INSTRUCTIONS ENTRANCE TEST SAMPLE FOR Ultima [X TO XI Moving]

Transcription

ENTRANCE TEST SAMPLE FOR Ultima [X TO XI Moving]
Duration : 3 hours
Max. Marks : 360
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
INSTRUCTIONS
Do not break the seal of the question paper booklet before instructed to do so by the invigilator.
This Paper contains 90 questions. Please ensure that the Question paper you have received contains ALL THE
QUESTIONS.
1.
QUESTION PAPER FORMAT
All the questions has four choices (A), (B), (C) and (D) out of which only ONE is correct & carry 4 marks
each. 1 mark will be deducted for each wrong answer.
NOTE : GENERALINSTRUCTION FOR FILLING THE OMRARE GIVEN BELOW :
1.
2.
3.
4.
Use only HB pencil or blue/black pen (avoid gel pen) for darkening the bubble.
Indicate the correct answer for each question by filling appropriate bubble in your OMR answer sheet.
The Answer sheet will be checked through computer hence, the answer of the question must be marked by
shading the circles against the question by dark HB pencil or blue/black pen.
While filling the bubbles please be careful about question paper format.
Name of the student
EW Roll Number
I have read all the instructions and shall
abide by them.
I have verified all the information filled in
by the candidate.
................................................................
Signature of the Student
................................................................
Signature of the invigilator
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.
MATHS
Q.1
The diagram shows a large equilateral triangle divided by three straight lines into seven regions.
The three grey regions are equilateral triangles with sides of length 5cm and the central black region is
an equilateral triangle with sides of length 2cm. What is the side length of the original large triangle ?
(A )18cm
Q.2
If x = 5 + 2 6 , find the value of
(A )
Q.3
(B) 19cm
3
(B) 2 3
x
(C) 20cm
(D) 21cm
(C) 3 2
(D)
1
x
2
A rectangle is divided into four smaller rectangles. The areas of three of these rectangles are 6, 15 and
25, as shown. Find the area of the shaded rectangle.
(A )10
(B) 20
(C) 25
(D) 15
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Add : 46, Rajiv Gandhi Nagar, Kota (Raj.) Ph. 9214211999, 9214213666
2
Q.4
In the diagram, PQRS is a parallelogram;  QRS = 50º;  SPT = 62º and PQ = PT..
Q
R
50º
P
S
62º
T
What is the size of  TQR?
(A) 84º
Q.5
(C) 96º
(D) 112º
If f (x) = ax7 + bx5 + cx3 – 6, and f (–9) = 3, find f (9).
(A) –10
Q.6
(B) 90º
(B) –3
(C) –15
(D) –4
Mohan has been challenged to place the numbers 1 to 9 inclusive in the nine regions formed by the
Olympic rings so that there is exactly one number is each region and the sum of the numbers in each ring
is 11. The diagram shows part of his solution.
*
9
8
5
What number goes in the region marked * ?
(A) 6
Q.7
(B) 4
(C) 3
(D) 2
An ant crawls 1 centimeter north, 2 centimeters west, 3 centimeters south, 4 centimeters east,
5 centimeters north and so on, at 1 centimeter per second. Each segment is 1 centimeter longer than the
preceding one, and at the end of a segment, the ant makes a left turn. In which direction is the ant
moving 1 minute after the start?
(A) North
(B) South
(C) east
(D) west
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Q.8
Q.9
In a triangle ABC,  BCA = 90º. Points E and F lie on the hypotenuse AB such that AE = AC and
BF = BC. Find  ECF..
(A) 30º
(B) 45º
(C) 60º
(D) 65º
Three circles are arranged in a row so that each is tangent to the circles nest to it. The radii of the two
circles at the two ends are 5 and 3. What is the length of the line segment AB that passes through the
center of each circle ?
O3
A
(A) 24
(B) 16  4 3
O2
O1
B
(C) 20
(D) 16  2 15
Q.10
A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope
tight and describes 88m when it has traced out 72º at the centre, find the length of the rope.
