Loading [MathJax]/jax/output/CommonHTML/jax.js

CBSE Questions for Class 11 Commerce Applied Mathematics Number Theory Quiz 10 - MCQExams.com

A number system with a base of two is referred as ______________.
  • Unary number system
  • Binary number system
  • Octal number system
  • None of these
If a register containing data (11001100)2 is subjected to arithmetic shift left operation, then the content of the register after 'ashl' shall be _____________.
  • (11001100)2
  • (1101100)2
  • (10011001)2
  • (10011000)2
C it refers to a _____________.
  • computer language.
  • CPU instruction.
  • 0 or 1 value.
  • digital representation of an alphabetic character.
Which of the following is true?
  • Byte is a single digit in a binary number
  • Bit represents a grouping of digital numbers
  • Eight-digit binary number is called a bit
  • Eight-digit binary number is called a byte
State true(T) or false(F).
The sum of primes cannot be a prime.
  • True
  • False
State true or false:
The product of primes cannot be a prime.
  • True
  • False
State true(T) or false(F).
Odd numbers cannot be composite.
  • True
  • False
State true(T) or false(F).
An even number is composite.
  • True
  • False
Mark the correct alternative of the following.
Which of the following numbers is prime?
  • 23
  • 51
  • 38
  • 26
The least prime is?
  • 1
  • 2
  • 3
  • 5
Mark the correct alternative of the following.
Which of the following are not twin-primes?
  • 3,5
  • 5,7
  • 11,13
  • 17,23
Mark the correct alternative of the following.
Which of the following numbers are twin primes?
  • 3,5
  • 5,11
  • 3,11
  • 13,17
Mark the correct alternative of the following.
The smallest number which is neither prime nor composite is?
  • 0
  • 1
  • 2
  • 3
Express the following complex numbers in the standard form a+ib :
(114i21+i)(34i5+i)
  • 307442+i599442i
  • 307442i599442i
  • 307442+i599442i
  • None of the above
Express the following complex numbers in the standard form a+ib :
(2+i)32+3i
  • 37131613i
  • 3713+1613i
  • 3713+1613i
  • None of the above
Find the modulus and argument of the following complex numbers and hence express each of them in the polar form:
1i
  • 2(cosπ/4+isinπ/4)
  • 2(cosπ/3isinπ/3)
  • 2(cosπ/4isinπ/4)
  • 2(cosπ/3+isinπ/3)
Express the following complex numbers in the standard form a+ib :
34i(42i)(1+i)
  • 14+34i
  • 1434i
  • 1434i
  • None of the above
Express the following complex numbers in the standard from a+ib :
5+2i12i
  • 122i
  • 1+2i
  • 1+22i
  • 12i
The real part of (i3)13 is
  • 2103
  • 2123
  • 2123
  • 2123
  • 2103
Let z be a complex number such that |ziz+2i|=1 and |z|=52. Then the value of |z+3i| is?
  • 72
  • 154
  • 23
  • 10
Mark against the correct answer in each of the following .
i91=?
  • 1
  • 1
  • i
  • i
(11)(1+1)(57)(5+7)=?
  • (25+7i)
  • (32+5i)
  • (293i)
  • none of these
Mark against the correct answer in each of the following .
i326=?
  • 1
  • 1
  • i
  • i
If z23∣=3z then the maximum value of z is
  • 1
  • 3+212
  • 2132
  • none of these
If z1 and z2 are any two complex numbers then
|z1+z21z22|+|z1z21z22| is equal to
  • |z1|
  • |z2|
  • |z1+z2|
  • None of these
(23i)(3+4i)=?
  • (6+17i)
  • (617i)
  • (6+17i)
  • none of these
Mark against the correct answer in each of the following .
i273=?
  • i
  • i
  • 1
  • 1
Compare List I with List II and choose the correct answer using codes given below:
List I (Complex number)List II (Its modulus)
(43i)10
(8+6i)15
1(3+4i)1
(34i)(3+4i)5
  • (i)(p),(ii)(s),(iii)(r),(iv)(q)
  • (i)(s),(ii)(p),(iii)(q),(iv)(r)
  • (i)(s),(ii)(p),(iii)(r),(iv)(q)
  • (i)(r),(ii)(p),(iii)(s),(iv)(q)
Which of the following is a composite number?
