XtraEdge Test Series # 3
Time : 3 Hours
Syllabus : Physics : Calorimetry, K.T.G.,Thermodynamics, Heat Transfer, Thermal expansion, Transverse wave, Sound wave, Doppler's effect. Chemistry : Chemical Equilibrium, Acid Base, Ionic Equilibrium, Classification &
Nomenclature, Isomerism , Hydrogen Family, Boron Family & Carbon Family, S-block elements. Mathematics:
Point, Straight line, Circle, Parabola, Ellipse, Hyperbola, Vector, 3-D Instructions :
Section - I
• Question 1 to 6 are multiple choice questions with only one correct answer. +5 marks will be awarded for correct answer and -2 mark for wrong answer.
Section - II
• Question 7 to 12 are passage based single correct type questions. +3 marks will be awarded for correct answer and -1 mark for wrong answer.
Section - III
• Question 13 to 14 are Column Match type questions 8 marks will be awarded for correct answer and 0 mark for wrong answer.
Section - IV
• Question 15 to 19 are numerical response questions (with single digit Answer). 3 marks will be awarded for correct answer and 0 mark for wrong answer.
Based on New Pattern
6. Figure shows cyclic process. From c to b, 40 J is transferred as heat from b to a, 130 J is transferred as heat, and work done is 80 J from a to c, 400 J is transferred as heat then –
P
V
a b
c
(A) Work done in process a to c is 310 J (B) Net work done is cycle is 230
(C) Net change in internal energy in cycle is 130 J (D) None of these
This section contains 2 paragraphs, each has 3 multiple choice questions. (Questions 7 to 12) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.
Passage : I (Ques. 7 to 9)
Many waveforms are described in terms of combinations of travelling waves. Superposition principle is used to analyse such wave combinations.
Two pulses travelling on same string are described by-
y1 =
2 ) t 4 – x 3 (
5
2+ , y2 =
2 ) 6 – t 4 x 3 (
5 –
2+ +
7. The direction in which each pulse is travelling is - (A) y1 is in positive x-axis, y2 is in positive x-axis (B) y1 is in negative x-axis, y2 is in negative x-axis (C) y1 is in positive x-axis, y2 is in negative x-axis (D) y1 is in negative x-axis, y2 is in positive x-axis 8. The time when the two waves cancel everywhere - (A) 1 sec (B) 0.5 sec (C) 0.25 sec (D) 0.75 sec 9. The point where two waves always cancel-
(A) 0.25 m (B) 0.5 m (C) 0.75 m (D) 1 m Passage: II (Ques. 10 to 12)
One mole of monoatomic gas is taken through above cyclic process. TA = 300 K
Process AB is defined as PT = constant P
B C 3P0
P0
T 10. Work done in process AB is -
(A) 400 R (B) – 400 R (C) 200 R (D) – 300 R
11. Change in internal energy in process CA (A) 900 R (B) 300 R (C) 1200 R (D) zero 12. Heat transferred in the process BC is -
(A) 1000 R (B) 500 R (C) 2000 R (D) 1500 R
This section contains 2 questions (Questions 13, 14).
Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S, T) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, A-T; B-Q, B-R; C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows :
A B C D
P
Q R S T
S T P
P P Q R
R R Q Q
S S T
T P Q R S T
Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.
13. Match the standing waves formed in column-II due to plane progressive waves in Column-I and also with conditions in Column-I
Column-I Column-II
(A) Incident wave is (P) y = 2A cos kx sin ωt y = A sin (kx – ωt)
(B) Incident wave is (Q) y = 2A sin kx cos ωt y = A cos (kx – ωt)
(C) x = 0 is rigid support (R) y = 2A sin kx cos ωt (D) x = 0 is flexible support (S) y = 2A cos kx cos ωt
(T) None of these
14. Column-I Column-II
(A) Specific heat capacity S (P) l1 – l2 = constant for l1α1 = l2α2 (B) Two metals (l1, α1) and (Q) Y is same (l2, α2) are heated uniformly
(C) Thermal stress (R) S = ∞ for ∆T = 0 (D) Four wires of same (S) Y α ∆t
material
(T) None of these
This section contains 5 questions (Q.15 to 19).
+3 marks will be given for each correct answer and no negative marking. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9.
The appropriate bubbles below the respective question numbers in the OMR has to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9 X Y Z W
15. If the volume of a block of metal changes by 0.12 % when heat is changed from 40ºC to 60ºC, find the linear expansion coefficient of the metal ?
[Ans. in …… × 10–5/ºK]
16. Calculate the pressure exerted by a mixture of 8 g of oxygen, 14 g of nitrogen and 22 g of carbon di-oxide in a container of 30 litres at a temperature of 27ºC.
[Ans. in …… × 105 N/m2]
17. A sphere and a cube of same material and total surface area placed in an evacuated chamber turn by turn and heated to the same temperature. Calculate the ratio of the rate of cooling of spherical to cubical surface. [Ans. in …… × 10–1]
18. Two oscillating waves have a phase difference of 2 π is 25 oscillations. What is the percentage difference in their frequency ?