(A) 88 m
(B) 70 m
(C) 60 m
(D) 100 m
Q.11
In the figure shown, O1 and O2 are centers of the circles, O1A is tangent to the circle centered at O2.
Find the area of the shaded region :
A
6
O1
(A) 18 3  7 
(B) 19 2  8
6
6
O2
(C) 18 3  9
(D) none of these
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Q.12
Two circles of radii 4cm and 1cm touch each other externally and is the angle contained by their
direct common tangents. Then sin is equal to
24
25
(A)
Q.13
(B)
If
(B) 1/4
(B) 175
82
36
(D) 1/5
(C) 25
(D) 100
ab bc ca
,
,
, there are
2
2
2
(B) at least an integer (C) at least two integers (D) all integers
30 books are to be packed into 5 boxes. Each box must have odd number of books. How can this be
done ?
(A) 1
Q.17
(D)
(C) 1/2
If a, b, c are random integers, then among the three numbers
(A) all non-integers
Q.16
42
16
x y z
  , and 4x – 5y + 2z = 10, find the value of 2x + 5y + z
3 4 5
(A) 150
Q.15
(C)
 1 1 1 1 1 1 1  1 1 1 1 1 1 1
Calculate  1             1          
 2 3 4  2 3 4 5  2 3 4 5  2 3 4
(A) 1/3
Q.14
25
24
Given that
(A)
2013
2014
(B) 3
(C) 0
(D) 5
ab
3 bc
ca
1007
abc
 ,
 3,

then find the value of
a b 2 bc
c  a 1006
ab  bc  ac
(B)
2010
2011
(C)
2012
2014
(D)
2014
2013
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Q.18
The slovenian hydra has five heads. Every time a head is chopped off, five new heads grow. Six heads
are chopped off one by one. How many heads will be hydra finally have ?
(A) 25
Q.19
(B) 29
(B) 22.5cm
(C) 36cm
(D) 45cm
The number x = 3.145 when expressed as a rational number in lowest form, then 55x is equal to
(A) 172
Q.21
(D) 35
A rectangle with area 125cm2 has sides in the ratio 4 : 5. What is the perimeter of the rectangle ?
(A) 18cm
Q.20
(C) 33
(B) 173
(C) 174
(D) None of these
In the triangle PQR, PS = 2; SR = 1;  PRQ = 45º; T is the foot of the perpendicular from P to QS
and  PST = 60º .
P
2
60º
S
T
1
45º
Q
R
What is the size of  QPR ?
(A) 45º
Q.22
(B) 60º
(C) 75º
(D) 90º
Find the number of zeroes in the value of N = 22 × 54 × 46 × 108 × 610 × 1512
(A) 8
(B) 15
(C) 24
(D) 32
(a  x)  (a  x)
Q.23
If
a
 , then find the value of x
(a  x)  (a  x) x
(A) a
(B) 2a
(C) 3a
(D) None of these
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Q.24
In the diagram, AC = 4, BC = 3, and BD = 10. The area of the shaded triangle is
(A) 14
Q.25
(D) 24
(B) 4
(C) 8
(D) 16
A polynomial p (x) leaves a remainder three when divided by x – 1 and a remainder five when divided
by x – 3. Find the remainder when p(x) is divided by (x – 1) (x – 3).
(A) x + 2
Q.27
(C) 20
If 2x log4 3  3log4 x  27 then x =
(A) 2
Q.26
(B) 16
(B) x – 2
(C) 5
(D) 15
5% of the passengers who boarded Guwahati-New Delhi Rajdhani Express on 14th February, 2013
do not like coeffee, tea and ice cream and 10% like all the three 20% like coeffee and tea, 25% like ice
cream and coeffee and 25% like ice cream and tea 55% like coeffee, 50% like tea and 50% like ice
cream.
The percentage of passengers who like both tea and ice cream but not coffee is
(A) 15
Q.28
(B) 5
(C) 10
(D) 25
For the given diagram, find the value of  A +  B +  C +  D +  E +  F
(A)360º
(B) 270º
(C) 180º
(D) 420º
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Q.29
In the figure shown, ABC, AEB and CGB are semicircles F is the midpoint of AC and AF = FC =
1unit, AB = BC. What is the area of the shaded region ?
