PAPER SCHEME :
The paper contains 60 Objective Type Questions divided into three sections: Section - I, Section – II and
Section – III.
Section I contains 10 Multiple Choice Questions (1-10)
based on Mental Aptitude. Each question has
4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.
Section II contains 35 Multiple Choice Questions (11-45)
based on Mathematics. Each question has
4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.
Section III contains 15 Multiple Choice Questions (46-60) based on Science. Each question has 4 choices
(A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.
MARKING SCHEME :
Section I : For each question, 4 marks will be awarded for correct answer and –1 negative marking for
incorrect answer.
Section II : For each question, 5 marks will be awarded for correct answer and –1 negative marking for
incorrect answer.
Section III : For each question, 6 marks will be awarded for correct answer and –1 negative marking for
incorrect answer.
GENERAL INSTRUCTIONS :
For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Name,
Roll Number, Seat ID, Date of Birth and the PAPER CODE properly in the space provided
in the
ANSWER SHEET. IT IS YOUR OWN RESPONSIBILITY TO FILL THE OMR SHEET CORRECTLY.
A blank space has been provided on each page for rough work. You will not be provided with any
supplement or rough sheet.
The use of log tables, calculator and any other electronic device is strictly prohibited.
Violating the examination room discipline will immediately lead to the cancellation of your paper and no
excuses will be entertained.
No one will be permitted to leave the examination hall before the end of the test.
Please submit both the question paper and the answer sheet to the invigilator before leaving the
examination hall.
2 Sample Paper | 3 Year
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
SUGGESTIONS:
Before starting the paper, spend 2-3 minutes to check whether all the pages are in order and report
any issue to the invigilator immediately.
Try to attempt the Sections in their respective order.
Do not get stuck on a particular question for more than 3-4 minutes. Move on to a new question as
there are 60 questions to solve.
SECTION - I [MENTAL APTITUDE]
1. Three out of the four options are same in a certain way and so form a group. Find the odd option that
does not belong to the group.
(A)
3:15
(B)
6 : 30
(C)
12 : 42
(D)
9 : 45
2. The 2 groups of letters on the left have some relationship between them. Replace the '?' with a group
of letters so that the 2 groups of letters on the right have the same relationship.
: :: :
EJO GNU FLR
?
(A) HPY (B) GNX (C) GPU (D) HPX
3. What is the next term in the given series ?
97, 103, 109, 127, ......
(A) 131 (B) 150 (C) 156 (D) 137
4. Which of the given group of letters will complete the given series ?
_ _ _ _
a cc bbc a c
(A)
accb
(B)
abcb
(C)
baab
(D)
abba
5. A cube of side 4cm is painted black on the pair of one opposite surfaces, blue on the pair of another
opposite surfaces and red on the remaining pair of opposite surfaces. The cube is now divided into
smaller cubes of equal side of
1
cm
each. How many smaller cubes have atleast 2 sides painted ?
(A) 16 (B) 24 (C) 32 (D) 36
6.
What is b ?
(A) 3 (B) 4 (C) 5 (D) 6
7. What is the next term in the given series
11, 13, 17, 19, .......
?
(A) 23 (B) 25 (C) 27 (D) 30
8. What is the next term in the given series
27, 64, 125, 216, .......
?
(A) 300 (B) 299 (C) 343 (D) 450
4
3 4
1 8 4
1 3 8
9 1
1 0 7 0 4
b c
a
a
c
a
c
3 Year | Sample Paper 3
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
9. The figures given below show the 2 different positions of a dice.
Which number will come opposite to 2 ?
(A) 5 (B) 1 (C) 6 (D) 3
10. The figures given below show the 2 different positions of a dice.
Which number will come opposite to 1 ?
(A) 5 (B) 2 (C) 4 (D) 6
SECTION - II [MATHEMATICS]
11. The value of
2 3 1
3 4 5
1 1 1
216 256 32
is:
(A) 102 (B) 105 (C) 107 (D) 109
12. The LCM of two numbers is x and their HCF is y. The product of two number is:
(A)
x
y
(B)
y
x
(C)
x y
(D) xy
13. The value of
3 2 3 1
1 3
2 3 5 6
6 10 15
m m n m n n
m n m
is equal to:
(A) 0 (B) 1 (C)
2
m
(D) None of these
14. An alloy of gold, sliver and bronze contains 90% bronze, 7% gold and 3% silver. A second alloy of
bronze and sliver only is melted with the first and the mixture contains 85% of bronze, 5% of gold
and 10% of silver. Find the percentage of bronze in the second alloy.
(A) 75% (B) 72.5% (C) 70% (D) 67.5%
15. PQRS is square and POQ is an equilateral triangle.
What is the value of angle SOR ?
