals
(A) 16 (B) 28 (C) 54 (D) 36
Q.13 Number of selections that can be madeof 6 letters from the word "COMMITTEE" is
(A) 20 (B) 17 (C) 34 (D) 35

4. ROUGHWORK
Q.14 Acircle of radius r touches the lines given bythe equation 4x2 – 4xy+ y2 – 18x + 9y– 36 = 0.Area of
thecircleinsquareunitsis
(A) 45  (B) 75  (C) 45/2 (D) 45/4
Q.15 Ifthemaximum andminimumvalueoftheexpression
6
x
3
x
2
2
x
2



(x R)are Mand mrespectively
then the value of
m
1
M
1
 equals to
(A) – 13 (B) – 10 (C) 10 (D) 16
Select the correct alternatives. (more than one are correct) [5 × 5 = 25]
ThereisNO NEGATIVE marking.
Q.16 If sin (x + 20°) = 2 sin x cos 40° where x  




 
2
,
0 then which of the following hold good
(A) sec
2
x
= 2
6  (B) cot
2
x
= (2 + 3 )
(C) tan 4x = 3 (D) cosec 4x = 2
Q.17 If the vertices of an equilateral triangleABC are (1, 1); (–1, –1) and (a, b) then
(A) a2 + b2 must be equals to 6 (B) a + b must be equals to zero
(C) a + b can be equal to 3
2 (D)lengthofits median is 6
Q.18 The sides ofa right triangleT1 are 20, xand hypotenuse y.Thesides ofanotherright triangleT2 are30,
x – 5 and hypotenuse y+ 5. If P1 and P2 are the radii of the circles inscribed and 1 and 2 arethe areas
ofthetriangles T1 and T2 respectivelythenwhichofthefollowinghold good?
(A) 61 = 52 (B) 81 = 72 (C) P1 = P2 (D) 2P1 = P2

5. ROUGHWORK
Q.19 ABCD is aquadrilateral co-ordinates of whosevertices areA(1, 0),B(–1, 0), C(3,4) andD(–3, 4) then
(A)Thediagonals of the quadrilateral are equal but not at right angle
(B)Areaofthe quadrilateral is 16
(C) Circlepassingthrough anythreepoints of this quadrilateralalso passes through thefourthpoint
(D)ThequadrilateralABCDisanequilateral trapezium
Q.20 LetA (1, 2); B  (3, 4) and C  (x, y) be any point satisfying (x – 1)(x – 3) + (y– 2)(y – 4) = 0 then
whichofthefollowingholdgood?
(A) Maximum possible area of thetriangleABC is 2 squareunits
(B) MaximumnumberofpositionsofCintheXYplanefortheareaofthetriangleABCtobeunity,is4
(C) Least radius of the circle passing throughAand B is 2
(D) If'O'is theoriginthen the orthocentre aswell as circumcentre ofthe triangle OABlies outside this
triangle

6. ROUGHWORK
PART-B
MATCH THE COLUMN [3 × 8 = 24]
There is NEGATIVE marking. 0.5 Marks will be deducted for each wrong match.
INSTRUCTIONS:
Column-Iand column-IIcontainsfour entries each. Entries ofcolumn-Iareto bematchedwith some
entriesofcolumn-II.Oneormorethanoneentriesofcolumn-Imayhavethematchingwiththesameentries
ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethanonematchingwithentriesofcolumn-II.
Q.1 ColumnI ColumnII
(A) Numberofincreasingpermutationsof msymbols (P) nm
are there from the n set numbers {a1, a2, , an}
where theorder amongthenumbersis given by
a1 < a2 < a3 <  an–1 < an is
(B) There are m men and n monkeys. Number of ways (Q) mCn
in whicheverymonkeyhas a master, ifa man can
haveanynumberofmonkeys
(C) Number of ways in which n red balls and (m – 1) green (R) nCm
balls canbe arranged in a line, so that no two red balls
are together, is (balls of the same colour are alike)
(D) Number of ways in which 'm'different toys can be (S) mn
distributed in 'n'childrenifeverychildmayreceive
anynumberof toys, is

7. ROUGHWORK
Q.2 ColumnI ColumnII
(A) If the lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 (P) ArithmeticProgression
and cx + 4y+ 1 = 0 passes through the same
point, then a, b, c are in
(B) Let a, b, c be distinct non-negative numbers. (Q) GeometricProgression
If the lines ax + ay + c = 0, x + 1 = 0 and
cx + cy + b = 0 passes through the same point,
then a, b, c are in
(C) If the lines ax + amy + 1 = 0, bx + (m + 1)by + 1 = 0 (R) HarmonicProgression
and cx + (m + 2)cy + 1 = 0, where m  0 are
concurrent then a, b, c are in
(D) If the roots of the equation (S) None
x2 – 2(a + b)x + a(a + 2b + c) = 0
be equal then a, b, c are in

8. ROUGHWORK
Q.3 ColumnI ColumnII
(A) 



n
1
n
n
2
n
n 2
C
Lim equals (P) 0
(B) Let the roots of f (x) = 0 are 2, 3, 5, 7 and 9 (Q) 1
and the roots of g (x) = 0 are – 1, 3, 5, 7 and 8.
Number of solutions of the equation
)
x
(
)
x
(
g
f
=0 is
(C) Let y =
x
cos
x
sin3
+
x
sin
x
cos3
where 0 < x <
2

, (R) 3/2
thentheminimumvalueofyis
(D) Acircle passesthrough vertex D of the squareABCD, (S) 2
and is tangent to the sidesAB and BC. IfAB = 1, the
radius of the circle can be expressed as p + 2
q ,
then p + q has the value equal to

9. PART-C
SUBJECTIVE: [4 × 9 = 36]
ThereisNO NEGATIVE marking.
Q.1 If x1 and x2 arethe twosolutions oftheequation
3
16
2
3
3
9
log
x
log
3
1
log
x
12
3 






 , then find thevalue of
2
2
2
1 x
x  .

10. Q.2 A circle with center in thefirst quadrant is tangent to y = x + 10, y= x – 6, and the y-axis. Let (h, k) be
the center of the circle. If the value of (h + k) = a + a
b where a is a surd, find the value of a + b.

11. Q.3 Suppose that there are 5 red points and 4 blue points on a circle. Find the number of convex polygons
whose vertices areamongthe 9 points and having at least one blue vertex.

12. Q.4 TriangleABC lies intheCartesianplaneand has an areaof 70sq. units.The coordinates of Band C are
(12, 19)and(23, 20) respectivelyand the coordinates ofAare (p, q).The line containing themedian to
the side BC has slope –5. Find the largest possible value of (p + q).