(A)
Q.30
1
2
(B)
Q.33
F
 1

8 2
G
C
(C) 1
(D)

4
(C) n–2
(D) 0
Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A  B) = 100, then n(AC  BC) is
(B) 600
(C) 300
(D) 200
Let F1 be the set of all parallelogram, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of
squares and F5 the set of trapeziums in a plane the F1 is equal to
(A) F2  F3
(B) F2  F3  F4  F1
(C) F3  F4
(D) None of these
Find the value of 3 (sin x – cos x)4 + 6 (sin x + cos x)2 + 4 (sin6x + cos6x)
(A) 12
Q.34
A
(B) n–1
(A) 400
Q.32
B
If sin2 1 + sin2 2 + ... + sin2 n = 0, then find the maximum value of cos1 + cos2 + ....+ cos n
(A) n
Q.31
E
(B)13
(C) 15
(D) 14
Which of these four numbers 2 , 4 0.00256, 3 –8, 4 (0.04) –1 , is(are) rational ?
(A) only the fourth
(C) the first and fourth
(B) only the first
(D) last three
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Q.35
Let x be the LCM of 32002 – 1 and 32002 + 1. Find the last digit of x.
(A) 1
Q.36
(C) 80%
(D) 60%
(B) 2a
(C) 2b
(D) 1
(B) 15
(C) 18
(D) 19
A bag contains 3 red, 6 white and 7 black balls. Two balls are drawn at random what is the probability
that both are black ?
(A) 1/8
Q.40
(B) 20%
When 144 is divided by the positive integer n, the remainder is 11. When 220 is divided by the positive
integer n, the remainder is also 11. What is the value of n ?
(A) 11
Q.39
(D) 3
ab 1
If log e 
  (log e a  log e b) then a – b = ?
 2  2
(A) 0
Q.38
(C) 0
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls
combined is 50. The percentage of boys in the class is
(A) 40%
Q.37
(B) 2
(B) 7/40
(C) 12/40
(D) 13/40
The slant height of the frustum of a lone is 5 cm and the perimeters of its circular ends 20 cm and 8 cm.
Find the curved surface area of the frustum.
(A) 60 cm2
(B) 70 cm3
(C) 80 cm2
(D) 84 cm2
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SCIENCE
Q.41
Which of the following is an action-reaction pair for a space station containing astronauts in orbit about
the earth ?
(A) the weight of the space station and the centripetal force on the space station
(B) the weight of the astronauts and the centripetal force on the space station
(C) the weight of the space station and the gravitational force of the space station on the earth
(D) the weight of the astronauts and the gravitational force of the space station on the astronauts
Q.42
A person who weighs w newtons stands on a scale in an elevator that is initially at rest. The elevator
accelerates upward to a constant speed and then slows to a stop. Which of the following graphs best
represents the reading on the scale ?
(A)
(B)
time
Q.43
w
w
w
w
(C)
time
(D)
time
time
Which position versus-time graph goes with the velocity-versus-time graph below. The particle’s position
at ti = 0s is xi = –10m.
(A)
(B)
(C)
(D)
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Q.44
If the same object were released in air, the magnitude of its acceleration would begin at the free-fall
value, but it would decrease continuously to zero as the object continued to fall.
For which one of the choices given does the solid line best represent the speed of the object as a
function of time when it is dropped from rest in air?
Note: The dashed line shows the free-fall under vacuum graph for comparison.
v
(A)
(B)
0
Q.45
t
v
v
v
(C)
0
(D)
0
t
t
0
t
A cup containing 25 mL of hot water and a similar cup containing 25 mL of cold water are placed on
a table in a room at 21°C. Which of the following graphs shows the most likely change in temperature
for each cup from 0 min to 40 min?
(A)
(B)
(C)
(D)
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Q.46
Which of the following conditions results in the buildup of static charge on an object?
