IIT-JEE 2013
17. Which of the above element is likely to be alkali metal ?
Passage # 2 (Ques. 17 to 19)
The IE1 and IEII in kJ/mol of a few elements are given in the following table
Element IEI in kJ/Mol IEII in kJ//mol
P 2372 5251
Q 520 7300
R 900 1760
S 1680 3380
17. Which of the above element is likely to be alkali metal ?
(A) P (B) Q (C) R (D) S
18. Which of the above element is likely to be alkaline earth metal ?
(A) P (B) Q (C) R (D) S 19. Which of the above element is likely to be noble gas?
(A) P (B) Q (C) R (D) S
This section contains 3 questions (Questions 20 to 22).
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) 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, B-Q, B-R, C-P, C-Q and D-S, then the correctly bubbled 4 × 4 matrix should be as follows :
A B C D
P
Q R S
S P
P P Q R
R R Q Q
S S P Q R S
Mark your response in OMR sheet against the question number of that question in section-II. + 6 marks will be given for complete correct answer and No Negative marks for wrong answer. However, 1 mark will be given for a correctly marked answer in any row.
20. Column-I Column-II
(A) Primary standard base (P) Na2C2O4
(B) Equiv. wt = 2
wt Molecular
(Q) Na2B4O7
(C) Primary standard reducing (R) Na2CO3
agent
(D) Capable of reducing (S) As2O3
hardness of water due to the presence of Ca2+
21. Column-I Column-II
(A) Tc/Pc (P) Z (B) Tc/Vc (Q) a/Rb
(C) TB (R) 8b/R
(D) Ti/TB (S) 8a/81 Rb2
22. Column-I Column-II
(A)
V
P A
B
(P)
(B)
T
P A B
(Q) Isotherm
(C)
T P
A
B (R) Isochoric
Temperature is increasing
(D)
B
A
T
P (S) Pressure is increasing
MATHEMATICS
Questions 1 to 9 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. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.
1. In a ∆ABC, if r = r2 + r3 –r1 and ∠A > π/3 then range of a
s is equal to-
(A)
,2 2
1 (B)
,∞ 2
1 (C)
,3 2
1 (D) (3, ∞)
2. Vector perpendicular to iˆ– jˆ–kˆ and in the plane of iˆ+ jˆ+kˆ and –iˆ+ jˆ+kˆ is
(A) iˆ+kˆ (B) 2iˆ+ jˆ+kˆ (C) 3iˆ+2jˆ+kˆ (D) 4iˆ– 2jˆ–2kˆ
3. If a, b ∈ R, a ≠ 0 and roots of ax2 – bx + 1 = 0 imaginary, then a + b + 1 is
(A) Zero (B) Positive (C) Negative (D) None of these
4. Number of distinct normals that can be drawn to the curve x2 = 4y from point (1, 2), is
(A) 0 (B) 1 (C) 2 (D) 3
5. ABC is a triangle whose medians AD and BE are perpendicular to each other. If AD = p and BE = q then area of ∆ABC is-
(A) pq
3
2 (B) pq 2
3 (C) pq
3
4 (D) pq 4 3
6. If (21.4)a = (0.00214)b =100, then the value of a
1 – b 1 is :
(A) rational but not integral
(B) prime
(C) irrational (D) composite 7. For 3 ≤ r ≤ n
nCr + 3 nCr–1+ 3 nCr–2 + nCr–3 is-
(A) n+3Cr (B) 2 n+2Cr+2 (C) 3 n+1Cr+1 (D) 3 nCr
8. Point of intersection of straight lines represented by 6x2 + xy – 40y2 – 35x – 83y + 11 = 0 is-
(A) (3, 1) (B) (3, –1) (C) (–3, 1) (D) (–3, –1) 9. Number of points outside the hyperbola
3x2 – y2 = 48 from where two perpendicular tangents can be drawn to the hyperbola is/are -
(A) 1 (B) 2 (C) infinite (D) None This section contains 4 questions numbered 10 to 13, (Reason and Assertion type question). Each question contains Assertion (A) and Reason (R). 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 following questions given below consist of an
"Assertion" (A) and "Reason" (R) Type questions. Use the following Key to choose the appropriate answer.