19. For a certain organ pipe, three successive resonance observed are 425, 595 and 765 Hz. Taking the speed of sound to be 340 ms–1 , find the length of the pipe, in metre.
C HEMISTRY
Questions 1 to 6 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 5 marks will be given for each correct answer and – 2 mark for each wrong answer.
1. The IUPAC name of the given compound
CH3–CH–CH–CH–CH–COOH | |
| |
OHC CONH2
Br COCl
is -
(A) 2-Bromo-4-carbamoyl-5-chloroformyl-3-formyl hexanoic acid
(B) 5-Bromo-3-carbamoyl-2-chloroformyl-4-formyl hexanoic
(C) 4-Formyl-2-chloroformyl-3-carbamoyl-5-bromo hexanoic acid
(D) 2-Chloroformyl-3-carbamoyl-4-formyl-5-bromo hexanoic acid
2. Geometry in the given compound is CH3
CH3 H
H
(A) cis (B) trans
(C) cis as well as trans (D) no geometrical isomerism 3. The structure of spiro [3,3] heptane is -
(A) (B)
(C) (D)
4. The pH of a 10–8 molar solution of HCl in water is -
(A) 8 (B) – 8
(C) between 7 and 8 (D) between 6 and 7
5. Consider the following equilibrium in a closed container N2O4(g) 2NO2(g). At a fixed temperature, the volume of the reaction container is halved. For this change, which of the following statements holds true regarding the equilibrium constant (kp) and degree of dissociation (α) ?
(A) neither kp nor α changes (B) both kp and α change
(C) kp changes, but α does not change (D) kp does not change, but α changes 6. For H3PO3 and H3PO4 the correct choice is -
(A) H3PO3 is dibasic and reducing (B) H3PO3 is dibasic and non-reducing (C) H3PO4 is tribasic and reducing (D) H3PO3 is tribasic and non-reducing
This section contains 2 paragraphs, each has 3 multiple choice questions. (Questions 7 to 12) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.
Passage : I (Ques. 7 to 9)
In a reversible chemical reaction, the rate of forward reaction decreases and that of backward reaction increases with the passage of time; at equilibrium the rate of forward and backward reaction become same.
Let us consider the formation of SO3(g) in the following reversible reaction :
2SO2(g) + O2(g) 2SO3 (g)
Following graphs are plotted for this reactions
Conc.
time t1 t2 t3
A.
B.
C.
t4
7. In the above graph, A,B & C respectively are - (A) SO3, SO2 and O2 (B) SO3, O2 and SO2 (C) SO2, O2 and SO3 (D) O2, SO2 and SO3
8. In the above graph, the equilibrium state is attained at time -
(A) t1 (B) t2
(C) t3 (D) t4
9. Which of the following represent the rates of forward reaction (rf) and rates of backward reaction (rb) at equilibrium ?
(A) rate of reaction
time rb
rf
(B) rate of reaction
time rb rf
(C) rate of reaction
time rb rf
(D) rate of reaction
time rb
rf
Passage: II (Ques. 10 to 12)
Different spatial arrangements of the atoms that result from restricted rotation about a single bond are conformers. n-Butane has four conformers eclipsed, fully eclipsed, gauche and anti. The stability order of these conformers are as follows:
anti > gauche > partial eclipsed > fully eclipsed Although anti is more stable than gauche but in some cases gauche is more stable than anti.
10. Which one of the following is most stable conformer?
(A)
Cl
Cl CH3
CH3 H
H (B)
Cl
H CH3
Cl CH3
H
(C) Cl
CH3 CH3
H Cl
H (D)
Cl
CH3
CH3
H Cl
H
11. Which one of the following is the most stable conformer ?
(A)
CH3
CH3
OH
HO H
H (B)
CH3
OH OH
H CH3
H
(C) CH3
CH3 OH
H OH
H (D)
OH
OH CH3
H CH3
H
12. Number of possible conformers of n-butane is -
(A) 2 (B) 4
(C) 6 (D) infinite
This section contains 2 questions (Questions 13, 14).
Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S, T) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, A-T; B-Q, B-R; C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows :
A B C D
P
Q R S T
S T P
P P Q R
R R Q Q
S S T
T P Q R S T
Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.
13. Match the following : Column-I
(A) N2(g) + 3H2(g) 2NH3(g) ; ∆H = –ve
(B) N2(g) + O2(g) 2NO(g); ∆H = +ve (C) A(g) + B(g) 2C(g) + D(g); ∆H = +ve
(D) PCl5(g) PCl3(g) + Cl2(g); ∆H = +ve Column-II
(P) K increases with increase in temperature (Q) K decreases with increase in temperature (R) Pressure has no effect
(S) Product concentration, increases due to addition of inert gas at constant pressure
(T) Product concentration, increases due to addition of inert gas at constant volume
14. Match the following :
Column-I Column-II
(A) Bi3+ → (BiO)+ (P) Heat (B) [AlO2]– → Al(OH)3 (Q) Hydrolysis (C) [SiO4]4– → [Si2O7]6– (R) Acidification (D) [B4O7]2– → [B(OH)3] (S) Dilution by water
(T) Basification
This section contains 5 questions (Q.15 to 19).
