Algebra Assignment - NTA Abhyas

Q1. The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + ..….. and 1 + 6 + 11 + 16 + ………. is

A

B

D

C

4000

4200

4020

4220

Q2. If the 2nd , 5th and 9th terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is

A

B

D

C

1

Q3. The first three terms of an arithmetic-geometric progression are 3, -1 and - 1. The next term of the progression is

A

B

D

C

2

-2

Q4. Three numbers a, b and c are in geometric progression. If 4a, 5b and 4c are in arithmetic progression and a + b + c = 70, then the value of |c - a| is equal to

A

B

D

C

10

20

40

30

Q5. The coefficient of the term independent of x in is

A

B

D

C 6

Q6. If in the expansion of (1 + x)m (1 - x)n, the coefficients of x and x2 are 3 and -6 respectively, then the value of m is (m, n ∈ N)

A

B

D

C

6

9

24

12

Q7. The first integral term in the expansion of , is the

A

B

D

C

2nd term

3rd term

5th term

4th term

Q8. In the expansion of , the coefficient of the 8th and 19th

terms are independent of x is given by

A

B

D

C

Q9. The number of ways in which 10 balls can be selected from 10 identical green balls, 10 identical blue balls and 9 identical red balls are

A

B

D

C

63

64

66

65

Q10. How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?

A

B

D

C

360

350

390

400

Q11. The number of four- digit numbers formed by using the digits 0, 2, 4, 5 and which are not divisible by 5, is

A

B

D

C

10

8

4

6

Q12. The number of five-digit numbers formed with the digits 0, 1, 2, 3, 4 and 5 (2ithout repetition) and divisible by 6 are

A

B

D

C

72

84

108

96

Q13. If x is rational and then the product

of all possible values of x is

A

B

D

C

4

3

1

2

Q14. Let two numbers have an arithmetic mean 9 and geometric mean 4, then these numbers are the roots of the quadratic equation

A

B

D

C

x2 + 18x - 16 = 0

x2 - 18x + 16 = 0

x2 - 18x - 16 = 0

x2 + 18x + 16 = 0

Q15. The range of a for which the equation x2 + ax - 4 = 0 has its smaller root in the interval (-1, 2) is

A

B

D

C

(-∞, -3)

(0, 3)

(-∞, -3) ∪ (0, ∞)

(0, ∞)

Q16. Let α and β be the roots of the equation x2 + ax + 1 = 0, a ≠ 0. Then

the equation whose roots are - is

A

B

D

C

x2 = 0

x2 + 2ax + 4 = 0

x2 - ax + 1 = 0

x2 - 2ax + 4 = 0

Q17. z ∈ C satisfies the condition |z| ≥ 3. Then the least value of

is

A

B

D

C

Q18. If z is a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be

A

B

D

C

Q19. If z and w are two non-zero complex numbers such that |zw| = 1

and arg(z) - arg(w) = then the value of is equal to

A

B

D

C

-5

5i

-5i

5

Q20. If z1, z2 and z3 are 3 distinct complex numbers such that

then the value of

is equal to

A

B

D

C

0

1

15

-1

Q21. Let ɑ and β be two numbers where ɑ < β. The geometric mean of these numbers exceeds the smaller number ɑ by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β, then the value of |β - ɑ| is

Integer Type

Q22. If , then the value of is

Integer Type

Q23. If the 6th term in the expansion of is 5600, then

the value of x is

Integer Type

Q24. The coefficient of x50 in (1 + x)41 (1 - x + x2)40 is

Integer Type

Q25. The number of ways in which 10 boys can be divided into 2 groups of 5, such that two tallest boys are in two different groups, is equal to

Integer Type

Q26. If the number of integral solutions (x, y, z) of the equation

xyz = 18 is t, then the value of is

Integer Type

Q27. The smallest possible natural number n, for which the equation x2 - nx + 2014 = 0 has integral roots, is

Integer Type

Q28. The value of a for which both the roots of the equation (1 - a2)x2 + 2ax - 1 = 0 lie between 0 and 1, will always be greater than

Integer Type

Q29. The value of is (where i is iota)

Integer Type

Q30. If |Z - 2| = 2 |Z - 1|, then the value of is (where Z is a

complex number and Re (Z) represents the real part of Z )

Integer Type

Algebra Assignment solutions - NTA Abhyas

Q1. The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + ..….. and 1 + 6 + 11 + 16 + ………. is

A

B

D

C

4000

4200

4020

4220

Solution :

