Math MCQs Chpater 7 book 1 (Probability)

1. A number is selected from first 50 prime numbers. What is the probability that it is an odd number?

a)    1/50

b)   1/2

c)    49/50

d)   None of these

2. A number is selected at number at random among the prime numbers between 300 and 500. What is probability that it is odd number?

a)    1

b)   2

c)    0

d)   ½

Answer:1

C

Answer:2

A

Important points Chapter 6 book 1

Sequences are also called progressions.

A sequence is a special set of a function from a subset of N to R or C.

If all the members of a sequence are real numbers, then it is called a real sequence.

Sequence is a function whose domain is a subset of the set of natural numbers.

Sum of n A.M’s between a and b is equal to n times their A.M.

In Geometric progression, r is the ratio of any term of the G.P to its predecessor.

No term in geometric progression is zero.

The n geometric mean between a and b are a (b/a)^n/n+1

Equivalent common fraction is also called vulgur fraction.

Zero cannot be the term of harmonic sequence.

In sigma notation k is called index of summation.

Some important MCQS:

Exercise 6.3 Q(1,7)  (page:196)

Exercise 6.6 Q(7,8,12) (page:206)

Exercise 6.7 Q(1,2,3,6)  (page:209)

Example :4 (page:221)

Exercise 6.10 Q9

Important points Chapter 4 book 1

If an expression is true for all the values of the variables involved then it is called identity.

If an expression is true for some values of the variables then it is called equation.

2^nd degree equation is known as quadratic equation.

Roots of the equation will always satisfy the equation.

Graph of the quadratic equation is parabola.

Number of roots is equal to the degree of the equation.

If an equation has imaginary roots then its roots will be conjugate of each other.

Exponential equation→If variable is in power or exponent.

Reciprocal equation → If x is changed by 1/x then the result will remains the same.

Radical equation → an equation having the sign of square root.

Extraneous roots → roots which do not satisfy the original equation.

Important points chapter 3 book 1

Determinant of a diagonal matrix is equal to the product of its main diagonal elements.

No common element is present between two diagonals of a matrix of even order.

A   _(n+1)/2 is common element of two diagonals o f a matrix of odd order n.

A² is always symmetric for A being either symmetric or skew-symmetric.

Non-homogenous system:

1.     A system is said to be consistent if its solution exists otherwise inconsistent.

2.     If |A|=0 then solution does not exists.

3.     If |A|≠ 0 then solution exist.

4.     Solution exists if A is non-singular.

5.     Solution will exist if

a.      Rank of A = rank of A_b

6.     If rank of A = rank of A_b= number of variables

a.      Then solution is unique.

7.     If rank of A = rank of A_{b <}  number of variables

a.      Then solutions are infinite.

Homogenous system:

1.     Every homogenous system has trivial or zero solution.

2.     For non-trivial solution |A|=0

3.     If |A≠0 then non-trivial solution does not exist.

Note:

In all above cases A is the matrix of co-efficient.

Important points chap 1 book 2

Range of constant function is singleton set.

The graph of identity function is a straight line which passes through origin and 

bisects 1^st and 4^th quadrant.

(0, ∞)= +ve real numbers

[0, ∞ )=non –ve real numbers

(-∞,0)= -ve numbers

(-∞, 0]=non +ve numbers

Symmetry of a curve:

Replace y by –y. if unchanged then it is symmetric about x-axis.

Replace x by –x. if unchanged then it is symmetric about y-axis.

Replace x by –x and y by –y . if unchanged then it is symmetric about origin.

Math Chapter 6 MCQs

1.     The sum of an indicated number of terms in a sequence is called

a)     Series

b)    Sequence

c)     Average

d)    Arithmetic mean

2.     Which term of A.P 5,2,-1,…. is -85.

a)     15^th

b)    30^th

c)     35^th

d)    31^th

Key points chapter 1 book 1

If  a set satisfies :

Closure property then it is called groupoid.

Closure + associative then it is called semi-group.

Closure+ Associative+ identity element then it is called monoid.

Closure+ Associative+ identity + inverse then it is called group.

If a set satisfies all the 11 properties then it is called field

Set of real numbers, rational numbers and complex numbers are field.

Note:

Identity element in a group is always unique.

Inverse of an element is always unique.

Total number of binary operations are 4.

Powers of i :

If you have to tackle an MCQ which has high powers of  then follow the following points:

1.     Divide the power by 4.

2.     If remainder is 0 then answer is +1.

3.     If remainder is 2 then answer is  -1.

4.     If remainder is 1 then answer is +i .

5.     If remainder is 3 then answer is   -i .

Sets:

Let n(A) = n     (let number of elements in set A is n)

2ⁿ = number of all possible subsets (or power sets)

2ⁿ-1=2ⁿ-2⁰= number of all proper subsets

2ⁿ-1= number of non-empty subsets.

And

2ⁿ-2 =2( 2^n-1-1) non-empty proper subsets.

Note:

Power set has only one improper subset.

Number of elements in a set= order of set(cardinality)

{ } this is null set.

{0} this is singleton set.

In singleton set:

All subsets are 2. 1 proper and 1 improper.

A set having no proper subset is empty set.

MCQs of chapter#6

1.     If 5,8 are the two A.M’s between a and b. what is a and b?

a)     2,9

b)    3,11

c)     2,11

d)    3,9

2.     For what value of n, is (aⁿ+bⁿ)/(a^n-1+b^n-1) the arithmetic mean between a and b.

a)     0

b)    ½

c)     -½

d)    None of these

3.     The sum of an indicated number of terms in a sequence is called

a)     Series

b)    Sequence

c)     Average

d)    Arithmetic mean