(A) 150°
(B) 120°
(C) 125°
(D) 100°
16. Four bells ring at intervals of 6, 7, 8 and 9 seconds respectively. All the bells ring together after
________ seconds.
(A) 504 (B) 516 (C) 508 (D) 512
17. When the polynomial x
3
+ 3x
2
+ 3x + 1 is divided by x + 1, the remainder is:
(A) 1 (B) 8 (C) 0 (D) –6
4 Sample Paper | 3 Year
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
18. The value of m for which x
2 is a factor of the polynomial
4 3 2
2 4
x x x mx
is:
(A) 10 (B)
10 (C) 4 (D) 9
19. The expression
3 3 3
( ) ( ) ( )
a b b c c a
is equal to:
(A) 3abc (B) 3a
3
b
3
c
3
(C) 3(a
b)(b
c)(c
a) (D) [a
(b + c)]
3
20. When
3 2 3 2
2 2 4 and 2 3 6
x x x x x x
are divided by x
2, the remainder are
1
R
and
2
R
respectively. Which of the following statements is true for
1 2
and
R R
?
(A)
1 2
2
R R
(B)
1 2
2
R R
(C)
1 2
R R
(D)
1 2
0
R R
21. If (x
a) is a factor of x
3
3x
2
a + 2a
2
x + b, then the value of b is:
(A) 0 (B) 2 (C) 1 (D) 3
22. If two lines intersected by a transversal, then each pair of corresponding angles so formed is:
(A) Equal (B) Complementary (C) Supplementary (D) None of these
23. The angle between the bisectors of two adjacent supplementary angles is:
(A) acute angle (B) right angle (C) obtuse angle (D) None of these
24. In the given figure, which of the following is the
correct inequality?
(A)
c a e b d
(B)
c a e d e
(C)
a c e b d
(D)
c a d b e
25. In the adjoining figure BO, CO are angle bisectors of external
angles of
Δ
ABC
. Then
BOC
is:
(A)
1
90
2
A
(B)
1
90
2
A
(C)
1
180
2
A
(D)
1
180
2
A
26. The value of polynomial
2
5 4 3
x x ,
when
1
x
is :
(A)
6
(B) 6 (C) 2 (D)
2
27. From the adjoining figure
||
AB DE
. Then the value of
x
is:
(A)
25
(B)
35
(C)
45
(D)
55
28. In the adjoining figure, AB || CD. The value of x is:
(A)
80
(B)
88
(C)
90
(D)
98
3 Year | Sample Paper 5
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
29. In the adjoining figure, the value of
A B C D E F
is:
(A)
360
(B)
270
(C)
540
(D)
180
30. ABC is a triangle in which AB = AC. The base BC is
produced to D and
130
ACD
. Then,
A
equals:
(A)
80
(B)
60
(C)
50
(D)
40
31. If ABCD is a square and DCE is an equilateral triangle in
the given figure, then
DAE
is equal to:
(A)
45
(B)
30
(C)
15
(D)
1
22
2
32. The equation of x-axis is of the form:
(A)
0
x
(B)
0
y
(C)
0
x y
(D)
x y
33. If the sides of a triangle are produced, then the sum of
the exterior angles i.e.
a b c
is equal to:
(A)
180
(B)
360
(C)
90
(D)
270
34. For a triangle ABC, the true statement is:
(A)
2 2 2
AC AB BC
(B)
AC AB BC
(C)
AC AB BC
(D)
AC AB BC
35.
6 6 6 .....
is equal to ________.
(A)
3
(B) 3 (C) 6 (D) 2
36. If
7 4 3
p , then
2
1
7
p
p
________.
(A) 2 (B) 1 (C) 7 (D)
3
37. The radius of sphere is 2r, then its volume will be :
(A)
3
4
3
r
(B)
3
4
r
(C)
3
8
3
r
(D)
3
32
3
r
38. Runs scored by Sachin in a charity match is 10 more than the balls faced by Lara. The number of balls
faced by Sachin in 5 less than the runs scored buy Lara. Together they have scored 105 runs and
Sachin faced 10 balls less than the ball Lara. How many runs were scored by Sachin?
(A) 45 (B) 60 (C) 50 (D) 55
6 Sample Paper | 3 Year
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
39. Amar and Bhavan have a certain amount with them. If Bhavan gives
Rs. 20
to Amar, he will have
half the amount with Amar. If Amar gives
Rs. 40
to Bhavan, he will have half the amount with
Bhavan. Find the amount with Bhavan.
(A)
Rs. 70
(B)
Rs. 90
(C)
Rs. 60
(D)
Rs. 80
40. In an election the supporters of two candidates A and B where taken to polling booth in two different
vehicles, capable of carrying 10 and 15 voters respectively. If at least 90 vehicles were required to
carry a total of 1200 voters, then find the maximum number of votes by which the election could be
won by the Candidate B.
(A) 900 (B) 600 (C) 300 (D) 500
41. Krishna and Sudheer have some marbles with them. If Sudheer gives 10 marbles to Krishna, then
Krishna will have 40 more marbles than Sudheer. If Sudheer gives 40 marbles to Krishna, Krishna
will have 5 times as may marbles as Sudheer. Find the number of marbles with Sudheer.