(A) If both (A) and (R) are true, and (R) is the correct explanation of (A).
(B) If both (A) and (R) are true but (R) is not the correct explanation of (A).
(C) If (A) is true but (R) is false.
(D) If (A) is false but (R) is true.
10. Assertion (A) : The length of the shortest intercept made by the family of lines (1 + λ) x + (λ – 1) y + 2 (1– λ) = 0 on the parabola x2 = 4(y – 1) is 5.
Reason (R) : Latus rectum is the shortest focal chord of the parabola.
11. Assertion (A) : If S1 and S2 are non-concentric circles then their radical axis must exist.
Reason (R) : S1,S2, S3 are three circles such that no two are concentric then their radical centre is defined.
12. Assertion (A) : If two straight lines intersect the x-axis at A and B and y-x-axis at C and D such that OA.OB = OC.OD, O being origin then points A, B, C, D are concyclic.
Reason (R) : If a secant through a point P intersects a circle at Q and R then PQ.PR is independent of the direction of the secant.
13. Assertion (A) : The equation
(log x)2 – log x3 + 2 = 0 has only one solution.
Reason (R) : log x2 = 2 log x if x > 0
This section contains 2 paragraphs; each has 3 multiple choice questions. (Questions 14 to 19) 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. +4 marks will be given for each correct answer and – 1 mark for each wrong answer.
Passage # 1 (Ques. 14 to 16) 19. Equation of plane containing these lines is
(A) x – y – 2 = 0 (B) 2x – y + 2 = 0 (C) x – y + 7 = 0 (D) None of these
This section contains 3 questions (Questions 20 to 22).
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) 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, B-Q, B-R, C-P, C-Q and D-S, then the correctly bubbled 4 × 4 matrix should be as follows :
A
Mark your response in OMR sheet against the question number of that question in section-II. + 6 marks will be given for complete correct answer and No Negative marks for wrong answer. However, 1 mark will be given for a correctly marked answer in any row.
20. Match the following
Consider a plane P = 0 on whom foot of perpendicular from point (1, 1, 1) is (2, 3, 4).
Column-I Column-II
(A) sum of intercepts of P = 0 (P) 52/7 on coordinate axis is
(B) perpendicular distance of (Q) 110/3 (0, 0, 0) from plane is λ then λ2 is (C) A line through (0, 0, 0) and (R) 120
perpendicular to plane is a (D) Radius of circle obtained by (S) 200/7
plane 'P' and sphere x2 + y2 + z2 with co-ordinate axis is
(C) Circumcentre of ∆ formed by (R) 2/5
Column-I Column-II
(A) Find the number of 6 digit (P) 1 natural numbers, where each digit appears at least twice
(B) In how many ways can five (Q) 677 different books be tied up in
three bundles
(C) How many non-empty (R) 11754 collections are possible by
using 5P's and 6 Q's (D) How many students do you (S) 25
need in a school to guarantee that there are atleast 2 students, who have the same 1st two initials in their 1st names
PHYSICS
1. The spectrum of hydrogen atom has many lines although hydrogen atom contain only one electron why ?
2. What happens to the frequency when light passes from one medium to another.
3. What are coherent sources of light
4. If the intensity of the incident radiation on a metal is doubled, what happens to the kinetic energy of the emitted photoelectrons.
5. Prove mathematically that the average power over a complete cycle of alternating current through an ideal inductor is zero.
6. Figure shows a branch of a circuit. Find out the value of potential difference between A and B.
A 1A
2Ω + – 1Ω B 2V
7. Write the following radiations in an ascending order in respect of their frequencies :
X–rays, microwaves, ultraviolet rays, radiowaves
8. In a closed surface incoming flux and outgoing flux is 5 × 105 and 4 × 105 V-m respectively then find out the charge enclosed by surface.
9. A freshly prepared radioactive substance of half life 2 hours emits radiation of intensity which is 64 times the permissible safe level. Find the minimum time after which it would possible to work with this source safely.
10. Why does the conductivity of a semiconductor change