(A) when neutrons outnumber electrons
(B) when there are more protons than neutrons
(C) when there are more electrons than protons
(D) when all neutrons have been removed from the object
Q.47
Q.48
In a competition, weightlifter 1 lifts a 100 kg weight from the floor. Weightlifter 2 also lifts a 100 kg
weight to the same height above the floor, but takes a longer time to do so. Which of the following
statements describes the work done and the power used by the weightlifters?
(A) Weightlifter 2 does the same work and uses less power compared with weightlifter 1.
(B) Weightlifter 2 does less work and uses the same power compared with weightlifter 1.
(C) Weightlifter 2 does the same work and uses more power compared with weightlifter 1.
(D) Weightlifter 2 does more work and uses the same power compared with weightlifter 1.
The graphs below give information for waves W and X. Both waves were produced in the same
medium and are moving at the same speed.
Which of the following statements describes another property of these waves?
(A) Wave W has a larger period than wave X.
(B) Wave W has a lower frequency than wave X.
(C) Wave W has a greater amplitude than wave X.
(D) Wave W has a shorter wavelength than wave X.
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Q.49
The diagram below shows copper wire wrapped around a cardboard tube, which is then attached
to a galvanometer. A galvanometer detects and measures small amounts of electric current.
Which of the following would cause the galvanometer needle to move?
(A) wrapping additional wire around the tube
(B) uncoiling the wire wrapped around the tube
(C) moving a magnet back and forth inside the tube
(D) moving an aluminium block up and down inside the tube
Q.50
At an amusement park, bumper car X moves at a speed of 2.5 m/s toward car Y, which is at rest,
as shown in the diagram below.
Car X collides with car Y. How does the momentum of each car change after the collision?
(A) Car X’s momentum increases, and car Y’s momentum decreases.
(B) Car X’s momentum decreases, and car Y’s momentum increases.
(C) Car X’s momentum is unchanged, and car Y’s momentum increases.
(D) Car X’s momentum is unchanged, and car Y’s momentum decreases.
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Q.51
Q.52
Which of the following actions would increase the current through a circuit component?
(A) decreasing the power in the component
(B) increasing the resistance of the component
(C) increasing the voltage across the component
(D) placing another identical component in series in the circuit
A simple circuit is shown in the diagram below.
In which of the following circuits will bulb X have the same brightness as in the circuit above, if all
batteries and all light bulbs are identical?
Q.53
(A)
(B)
(C)
(D)
To locate objects in their environments, bats in flight and porpoises under water both use ultrasound
waves with frequencies that are beyond human hearing. These animals produce an ultrasonic wave and
then detect echoes from nearby objects.
If a porpoise and a bat both produce ultrasonic waves when they are 16 m from an object, which
animal would hear its echo first and why?
(A) The bat would hear its echo first because sound travels faster in air than in water.
(B) The porpoise would hear its echo first because sound travels faster in water than in air.
(C) The bat would hear its echo first because the amplitude of sound waves is greater in air than in water.
(D) The porpoise would hear its echo first because the amplitude of sound waves is greater in water
than in air.
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Q.54
Q.55
Q.56
A car has an oil drip. As the car moves, it drips oil at a regular rate, leaving a trail of spots on the road.
Which of the following diagrams of the car’s trail of spots shows the car continuously slowing down?
(A)
(B)
(C)
(D)
Four students of different weights timed themselves walking up a set of stairs. Their data are shown
below.
Which student used the most power while walking up the stairs?
(A) student W
(B) student X
(C) student Y
The table below shows data from a heating experiment.
(D) student Z
Which of the following conclusions is supported by the data in the table?
(A) A given mass of silver requires less heat to change its temperature 1°C than an equal mass of iron.
(B) A given mass of silver requires less heat to change its temperature 1°C than an equal mass of lead.
(C) A given mass of copper requires less heat to change its temperature 1°C than an equal mass of lead.
(D) A given mass of copper requires less heat to change its temperature 1°C than an equal mass of
silver.