(A) 65 (B) 55 (C) 70 (D) 50
42. A goat is tied to a corner of a rectangular plot of dimensions
14 7
m m
with a rope 21 m long.
It cannot graze inside the plot but can graze outside it as far as it is permitted by the rope. Find the
area it can graze
2
(in )
m
.
(Take )
(A) 1104 (B) 1196 (C) 1380 (D) 1288
43. In the figure, ABCD is a rectangle with
9
AB cm
and
6 .
BC cm
O is the centre of the circle. Then the area of the
shaded region is equal to (in cm
2
) :
(A) 18 (B) 24
(C) 27 (D) 15
44. Any point on x-axis is of the form :
(A) (x, y) (B) (0, y) (C) (x, 0) (D) (x, x)
45. The value of
3 3
2 2
55 45
55 55 45 45
is :
(A) 100 (B) 105 (C) 125 (D) 75
SECTION - III [SCIENCE]
46. The splash is heard after 4.22 sec after the stone is dropped into a well of depth 78.4 m. The velocity
of sound is:
(A) 342 m/s (B) 372 m/s (C) 392 m/s (D) 356 m/s
47. A man of mass 90 kg is standing in an elevator whose cable broke suddenly. If the elevator falls
freely, the force exerted by the floor on the man is:
(A) 90 N (B) 90 gN (C) Zero (D) any negative value
48. Two pieces of metal immersed in a liquid have equal upthrust on them, then:
(A) Both pieces must have equal weights (B) Both pieces must have equal densities
(C) Both pieces must have equal volume (D) Both are floating to the same depth
3 Year | Sample Paper 7
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
49. An electric motor creates a tension of 4500 N in hoisting cable and reels it at the rate of 2 m/s. What is
the power of electric motor?
(A) 15 kW (B) 9 kW (C) 225W (D) 9000kW
50. For the wave shown in figure, the wavelength and frequency, if its speed is 320 m/sec, are:
(A) 8 cm, 400 Hz (B) 80 cm, 40 Hz (C) 8 cm, 4000 Hz (D) 40 cm, 8000 Hz
51. Three gases A, B and C have the following boiling points respectively –120º, –110ºC and –80ºC on
cooling the gases. Which gas will liquefy first?
(A) A (B) B
(C) C (D) Can’t be predicted
52. Which of the following will decrease the rate of evaporation of water?
(A) Increase in temperature of water (B) Increase in surface area of water
(C) Adding common salt to water (D) Increase in wind speed
53. Which of the following formula is/are incorrectly matched with the compound?
(I) Magnesium phosphate:
3 4 2
Mg (PO )
(II) Ammonium chloride:
4
NH Cl
(III) Sodium nitrate:
3
NaNO
(A) I (B) I and III (C) II (D) None of these
54. Which of the following has the maximum number of atoms? (Molecular weight of N = 14g, H = 1g)
(A) 100 g of
2
N
(B) 100 g of
3
NH
(C) 100 g of
2
H
(D) 100 g of
2
O
55. Which of the following statements is/are incorrect?
(I) Tincture of iodine is a solution of iodine in alcohol
(II) Burning of wood is a chemical change
(III) Mercury and iodine are liquid at room temperature
(A) I (B) III (C) II (D) None of these
56. Protein is synthesized by:
(A) Ribosomes (B) Golgi Apparatus (C) Plastids (D) Mitochondria
57. Genes are located on the:
(A) Nuclear membrane (B) Cell membrane
(C) Chromosomes (D) Mitochondria
58. Phloem in the plants perform the function of:
(A) Conduction of food (B) Conduction of water
(C) Providing water (D) Photosynthesis
8 Sample Paper | 3 Year
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
59. Simple tissues are:
(A) Parenchyma, Xylem and Collenchyma
(B) Parenchyma, Collenchyma and Sclerenchyma
(C) Xylem, Phloem
(D) Parenchyma, Xylem, Sclerenchyma
60. Bacteria are placed under which kingdom?
(A) Protista (B) Fungi (C) Monera (D) Plantae
End of Sample Paper | 3 Year
3 Year | Sample Paper 9
Vidyamandir Classes | Gurukul for IITJEE & Medical Preparation
Answers to Sample Paper | 3 Year
SECTION - I
1 2 3 4 5 6 7 8 9 10
C D D C C C A C D C
SECTION - II
11 12 13 14 15 16 17 18 19 20
A D B B A A C A C C
21 22 23 24 25 26 27 28 29 30
A D B A A A B D A A
31 32 33 34 35 36 37 38 39 40
C B B D B A D B D B
41 42 43 44 45
A D A C A
SECTION - III
46 47 48 49 50 51 52 53 54 55
D C C B C C C D C B
56 57 58 59 60
A C A B C
