Fitjee Rank Improvement Test 4
Fitjee Rank Improvement Test 4
Fitjee Rank Improvement Test 4
Instructions
Note:
1. The question paper contains 3 sections (Sec-1, Chemistry, Sec-II, Physics & Sec-III, Mathematics.)
2. Each section is divided into two parts, PART-A and PART-C.
3. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided
for rough work.
4. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in
any form, are not allowed.
Filling of OMR Sheet
1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR
sheet.
2. On the OMR sheet, darken the appropriate bubble with Blue/Black Ball Point Pen for each character of
your Enrolment No. and write in ink your Name, Test Centre and other details at the designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.
Enrolment Number :
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IIT2020, (Two Year CRP(18-20)-RIT-IV-CPM-2
Section – I (Chemistry)
PART – A
(Single Correct Choice Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
only ONE option is be correct.
2. If Ksp of PbSO4 in 4 10–10, then what is the loss in wt of PbSO4 if it is washed with 5 litre of water
(mol. Wt of PbSO4 = 303 g/mol)
(A) 6.06 mg (B) 12.12 mg (C) 30.3 mg (D) 0.1 mg
3. Solubility of AgCl in water, 0.01 M CaCl2, 0.01 M NaCl and 0.05 M AgNO3 are S1, S2, S3 and S4
respectively, then (Ksp of AgCl = 10–10 M2)
(A) S1 > S2 > S3 > S4 (B) S1 > S3 > S2 > S4 (C) S1 > S2 = S3 > S4 (D) S1 > S3 > S4 > S2
(A) (B)
(C) (D)
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5.
6. Which of the following can form the highest no. of hyperconjugation structure?
(A) CH3 (B) H3C
C = CH 2
CH 3 - C
H3C
CH3
(C) (D) CH3CH = CHCH3
CH3
7. Which isomer of CH3 – CH = CH – CH2 – CH = CH2 can form salt when reacts with NaNH2?
(A) Chain isomer (B) Position isomer
(C) Functional isomer (D) Geometrical isomer
(A) (B)
O
O
O O
O
(C) (D)
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11
O
CH2OH
O
(C) (D)
OH
O
space for rough work
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C 2H 5 C 2H 5
(C) CH 3 (D) CH 3
C 2H 5 C 2H 5
15. The pH value(approximate) at 25oC of a solution containing the hydronium ion concentration
5 10–9 mole/dm3 is
(A) 6.98 (B) 8.3 (C) 9.7 (D) 8.7
17. Which of the following solution(s) form buffer if they are taken in 2 : 1 molar ratio?
(A) CH3COOH and CH3COONa (B) NH4OH and CH3COOH
(C) NH4OH and NH4Cl (D) NaHCO3 and Na2CO3
space for rough work
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18.
19. When HCl(g) is passed through a saturated solution of common salt, pure NaCl is precipitated
because
(A) HCl is highly soluble in water
(B) Ionic product [Na+][Cl-] exceeds its solubility product(Ksp)
(C) The Ksp of NaCl is lowered by presence of Cl– ions
(D) None of these
R
Energy
T
P
Progress of reaction
In the energy profile, state what kind of reacting species occupy the positions (marked as P, Q, R, S,
T) in the diagram.
(A) P → H2 and Cl2 (B) Q → H• and Cl• (C) R → H• and Cl• (D) T → HCl
space for rough work
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PART – C
This section contains 06 multiple choice questions. The answer to each question is a single digit integer, ranging from 0
to 9 (both inclusive)
3. How many maximum no. of structural isomer(s) is/are possible with formula C 4H10O?
4. Aspirin(MW = 180) is a pain reliever with PKa = 2. Two tablets each containing 0.09 gms of aspirin are
dissolved in 100 mL solution. What will be the pH of the solution?
C2H5OH, , , , ,
NO 2
6. Calculate number of structurally different diene isomers of C7H10 having 6 member rings.
space for rough work
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Section – II (Physics)
PART – A
(Single Correct Choice Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
only ONE option is be correct.
1. A cuboidal block of mass m, side lengths are , b and h slides down a rough inclined plane of
inclination with a uniform speed. Then line of action of the resultant of normal reaction and friction
will pass
(A) through centre of mass of the block
(B) through some distance left from centre of mass of the block
(C) through some distance right from centre of mass of the block.