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Q.57
Use the diagram below to answer the question that follows.
A right circular cylinder has a mass m, radius r, and a height h. The cylinder is completely submerged in
a fluid of density , as shown in the diagram. What is the magnitude of the net force on the cylinder?
(A) rgh + mg
Q.58
(B) rgh – mg
(C) r2gh + mg
(D) r2gh – mg
A 6.0kg mass is moving to the right at 10m/s. A 0.25kg mass is fired toward the left at the larger
mass. What speed (v) must the smaller mass have to completely stop both massless ?
(A) 4.2 m/s
(B) 15 m/s
(C) 150 m/s
(D) 240 m/s
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Q.59
P1
P2
An object at rest in deep space explodes into three pieces. The momentum of two of the pieces
is shown in the diagram. Which of the following vectors best represents the momentum of the third
piece ?
(A)
(B)
(C)
(D)
Q.60
Q.61
Given the electric field lines shown figure, what are the charge pairs?
(A) Q1 positive, Q2 positive
(B) Q1 positive, Q2 negative
(C) Q1 negative, Q2 positive
(D) Q1 negative, Q2 negative
The diagram shows two mirrors attached at a right angle. A ray of light is incident on one mirror with an
angle of incidence of . What is the angle of reflection from the second mirror ?
(A)
1

2
(B) 
(C) 90 – 
(D) 180 – 2
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Q.62
The diagram shows a concave mirror with focal point F and center of curvature C. An object placed at
which of the following positions in front of the concave mirror will produce a magnified, virtual image?
(A) I
Q.63
(B) II
(C) III
(D) IV
A light ray passes through substances 1, 2 and 3, as shown in the figure. The indices of refraction for
these three substances are n1, n2, and n3 respectively. Ray segments in 1 and in 3 are parallel. From the
directions of the ray, one can conclude that
(A) n3 must be the same as n1
(B) n2 must be less than n1
(C) n2 must be less than n3
(D) all the three indices must be different
Q.64
The diagram shows a straight wire carrying a flow of electrons into the page. The wire is between the
poles of a permanent magnet. The direction of the magnetic force exerted on the wire is:
(A) 
Q.65
(B) 
(C) 
(D) 
A current is clockwise around the outside edge of this page and a uniform magnetic field is directed
parallel to the page, from left to right. If the magnetic force is the only force acting on the page, the page
will turn so the right edge:
(A) moves toward you
(B) moves away from you
(C) moves to your right
(D) moves to your left
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Q.66 The pH of a solution changes from 6 to 5 hydrogen ion concentration of solution is increased by.
(A) 100 times
(B) 5 times
(C) 10 times
(D) 2 times
Q.67 If one gram of He contains x atoms, then number of atoms present in one gram of oxygen atom are
(A) x/2
(B) x/4
(C) x/8
(D) x/16
18
Q.68 If x atom is available in the form of, two isotopes 16
8 x and 8 x and the average atomic mass of the
elements is 16.2, then percentage of 16
8 x in the sample is.