+3 marks will be given for each correct answer and no negative marking. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9.
The appropriate bubbles below the respective question numbers in the OMR has to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9 X Y Z W
15. Calculate the pH at which the following conversion (reaction) will be at equilibrium in basic medium I2 (s) I–(aq.) + IO3– (aq.)
When the equilibrium concentrations at 300 K are [I–]
= 0.10 M and [IO3–] = 0.10 M.
{Given → ∆Gfº (I–, aq.) = – 50 kJ./mol, ∆Gfº (IO3–, aq) = – 123.5 KJ/mol, ∆Gfº (H2O, l) = –233 KJ/mol ∆Gfº (OH–, aq.) = – 150 KJ/mol
R(Gas constant) = 3
25 J/mol–K Log e = 2.3}
16. Number of configurational isomers of 2,3-dibromocinnamic acid is .
17. Consider the reaction AB2(g) ABg + B(g). It the initial pressure of AB2 is 100 torr and equilibrium pressure is 120 torr. The equilibrium constant Kp in terms of torr is.
18. Dissociation of H3PO3 occurs in ... stages.
19. The number of hydroxyl groups in pyrophosphoric acid is.
MATHEMATICS
Questions 1 to 6 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 5 marks will be given for each correct answer and – 2 mark for each wrong answer.
1. A circle C1 of radius b touches the circle x2 + y2 = a2 externally and has its centre on the positive x-axis;
another circle C2 of radius c touches the circle C1
externally and has its centre on the positive x-axis.
Given a < b < c, then the three circles have a common tangent if a, b, c are in -
(A) A.P. (B) G.P.
(C) H.P. (D) None of these
2. P is a point on the axis of the parabola y2 = 4ax;
Q and R are the extremities of its latus rectum, A is its vertex. If PQR is an equilateral triangle lying within the parabola and ∠AQP = θ, then cos θ = (A) 2 5
3 –
2 (B)
5 8
9
(C) 3 2
2 –
5 (D) None of these
3. The length of the diameter of the ellipse 25 x2
+ 9 y2
= 1, perpendicular to the asymptote of the hyperbola
16 x2
– 9 y2
= 1 passing through the first and third quadrants is :
(A) 431
100 (B)
481 150
(C) 3
25 (D) 11 2
4. If →a , →b, →c are such that [→a, →b, →c] = 1,
5. Equation of a plane which passes through the point of intersection of lines
3 tangent to ellipse and p3, p4 are perpendiculars from extremities of major axis and p from centre of ellipse on same tangent, then 2
4
This section contains 2 paragraphs, each has 3 multiple choice questions. (Questions 7 to 12) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.
the major axis of the ellipse E meets the ellipse at M, then centre O, then equation of the tangent at M to the ellipse E is -
(A) x + 3y = 3 5 (B) 4x + 3y = 5 (C) x + 3y + 5 = 0 (D) 4x +3y + 5 = 0
9. Equation of the diameter of the ellipse E conjugate to the diameter represented by L is -
(A) 9x + 2y = 0 (B) 2x + 9y = 0 (C) 4x + 9y = 0 (D) 4x – 9y = 0 Passage: II (Ques. 10 to 12)
In a parallelogram OABC vector →a , →b, →c are respectively the position vectors of vertices A, B, C with reference to O as origin. A point E is taken on the side BC which divides it in the ratio of 2 : 1. Also the line segment AE intersects the line besecting the angle O internally in point P. If CP when extended meets AB in point F, then
This section contains 2 questions (Questions 13, 14).
Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S, T) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, A-T; B-Q, B-R; C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows :
A
Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.
13.
Column-I Column-II (A) If lines x + 2y – 1 = 0, ax + y + 3 = 0 (P) 4
and bx – y + 2 = 0 are concurrent, the least distance from origin to (a, b) is S. The value of 58. S is hyperbola
)
preduced both side to meet asymptotes in Q and Q'. The measured parallel to the line
2
This section contains 5 questions (Q.15 to 19).
+3 marks will be given for each correct answer and no negative marking. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9.
The appropriate bubbles below the respective question numbers in the OMR has to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :
0
15. Two circle of radii 'a' and 'b' touching externally are inscribed in area bounded by y = 1–x2 and circle, what is the radius of that circle.
18. In a regular tetrahedron let θ be the angle between any edge and a face not containing the edge.
If cos2θ = b
a where a, b ∈ I+ also a and b are
coprime, then find the value of 13
5 (10a + b)
19. Let A (1, 2), B (3, 4) be two point and C (x,y) be a point such that (x – 1) (x – 3) + (y – 2) (y – 4) = 0. If area of ∆ABC is 1 sq, unit. Then maximum number of positions of C in xy plane is.