  • 23
  • 29
  • 32
  • none of these
State whether the following statements are true (T) or false (F) :
There are infinitely many prime numbers.
  • True
  • False
State whether the following statements are true (T) or false (F):
A natural number is called a composite number if it has at least one more factor other than 1 and the number itself. 
  • True
  • False
Which of the following is an odd composite number ?
  • 7
  • 9
  • 11
  • 12
The modulus of ¯6+i3+¯6+i+¯6+i2 is
  • 17
  • 533
  • 456
  • 49
Given z is a complex number with modulus 1. Then the equation in a, (1+ia1ia)4=z has
  • all roots real and distinct.
  • two real and two imaginary.
  • three roots real and one imaginary.
  • one root real and three imaginary.
If z0=1i2,  then (1+z0)(1+z210)(1+z220)..........(1+z2n0)  must be
  • (1i)(1+122n) for n>1
  • (1i)(1122n) for n>1
  • 1+i2 for n>1
  • (1i)(1122n+1) for n>1
Dividing f(z) by zi, we obtain the remainder i and dividing it by z+i, we get the remainder 1+i, then remainder upon the division of f(z) by z2+1 is
  • 12(z+1)+i
  • 12(iz+1)+i
  • 12(iz1)+i
  • 12(z+i)+1
The number of solutions of log15log12(|z|2+4|z|+3)<0 is/are?
  • 0
  • 2
  • 4
  • infinite
Let z be a complex number and c be a real number  1 such that z + c|z+1|+i=0, then c belongs to 
  • [2,3]
  • (3,4)
  • [1,2]
  • None of these
lf logtan30(2|Z|2+2|Z|3|z|+1)<2 then
  • |z|<32
  • |z|>32
  • |z|>2
  • |z|<2
If x=2+5i(where 1i=1) and 2(11!9!+13!7!)+15!5!=2ab! then x35x2+33x10=
  • a+b
  • ba
  • ab
  • ab
  • (ab)(a+b)
If |log3|z|2|z|+12+|z||<2, then
  • |z|<13
  • |z|=1
  • |z|=5
  • 1<|z|<5
If z be a complex number satisfying z4+z3+2z2+z+1=0 then  |z| is 
  •  12
  •  34
  •  1
  • None of these
If the expression (1+ir)3 is of the form of s(1+i) for some real s where r is also real and i=1, then the value of r can be
  • cotπ8
  • secπ
  • tanπ12
  • tan5π12
Find the value of x such that (x+α)2(x+β)2α+β=sin2θsin2θ. when α and β are the roots of t22t+2=0
  • x=icotθ1
  • x=(icotθ+1)
  • x=icotθ
  • x=itanθ1
If z1,z2 be two non zero complex numbers satisfying the equation |z1+z2z1z2|=1 then z1z2+(z1z2) is
  • zero
  • 1
  • purely imaginary
  • 2
Find the range of real number α for which the equation z+α|z1|+2i=0;z=x+iy has a solution. Find the solution.
  • x=5/2,y=2
  • x=2,y=5/2
  • x=5/2,y=2
  • x=2,y=5/2
If n is a natural number 2, such that zn=(z+1)n, then
  • Roots of equation lie on a straight line parallel to the yaxis
  • Roots of equation lie on a straight line parallel to the xaxis
  • Sum of the real parts of the roots is [(n1)/2]
  • None of these
Let  z1=a+ib,z2=p+iq be two unimodular complex numbers such that  Im(z1z2)=1. If ω1=a+ip,ω2=b+iq then
  •  Re(ω1ω2)=1
  •  Im(ω1ω2)=1
  •  Rm(ω1ω2)=0
  •  Im(ω1¯ω2)=0
Find the regions of the z-plane for which |zaz+¯a|<1,=1 or >1. when the real part of a is positive.
  • The required regions are the right half of the z-pane, the imaginary axis and the left half of the z-plane respectively.
  • The required regions are the left half of the z-pane, the imaginary axis and the right half of the z-plane respectively.
  • The required regions are the right half of the z-pane the real axis and the left half of the z-plane respectively.
  • The required regions are the left half of the z-pane the real axis and the right half of the z-plane respectively.
Find all complex numbers satisfying the equation 2|z|2+z25+i3=0
  • ±(62+12i);±(16+32i)
  • ±(6212i);±(2632i)
  • ±(6213i);±(1632i)
  • ±(6212i);±(1632i)
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers