Question 1 :
The domain of {tex} f ( x ) = \left( x ^ { 2 } - 1 \right) ^ { - 1 / 2 } {/tex} is
Question 2 :
The number of proper subsets of the set {1, 2, 3} is
Question 3 :
If {tex} f ( x ) = \sin \sqrt { [ a ] } x , {/tex} (where [.] denotes the greatest integer func- tion), has {tex} \pi {/tex} as its fundamental period, then
Question 4 :
If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then
Question 5 :
Let A = {a, b, c}, B = {b, c, d}, C = {a, b, d, e}, then A ∩ (B ∪ C) is
Question 6 :
Let {tex} y = f ( x ) {/tex} be a real-valued function with domain as all real numbers. If the graph of the function is symmetrical about the line {tex} x = 1 , {/tex} then {tex} \forall \alpha \in R , {/tex} which one is correct?
Question 8 :
The number of non-empty subsets of the set {1, 2, 3, 4} is
Question 9 :
In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is
Question 10 :
The interval for which {tex} \sin ^ { - 1 } \sqrt { x } + \cos ^ { - 1 } \sqrt { x } = \frac { \pi } { 2 } {/tex} holds
Question 12 : State whether the given statement is true or false:<div>P $\cap$ (Q $\cup$ R) = (P $\cap$ Q) $\cup$ R</div>
Question 13 :
If $A$ is a finite set having $n$ elements, then the number of relations which can be defined in $A$ is
Question 14 :
Let $R = \{ ( 3,3 ) , ( 6,6 ) , ( 9,9 ) , ( 6,12 ) , ( 3,9 ) , ( 3,12 ) , ( 3,6 ) \}$ be a relation on the set $A=\{ 3,6,9,12\} .$ Then the relation $R ^ { - 1 }$ is
Question 15 :
If $\displaystyle :n(A)= m, $ then number of relations in $A$ are<br/>
Question 16 :
If {tex} f: R \rightarrow S , {/tex} defined by {tex} f ( x ) = \sin x - \sqrt { 3 } \cos x + 1 {/tex} is onto, then the interval of {tex} S {/tex} is
Question 17 :
The function {tex} f ( x ) = | \sin 4 x | + | \cos 2 x | , {/tex} is a periodic function with period
Question 18 :
If $R$ is the relation 'less than' from $A=\{1, 2, 3, 4, 5\}$ to $B=\{1, 4\}$, the set of ordered pairs corresponding to $R$, then the inverse of $R$ is
Question 19 :
If x is real, then $\dfrac{x^2+2x+c}{x^2+4x+3c}$ can take all real values if?
Question 20 :
A survey shows that $63$% of Americans like cheese where as $76$% like apples. If $x$% of the american like both cheese and apples, then
Question 21 :
If A = {1, 2, 3}, B = {a, b}, then A × B mapped A to Bis
Question 22 :
If $A = \left\{ n:\frac{n^{3} + 5n^{2} + 2}{n}\ \text{is\ an\ integer\ and\ itself\ is\ an\ integer} \right\},$ then the number of elements in the set A, is
Question 23 :
Let A and B be two non-empty subsets of a set X such that A is not a subset of B. Then,
Question 24 :
If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
Question 25 :
In a rehabilitation programme, a group of 50 families were assured new houses and compensation by the government. Number of families who got both is equal to the number of families who got neither of the two. The number of families who got new houses is 6 greater than the number of families who got compensation. How many families got houses?
Question 26 :
The finite sets A and B have m and n elements respectively. if the total number of subsets of A is 112 more than the total number of subsets of B, then the volume of m is
Question 27 :
A function {tex} f ( x ) {/tex} is defined for all real {tex} x {/tex} and satisfied {tex} f ( x + y ) = {/tex} {tex} f ( x y ) \forall x , y . {/tex} If {tex} f ( 1 ) = - 1 , {/tex} then {tex} f ( 2006 ) {/tex} equals
Question 28 :
If A = {1, 2, 3, 4}, then the number of subsets of A that contain the element 2 but not 3, is
Question 29 :
If A = {x, y}, then the power set of A is
Question 30 :
If A = {ϕ,{ϕ}}, then the power set of A is