(D) none of these
2. A thin uniform rod of mass ‘m’ and length ‘’ is standing on a smooth horizontal surface. A slight
disturbance causes the lower end to slip on the smooth surface. The velocity of centre of mass of the
rod at the instant when it makes an angle 60° with vertical will be
9g g
(A) downward (B) , 30° with downward vertical
26 13
3g 3g
(C) horizontal (D) , 60° with downward vertical
26 13
3. The moment of inertia of a rectangular lamina of mass ‘m’, length ‘’ and width ‘b’ about an axis
passing through its centre of mass, perpendicular to its diagonal and lies in the plane.
2
+ b2 m 4
+ b4 m 4
+ b4
(A) m (B) (C) (D) none of these
12 12 2
+ b2 6 2
+ b2
5. A rod collides elastically with smooth horizontal surface after falling from a height. For maximum
angular speed of the rod just after impact, the rod should be released in such a way that it makes an
angle with horizontal, the value of will be
1 1 1
(A) 0° (B) cos−1 (C) cos−1 (D) cos−1
2 3 6
space for rough work
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6. Two small balls A and B, each of mass m, are joined rigidly at the ends of a
light rod of length L. They are placed on a frictionless horizontal surface.
Another ball of mass 2 m moving with speed u towards one of the ball and m
perpendicular to the length of the rod on the horizontal frictionless surface
as shown in the figure. If the coefficient of restitution is 1/2 then the angular
speed of the rod after the collision will be L
4 u u
(A) (B) 2m
3 u m
2 u
(C) (D) None of these
3
7. A uniform thin rod of mass ‘m’, length ‘’ is hanged with the
help of two identical massless springs of spring constant ‘k’ as
shown in figure. Just after one of the spring is cut, the
acceleration of the other end of the rod will be k k
(A) zero
(B) g upward
m
(C) g downward
3g L
(D) upward
2
m
8. A solid hemisphere of mass ‘m’ is released from rest from a position
shown in figure. If there is no slipping then the magnitude of the
friction on the sphere at just after the released will be
15
(A) 0 (B) mg
28
15
(C) mg (D) none of these
56
Horizontal surface
9. A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity .
Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The
ring now rotates with an angular velocity =
m m (m + 2M) (m − 2M)
(A) (B) (C) (D)
(m + M) (m + 2M) m (m + 2M)
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11. A particle of mass m is projected with a velocity v making on angle with horizontal. The magnitude
of angular momentum of the projectile about the point of projection when the particle is at its
maximum height ‘H’ is proportional to
(A) V3/2 (B) V3 (C) H3/2 (D) H3
13. A bob is circulating in horizontal plane whose radius is constant with the help of ideal string so that it
forms a conical pendulum. Then choose the correct option(s).
(A) Angular velocity of the string is constant.
(B) Magnitude of angular velocity of the string is constant.
(C) Direction of angular velocity of the string is varying.
(D) Both magnitude and direction of angular velocity are varying.
14. A person sitting firmly over a rotating stool has his arms folded with two identical balls. If he stretched
his arms along with balls and then the work done by him
(A) zero (B) positive (C) negative (D) any of these
15. A horizontal disc rotates freely about a vertical axis through its centre. A ring, having the same mass
and radius as the disc, is now gently placed on the disc in such a way that their axes coincide. After
some time, both rotate with a common angular velocity
(A) some friction exists between the disc and the ring.
(B) the angular momentum of the disc plus ring is conserved.
2
(C) the final common angular velocity is rd of the initial angular velocity of the disc.
3
2
(D) rd of the initial kinetic energy changes to heat.
3
space for rough work
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16. A particle A starts circulating along a circle of radius R so that its position
vector r relative to a point O rotates with the constant angular acceleration r A
as shown in figure then O R
(A) magnitude of velocity of the particle in the first t sec = 2 tR
(B) the angle subtended by path followed by the particle at the centre of the
circle in the first t sec = t2.
(C) magnitude of its acceleration in the first t sec = 2 R.
(D) none of the above
17. A solid body rotates about a fixed axis with an angular velocity = a − b where a, b are constant
and is an angle of rotation from the initial position, then
b
(A) angular acceleration = −
2
bt
(B) angle of rotation in first t sec = a − t
4
bt
(C) angle of rotation in first t sec = a + t
4
(D) none of the above
18. A uniform rod of mass m and length l is placed in gravity free space
A
and linear impulse J is given to the rod at a distance
x = l / 4 from centre and perpendicular to the rod. Point A is at a x
distance l / 3 from centre as shown in the figure. Then
J
J
(A) Speed of centre of rod is (B) Speed of point A is zero
m
J 5 J
(C) Speed of upper end of rod is (D) Speed of lower end of rod is
2m 2m
19. A ladder is resting with one end on the vertical wall and other end on a horizontal floor. It is more
likely to slip when a person stands.
(A) near the bottom (B) near the top
(C) at the middle (D) independent of the position of the person
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PART – C
This section contains 06 multiple choice questions. The answer to each question is a single digit integer, ranging from 0
to 9 (both inclusive)
nMR 2
3. Moment of Inertia of solid sphere of mass M radius R about its tangential axis is , then ‘n’ is
5
4. A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s –1
about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2
m, are gently place symmetrically on the disc in such a manner that they are touching each other
along the axis of the disc and are horizontal. Assume that the friction is large enough such that the
rings are at rest relative to the disc and the system rotates about the original axis. The new angular
velocity (in rad s–1) of the system is
B F
5. A uniform bar AB of mass m and length is resting on a smooth
horizontal surface. A force F is applied at end B perpendicular to
AB. The initial acceleration of end B w.r.t. ground is nF/m, find n.
A
I1
I2
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1. ( ) ( )
A variable circle C has the equation x 2 + y 2 − 2 t 2 − 3t + 1 x − 2 t 2 + 2t y + t = 0 , where t is a
parameter. If the power of point P (a, b) w.r.t. the circle C is constant then the ordered pair (a, b) is
1 1 1 1 1 1 1 1
(A) ,− (B) − , (C) , (D) − ,−
10 10 10 10 10 10 10 10
2. Three parallel chords of a circle have lengths 2, 3, 4 and subtend angles , , + at the
centre respectively (given + ), then cos is equal to
15 17 17
(A) (B) (C) (D) none of these
31 35 32
( )
1/2
The maximum and minimum value of p + q − 2p + 6q + 9
2 2
3. are 1 and 2 respectively. If
2 3 1
(A) (B) (C) 6 (D)
3 5 2
3 7
4. (
The orthocentre of triangle ABC with vertices A −1, 0 , B −2, ) & C −3, − is H. The
4 6
orthocentre of triangle BCH is
(A) ( −3, − 2 ) (B) (1, 3 ) (C) ( −1, 0 ) (D) None of these
6. ABCD is a square having vertices A and B on positive y axis and positive x axis respectively. If the
coordinates of point D are (12, 17 ) then the coordinates of C are
(A) (12,0 ) (B) (17, 5 ) (C) (12, 5 ) (D) (17, 12 )
space for rough work
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13
Let M 2, is the circumcentre of PQR whose sides PQ and PR are represented by the
8
7.
straight lines 4x − 3y = 0 and 4x + y = 16 respectively. The orthocentre of PQR is
7 4 4 7 3 3
(A) , (B) , (C) 3,
4
(D) , 3
3 3 3 3 4
8. A regular hexagon ABCDEF is inscribed in a circle of unit radius. A point P is taken on the
circle of radius 2 units having same centre. Then PA + PB + PC + PD + PE + PF is
2 2 2 2 2 2
equal to
(A) 18 (B) 12 (C) 24 (D) 30
9. (
Let AB be the chord of contact of the point 5, − 5 w.r.t. the circle) x2 + y2 = 5. If P is a
variable point on this circle, then the locus of the orthocenter of triangle PAB is
5
( x − 1) + ( y + 1) ( x − 1) + ( y + 1)
2 2 2 2
(A) =5 (B) =
2
5
( x + 1) + ( y − 1) (D) ( x + 1) + ( y − 1) =
2 2 2 2
(C) =5
2
10. Consider a triangle ABC with vertex A 4, − 1 and ( ) x − 1 = 0 and x − y − 1 = 0 are internal angle
bisectors through vertices B and C respectively. Let D, E, F be the points of contact of sides BC, CA
and AB with the incircle of triangle ABC respectively. If D’, E’, F’ are images of D, E, F in internal
angle bisectors of A, B and C respectively, then the equation of circumcircle of triangle D’E’F’ is
( x − 1) + y2 = 5 x2 + ( y − 1) = 25
2 2
(A) (B)
(C) ( x − 1) + ( y − 1) = 25
2 2
(D) none of these
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13. If a circle passes through the point 3,
and touches x + y = 1 and x − y = 1, then the centre of
2
the circle is at:
(A) ( 4, 0 ) (B) ( 4, 2) (C) ( 6, 0 ) (D) ( 7, 0 )
14. The equations of the lines passing through the point (2, 3) and having an intercept of length 2 units
between the lines 2x + y = 3 and 2x + y = 5 are
(A) y = 3 (B) x = 2 (C) y = x + 1 (D) 4y + 3x = 18
15. The sides of a triangle are the straight lines x + y = 1, 7y = x and 3y + x = 0 . Which of the
following is an interior point of the triangle?
(A) Circumcentre (B) centroid (C) incentre (D) orthocentre
16. Two sides of a triangle have the joint equation ( x − 3y + 2)( x + y − 2) = 0, then third side which is
variable always passes through the point (–5, –1), then possible values of slope of third side such that
origin is an interior point of triangle is/are:
−4 −2 −1 1
(A) (B) (C) (D)
3 3 3 6
17. Two lines having joint equation 3x2 + 10xy + 8y2 + 14x + 22y + 15 = 0 intersect at the point P and
have gradients m1 and m2 . The acute angle between them is . Which of following relations holds
good?
5
(A) m1 + m2 =
4
3
(B) m1m2 =
8
2
(C) = sin−1
5 5
(D) sum of the abscissa and the ordinate of point P is –1
18. Consider the circle x2 + y2 − 10x − 6y + 30 = 0 . Let O be the centre of the circle and tangent at
(7, 3) and B (5, 1) meet at C. Let S = 0 represents family of circles passing through A and B, then:
(A) Area of quadrilateral OACB = 4
(B) the radical axis for the family of circles S = 0 is x + y = 10
(C) the smallest possible circle of the family S =0 is x2 + y2 − 12x − 4y + 38 = 0
(D) the coordinates of point C are (7, 1)
space for rough work
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19. ABCD is a rectangle with A (–1, 2), B (3, 7) and AB : BC = 4 : 3. If d is the distance of origin from the
intersection point of diagonals of rectangle, then possible values of d is/are (where [.] denote
greatest integer function)
(A) 3 (B) 4 (C) 5 (D) 6
20. If the area of the quadrilateral formed by the tangents from the origin to the circle
x2 + y2 + 6x − 10y + c = 0 and the radii corresponding to the points of contact is 15, then a value of
c is
(A) 9 (B) 4 (C) 5 (D) 25
PART – C
This section contains 06 multiple choice questions. The answer to each question is a single digit integer, ranging from 0
to 9 (both inclusive)
angles differ by
3
(
2 2 2
)
is k x + y = 4a , then the value of k is
2. In a ABC, the vertex A is (1, 1) and orthocentre is (2, 4). If the sides AB and BC are members of the
family of straight lines ax + by + c = 0 . Where a, b, c are in A.P. then the coordinates of vertex C are
(h, k). Find the value of h + 6k .
3. Let P be any point on the line x − y + 3 = 0 and A be a fixed point (3, 4). If the family of lines given by
the equation (3sec + 5cosec ) x + (7sec − 3cosec ) y + 11(sec − cosec ) = 0 are
concurrent at a point B for all permissible values of and maximum and maximum value of
PA − PB = 2 2n (n N) , then find the value of n.
4. A point D is taken on the side AC of an acute triangle ABC, such that AD = 1, DC = 2 and BD is an
altitude of ABC . A circle of radius 2, which passes through points A and D, touches at point D a
A2
circle circumscribed about the BDC . The area of ABC is A, then =
15
5. Let two parallel lines L1 and L2 with positive slope are tangent to the circle
C1 :x + y − 2x − 16y + 64 = 0 . If L 1 is also tangent to the circle C2 :x + y − 2x + 2y − 2 = 0 and
2 2 2 2
a+b+c
equation of L 2 is a ax − by + c − a a = 0 where a,b,c N, then find the value of .
2
6. The number of possible straight lines, passing through (2, 3) and forming a triangle with coordinate
axes, whose area is 12 sq. units, is
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SECTION – II (Physics)
Part – A
1. A 2. A 3. B 4. D
5. C 6. C 7. B 8. C
9. B 10. C 11. BC 12. AD
13. AB 14. C 15. ABD 16. AB
17. AB 18. ABCD 19. B 20. BD
Part – C
1. 6 2. 3 3. 7 4. 8
5. 4 6. 5
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