Algebra Assignment - NTA Abhyas
94
Algebra Assignment - NTA Abhyas
Transcript of Algebra Assignment - NTA Abhyas
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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