1. QUIZ-1 (CLASS-XII)
Q.1 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
Q.2 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.3 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
Q.4 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.5 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
Q.6 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
Q.7 The valueoftheseries
1 + 2 – 3 – 4 + 5 + 6 – 7 – 8 + 9 + ... – 99 – 100, is
(A) –100 (B) 0 (C) 1 (D) 100
QUIZ-2 (CLASS-XII)
One or more than one is/are correct.
Q.1 If x = t3 + t + 5 & y = sin t then
d y
dx
2
2 =
(A) 
 
 
3 1 6
3 1
2
2
3
t t t t
t
 

sin cos
(B)
 
 
3 1 6
3 1
2
2
2
t t t t
t
 

sin cos
(C) 
 
 
3 1 6
3 1
2
2
2
t t t t
t
 

sin cos
(D)
cost
t
3 1
2

Q.2 If y =
1
2 3 1
2
x x
 
then
d y
dx
2
2 at x =  2 is :
(A)
38
27
(B) 
38
27
(C)
27
38
(D) none
MATHEMATICS
Quiz from 1 to 5

2. Q.3 If y2 = P(x), is a polynomial of degree 3, then 2
d
dx





 y
d y
dx
3
2
2
.





 equals :
(A) P  (x) + P  (x) (B) P  (x) . P  (x) (C) P (x) . P  (x) (D) a constant
Q.4 If f (x) = x  2 & g (x) = f ( f (x)) then for x > 20, g  (x) =
(A) 1 (B)  1 (C) 0 (D) none
Q.5 PeoplelivingatMars,insteadoftheusualdefinitionofderivativeDf(x),defineanewkindofderivative,
D*f(x)bytheformula
D*f(x) = Limit
h
f x h f x
h

 
0
2 2
( ) ( )
where f(x) means [f(x)]2. If f(x) = x lnx then
D f x x e
* ( )  has the value
(A) e (B) 2e (C) 4e (D) none
Q.6 If f(x) = x . x, then its derivative is :
(A) 2x (B) 2x (C) 2x (D) 2x sgn x
QUIZ-3 (CLASS-XII)
Q.1 If y =
1
x
3
x
1
x
x
2
2
4




and
dx
dy
= ax + b then the value of a + b is equal to
(A) cot
8
5
(B) cot
12
5
(C) tan
12
5
(D) tan
8
5
Q.2 Valueofsin 705° is
(A)
4
2
6 
(B)
4
6
2 
(C)
4
2
3 
(D)
2
3
1
Q.3 Findallrealfunctionsofonerealvariablethatsatisfythefollowingfunctionalequation,
f (x) + 2 f 





x
1
= x
Q.4 In the figure, each region T represents an equilateral triangle and each
region S a semicircle. The complete figure is a semicircle of radius 6
withitscentreO.Thethreesmallersemicirclestouchthelargesemicircle
at pointsA, B and C.What is the radius of a semicircle S?
Q.5 Solve 3
3
28
x
6
28
x
6 

 = 2.
QUIZ-4 (CLASS-XII)
Q.1 If f (x) = x5 + 2x3 + 2x and g is the inverse of f then g'(–5) is equal to
(A)
13
1
(B) 1 (C)
7
1
(D) none
Q.2 Suppose thefunction f (x)– f (2x)has the derivative 5 at x = 1 and derivative 7 at x = 2.The derivative
of the function f (x) – f (4x) at x = 1, has the value equal to
(A) 19 (B) 9 (C) 17 (D) 14
Q.3 Findthenumberoftriangles withsides of integerlength whoseperimeteris 10.
(A) 4 (B) 3 (C) 2 (D) 0

3. Q.4 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.5 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-5 (CLASS-XII)
Q.1 Which of the followingcould be the sketch graph of y=
d
dx
(x ln x)?
(A) (B) (C) (D)
Q.2 If y = (A + Bx) emx + (m  1)2 ex then
d y
dx
2
2  2m
dy
dx
+ m2y is equal to :
(A) ex (B) emx (C) emx (D) e(1  m) x
Q.3 Number ofsides in aregularpolygonifthesumofits interioranglesis 2520°, is
(A) 14 (B) 16 (C) 18 (D) 20
Q.4 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.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.
ANSWER KEY
QuizOne
Q1. B Q2. A Q3. A Q4. D Q5. C Q6. C Q7. D
QuizTwo
Q1. A Q2. A Q3. C Q4. A Q5. C Q6. C
Quiz Three
Q1. B Q2. B Q3. f (x) = 





 x
x
2
3
1
Q4. 3( 1
3  ) Q5. x = 6
QuizFour
Q1. A Q2. A Q3. C Q4. D Q5. A
Quiz Five
Q1. C Q2. A Q3. B Q4. D Q5. 24 5