Q2. If the 2nd , 5th and 9th terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is

A

B

D

C

1

Solution :

Q3. The first three terms of an arithmetic-geometric progression are 3, -1 and - 1. The next term of the progression is

A

B

D

C

2

-2

Solution :

Q4. Three numbers a, b and c are in geometric progression. If 4a, 5b and 4c are in arithmetic progression and a + b + c = 70, then the value of |c - a| is equal to

A

B

D

C

10

20

40

30

Solution :

Q5. The coefficient of the term independent of x in is

A

B

D

C 6

Solution :

Q6. If in the expansion of (1 + x)m (1 - x)n, the coefficients of x and x2 are 3 and -6 respectively, then the value of m is (m, n ∈ N)

A

B

D

C

6

9

24

12

Solution :

Q7. The first integral term in the expansion of , is the

A

B

D

C

2nd term

3rd term

5th term

4th term

Solution :

Q8. In the expansion of , the coefficient of the 8th and 19th

terms are independent of x is given by

A

B

D

C

Solution :

Q9. The number of ways in which 10 balls can be selected from 10 identical green balls, 10 identical blue balls and 9 identical red balls are

A

B

D

C

63

64

66

65

Solution :

- -

Q10. How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?

A

B

D

C

360

350

390

400

Solution :

Q11. The number of four- digit numbers formed by using the digits 0, 2, 4, 5 and which are not divisible by 5, is

A

B

D

C

10

8

4

6

Solution :

Q12. The number of five-digit numbers formed with the digits 0, 1, 2, 3, 4 and 5 (2ithout repetition) and divisible by 6 are

A

B

D

C

72

84

108

96

Solution :

Q13. If x is rational and then the product

of all possible values of x is

A

B

D

C

4

3

1

2

Solution :

Q14. Let two numbers have an arithmetic mean 9 and geometric mean 4, then these numbers are the roots of the quadratic equation

A

B

D

C

x2 + 18x - 16 = 0

x2 - 18x + 16 = 0

x2 - 18x - 16 = 0

x2 + 18x + 16 = 0

Solution :

Q15. The range of a for which the equation x2 + ax - 4 = 0 has its smaller root in the interval (-1, 2) is

A

B

D

C

(-∞, -3)

(0, 3)

(-∞, -3) ∪ (0, ∞)

(0, ∞)

Solution :

Q16. Let α and β be the roots of the equation x2 + ax + 1 = 0, a ≠ 0. Then

the equation whose roots are - is

A

B

D

C

x2 = 0

x2 + 2ax + 4 = 0

x2 - ax + 1 = 0

x2 - 2ax + 4 = 0

Solution :

Q17. z ∈ C satisfies the condition |z| ≥ 3. Then the least value of

is

A

B

D

C

Solution :

Q18. If z is a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be

A

B

D

C

Solution :

Q19. If z and w are two non-zero complex numbers such that |zw| = 1

and arg(z) - arg(w) = then the value of is equal to

A

B

D

C

-5

5i

-5i

5

Solution :

Q20. If z1, z2 and z3 are 3 distinct complex numbers such that

then the value of

is equal to

A

B

D

C

0

1

15

-1

Solution :

Q21. Let ɑ and β be two numbers where ɑ < β. The geometric mean of these numbers exceeds the smaller number ɑ by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β, then the value of |β - ɑ| is

Integer Type

Solution :

Q22. If , then the value of is

Integer Type

Solution :

Q23. If the 6th term in the expansion of is 5600, then

the value of x is

Integer Type

Solution :

Q24. The coefficient of x50 in (1 + x)41 (1 - x + x2)40 is

Integer Type

Solution :

Q25. The number of ways in which 10 boys can be divided into 2 groups of 5, such that two tallest boys are in two different groups, is equal to

Integer Type

Solution :

Q26. If the number of integral solutions (x, y, z) of the equation

xyz = 18 is t, then the value of is

Integer Type

Solution :

Q27. The smallest possible natural number n, for which the equation x2 - nx + 2014 = 0 has integral roots, is

Integer Type

Solution :

Q28. The value of a for which both the roots of the equation (1 - a2)x2 + 2ax - 1 = 0 lie between 0 and 1, will always be greater than

Integer Type

Solution :

Q29. The value of is (where i is iota)

Integer Type

Solution :

Q30. If |Z - 2| = 2 |Z - 1|, then the value of is (where Z is a

complex number and Re (Z) represents the real part of Z )

Integer Type

Solution :

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