Maths-
General
Easy
Question
Statement-I : Integral curves denoted by the first order linear differential equation 
are family of parabolas passing through the origin.
Statement-II : Every differential equation geometrically represents a family of curve having some common property.
- Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
- Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I.
- Statement-I is true, Statement-II is false.
- Statement-I is false, Statement-II is true.
The correct answer is: Statement-I is false, Statement-II is true.
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A function f(x) satisfying 
where x>0 , is
A function f(x) satisfying where x>0 , is
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(where c is an arbitrary constant) is the general solution of the differential equation 
then the function 
(where c is an arbitrary constant) is the general solution of the differential equation then the function
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A function y = f (x) satisfies the condition f '(x) sin x + f (x) cos x = 1, f (x) being bounded when x 
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A function y = f (x) satisfies the condition f '(x) sin x + f (x) cos x = 1, f (x) being bounded when x 0. If
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Statement-I : In throwing of two dice, let the events A, B and C be 'the first dice shows an even number', 'the second dice shows an odd numbers' and 'both the dice show an odd numbers or both the dice show an even number’ respectively. Then 
and 
Therefore A, B and C are mutually independent events
Statement-II : Three events A, B and C are mutually independent if and only if P(A Ç B) = P(A) . P(B), P(B Ç C) = P(B) . P(C), 
= P(C) . P(A) and 
= P(A) . P(B) . P(C)
Statement-I : In throwing of two dice, let the events A, B and C be 'the first dice shows an even number', 'the second dice shows an odd numbers' and 'both the dice show an odd numbers or both the dice show an even number’ respectively. Then and Therefore A, B and C are mutually independent events
Statement-II : Three events A, B and C are mutually independent if and only if P(A Ç B) = P(A) . P(B), P(B Ç C) = P(B) . P(C), = P(C) . P(A) and = P(A) . P(B) . P(C)
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The probability that 4th power of a positive integer ends in the digit 6 is:
The probability that 4th power of a positive integer ends in the digit 6 is:
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Let A, B, C be pairwise independent events with P(C)> 0 and 
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Let A, B, C be pairwise independent events with P(C)> 0 and . Then
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Let A and B be two events such that 
and 
stands for complement of event A. Then events A and B are-
Let A and B be two events such that and stands for complement of event A. Then events A and B are-
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A random variable X has the probability distribution :
For the events E = {X is a prime number} and F = {X < 4}, the probability 
is-
A random variable X has the probability distribution :
For the events E = {X is a prime number} and F = {X < 4}, the probability is-
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A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.
A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.
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then the correct order sequance is
An experiment resulting in sample space as S = {a, b, c, d, e, f} Let three events A, B and C are defined as A = {a, c, e,}, B = {c, d, e, f} and C = {b, c, f}. then the correct order sequance is
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An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is
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Locus of circumcentre of triangle PQR is
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The least integral value that contained is the range of the function f defined by 
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Let 
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If m is the slope of tangent to the curve 
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