(A) 10%
(B) 80%
(C) 70%
(D) 90%
Q.69 The possible oxidation state of hydrogen atom is(A) 1
(B) –1
(C) zero
(D) All of these
Q.70 Which of the following is not the property of metals
(A) It has ductile property
(B) It has malleability property
(C) It has sonorous property
(D) Metals are non conductor of electricity
Q.71 Which of the following is addition reaction
(A) CH3 – CH = CH – CH3
H2/Ni
high temp & pressure
CH3 – CH2 – CH2 – CH3
Cl
(B)
+ Cl2
+ HCl
(C) CH3 – C – OH + C2H5OH
||
O
(D) CH3 – CH2 – Cl
Conc. H2SO4
NaOH (aq)
CH3 – C – OC2H5
||
O
CH3 – CH2 – OH
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Q.72 Consider the following compound
NH2
O
COOH
OH
Cl
Which of the following functional group is not present in given compound
(A) Alcohol
(B) Carboxylic acid
(C) Ketone
(D) Aldehyde
Q.73 Which of the following is the correct order of melting point
(A) NaCl\ > MgCl2
(B) NaCl = MgCl2
(C) NaCl < MgCl2
(D) cannot predict
(C) Gold
(D) All of these
Q.74 Metal which is refined by electrolyte method
(A) Copper
(B) Silver
Q.75 Food cans are coated with tin, not with zinc because(A) Zinc is costlier than tin
(B) Zinc has higher melting point than tin
(C) Zinc is more reactive than tin
(D) Zinc is less reactive than tin
Q.76 How many elements are presents in 4th period in long form periodic table(A) 8
(B) 18
(C) 20
(D) 32
(C) 92
(D) 192
Q.77 What is the atomic number of Uub element
(A) 111
(B) 112
Q.78 Element X forms a chloride with the formula XCl2 which is a solid with high melting point. X would
most likely be in the same group of the periodic table as
(A) Na
(B) Mg
(C) Al
(D) Si
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20
Q.79 How many sigma bonds are persent in buckminsterfullerene C60 molecule
(A) 60
(B) 70
(C) 90
(D) 80
Q.80 Which of the following pairs are not homologus
(A) CH3 – CH2 – CH2 – OH & CH3 – CH2 – OH
(B) CH3 – CH2 – COOH & CH3 – CH2 – CH2 – COOH
(C) CH3 – CH2 – CH2 – CH2 – OH & CH3 – CH2 – CH2 – OCH3
(D) CH3 – C – CH3 & CH3 – CH2 – C – CH3
||
||
O
O
Q.81 Which of the following IUPAC name is not correctly matched
(A) CH3 – CH2 – CH2 – COOH
Butan-1-oic acid
(B) CH3 – C – CH2 – CH3 – CH3
||
O
Pentan-2-one
(C) CH3 – CH = CH – CH3
But-2-ene
(D) CH3 – CH2 – CH2 – CH2 – C – H Pentan-1-one
||
O
Q.82 Which of the following is saturated hydrocarbon.
(A) Ethylene
(B) Acetylene
(C) Octane
(D) Hexene
Q.83 Insulin contains 0.16% sulphur by mass minimum molar mass of Insulin could be (At w.t. of S = 32)
(A) 20000 g mol–1
(B) 10000 g mol–1
(C) 5000 g mol–1
(D) 40000 g mol–1
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Q.84 The number of moles of CaCl2 required to react with excess silver nitrate to produce 1435 g of AgCl
according to the following reaction. (At w.t. of Ag = 108, Cl = 35.5)
CaCl2 (aq) + AgNO3(aq) — Ca(NO3)2(aq) + AgCl (s)
(A) 10
(B) 5
(C) 15
(D) 20
Q.85 The mass of 70% pure H2SO4 required for neutralisation of 1 mole of NaOH
(A) 49 gram
(B) 98 gram
(C) 70 gram
(D) 38 gram
Q.86 For the given reaction
Al + H2SO4 — Al2(SO4)3 + H2
Select the correct statment
(A) 3 moles of H2SO4 are required for formation of 2 moles of Al2(SO4)3
(B) The mole ratio between consumed Al and produced H2 is 3 : 2
(C) When 6 moles of Al reacts with 9 moles of H2SO4, 3 moles of Al2(SO4)3 is formed
(D) 1 mole of Al2(SO4)3 is produced from 3 moles of Al
Q.87 What is the hybridiazation a nitrogen in NH3
(A) sp
(B) sp2
(C) sp3
(D) cannot predict
(C) Na2O
(D) Al2O3
(C) O2
(D) CO2
Q.88 Which of the following is amphoteric oxide
(A) B2O3
(B) Cl2O7
Q.89 Fe + steam  X(s) + Y(g), then Y(g) is(A) H2
(B) FeO
Q.90 How many electrons are persent in ‘M’ shell in phosphorous atom(A) 6
(B) 5
(C) 3
(D) 7
: Rough Space :
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INSTRUCTIONS ENTRANCE TEST SAMPLE FOR Ultima [X TO XI Moving]

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