i5 academy-Maths(MCQ) google form test

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Previous year Board Exam questions

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School *

1) Which one of the following relations on R is an equivalence relation? *

1 point

a R1 b⇔|a|=|b|

a R2 b⇔a>b

a R3 b⇔a divides b

a R4 b⇔a<b

2) Let A={1,2,3},then the number of relations containing (1,2) & (1,3) that are reflexive & symmetric but not transitive is------------. *

1 point

3) The function f:(−∞,−1)→(0,e^5) defined by f(x)=e^x^3−3x+2 is---------- *

1 point

Many-one & onto

Many-one & Into

One-one & Into

One-one & Onto

4) Let X={p,q,r,s} and R={(p,p),(q,q),(p,r}. Then the minimum number of elements to be included to make it an equivalence relation is -----------. *

1 point

5) If f:R→S defined by f(x)=sinx–√3 cosx+1 is onto,then S=-------. *

1 point

[-1,3]

(-1,3)

[-1,1]

(0,∞)

6) Let X={a,b,c,d} and R={(a,a),(b,b),(c,c),(d,d),(a,d),(a,b),(d,b)} . What must be excluded from R,to make it a symmetric relation? *

1 point

{(a,d)}

{(a,b),(a,d),(d,b)}

{(a,d),(d,b)}

{(a,b)}

7) On the set of natural numbers. Let R be a relation defined by x R y if 3x+2y=30. Then the relation R is ------. *

1 point

Refflexive

symmetric

Transitive

Equivalence

8) Let A=R\{3}; B=R\{1} and let f:A→B be defined by f(x)=x−2/x−3 is---------- *

1 point

One-one & onto

One-one but not onto

Onto but not one-one

Neither one-one nor onto

9) The number of symmetric relations on a set containing '4' elements is ---------. *

1 point

1024

256

512

10) Let R be a relation over the set N×N,it is defined by (a,b) R (c,d) ⇒a+d=b+c,then R is---------. *

1 point

Only Reflexive

Only Symmetric

Only Transitive

Equivalence Relation.

11) For real numbers a & b, we define a R b iff a−b+√2 is an irrational number. Then R is------- *

1 point

symmetric

transitive

Reflexive

Equivalence

12) Let f:{x,y,z}→{1,2,3} be a one-one mapping such that only one of the following three statements istrue & remaining two are false.Statement 1: f(x)≠2Statement 2: f(y)=2Statement 3: f(z)≠1 , then *

1 point

f(x)>f(y)>f(z)

f(x)<f(y)<f(z)

f(y)<f(x)<f(z)

f(y)<f(z)<f(x)

13) The number of one-one function if A & B are finite sets having m & n elements respectively is--------. *

1 point

m! if m<n

nPn n<m

0 if n>m

nPm n≥m

14) The relation R in the set A={1,2,3,4,5} is given by {(a,b):|a−b|is odd} is-------- relation. *

1 point

Only reflexive

Reflexive & Symmetric

Equivalence

Symmetric but not transitive and reflexive.

15) Let A={0,1,2,3}. Then which of the following relation R is reflexive,symmetric but not transitive. *

1 point

{(0,0),(1,1),(2,2),(3,3),(1,2),(2,3),(2,1)}

{(0,0),(1,1),(2,2),(3,3),(1,2),(2,3),(2,1),(3,2)}

{(0,0),(1,1),(2,2),(3,3),(1,2)}

{(0,0),(1,1),(2,2),(3,3)}

16) Let A=Z∪{√3}.Define a relation R in A by a R b if and only if a+b∈Z. The relation R is -----. *

1 point

Reflexive

Symmetric & transitive

Only transitive

None of these.

17) The largest cardinality of an equivalence relation on a set containing 4 elements is-----------. *

1 point

18) The function f:R→R defined by f(x)=sinx is ------------. *

1 point

One-one & onto

Neither one-one nor onto

one-one but not onto

Many-one & onto

19) An empty relation is -------------. *

1 point

Reflexive

Only symmetric

Symmetric & Transitive

Equivalence Relation

20) Let X be a non-empty set, p(x)=set of all subsets of x. The relation R is p(x)defined by For subsets A,B∈p(x), ARB if & only if A<B.Then the relation is ------------- . *

1 point

Reflexive & symmetric but not transitive

Reflexive & Transitive but not symmetric

Symmetric & Transitive but not reflexive

Equivalence relation.

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