Question
1
Let R be the set of real numbers. Statement1: A = {(x, y) ∈ R × R : y  x is an integer} is an equivalence relation on R. Statement2: B = {(x, y) ∈ R × R : x = αy for some rational number α} is an equivalence relation on R
Statement1 is false, Statement2 is true.


Statement1 is true, Statement2 is true;Statement2 is a correct explanation forstatement1


Statement1 is true, Statement2 is false


Statement1 is true, Statement2 is true;Statement2 is not a correct explanation forStatement1


Question
2
Consider 5 independent Bernoulli's trails each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32, then p lies in the interval.
3/4, 11/12


11/12, 1


0, 1/2


1/2, 3/4


Question
3
The two circles x2 + y2 = ax, and x2 + y2 = c2 (c > 0) touch each other if
a = 2c


a = c


2a = c


a = 2c


Question
4
If C and D are two events such that C ⊂ D andP(D)≠ 0, then the correct statement among the following is
P(CD) ≥ P(C)


P(CD) < P©


P(CD) = P(C)


P(CD) =P(D)/P(C)


Question
5
Statement – 1 : The point A(1, 0, 7) is the mirror image of thepoint B(1, 6, 3) in the line x/l = (y  1)/2 = (z  2)/3. Statement – 2 : The line x/l = (y  1)/2 = (z  2)/3 bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).
Statement1 is false, Statement2 is true.


Statement1 is true, Statement2 is false


Statement1 is true, Statement2 is true;Statement2 is a correct explanation forstatement1.


Statement1 is true, Statement2 is true;Statement2 is not a correct explanation forStatement1


Question
6
If A = sin^{2}^{ }x + cos^{4} x, then for all real x:
3/4 ≤ A ≤ 13/16


1 ≤ A ≤ 2


3/4 ≤ A ≤ 1


13/16 ≤ A ≤ 1


Question
7
Statement – 1 : Sky wave signals are used for long distance radio communication. These signals are ingeneral, less stable than ground wave signals. Statement – 2 : The state of ionosphere varies from hour tohour, day to day and season to season.
Statement – 1 is False, Statement – 2 isTrue


Statement – 1 is True, Statement – 2 isFalse.


Statement – 1 is True, Statement – 2 isTrue; Statement – 2 is not the correctexplanation for Statement – 1


Statement – 1 is True, Statement – 2 isTrue; Statement – 2 is a correctexplanation for Statement – 1


Question
8
A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R.Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley,
is
Question
9
The area of the region enclosed by the curves y = x, x = e, y = 1/x and the positive xaxis is
1 square units


1/2 square units


3/2 square units


5/2 square units


Question
10
A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 morethan the saving of immediately previous month.His total saving from the start of service will beRs. 11040 after.
21 months


19 months


18 months


20 months



