algebra assignment - nta abhyas
TRANSCRIPT
![Page 1: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/1.jpg)
Algebra Assignment - NTA Abhyas
![Page 2: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/2.jpg)
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
![Page 3: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/3.jpg)
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
![Page 4: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/4.jpg)
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
![Page 5: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/5.jpg)
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
![Page 6: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/6.jpg)
Q5. The coefficient of the term independent of x in is
A
B
D
C 6
![Page 7: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/7.jpg)
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
![Page 8: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/8.jpg)
Q7. The first integral term in the expansion of , is the
A
B
D
C
2nd term
3rd term
5th term
4th term
![Page 9: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/9.jpg)
Q8. In the expansion of , the coefficient of the 8th and 19th
terms are independent of x is given by
A
B
D
C
![Page 10: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/10.jpg)
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
![Page 11: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/11.jpg)
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
![Page 12: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/12.jpg)
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
![Page 13: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/13.jpg)
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
![Page 14: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/14.jpg)
Q13. If x is rational and then the product
of all possible values of x is
A
B
D
C
4
3
1
2
![Page 15: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/15.jpg)
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
![Page 16: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/16.jpg)
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, ∞)
![Page 17: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/17.jpg)
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
![Page 18: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/18.jpg)
Q17. z ∈ C satisfies the condition |z| ≥ 3. Then the least value of
is
A
B
D
C
![Page 19: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/19.jpg)
Q18. If z is a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be
A
B
D
C
![Page 20: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/20.jpg)
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
![Page 21: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/21.jpg)
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
![Page 22: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/22.jpg)
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
![Page 23: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/23.jpg)
Q22. If , then the value of is
Integer Type
![Page 24: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/24.jpg)
Q23. If the 6th term in the expansion of is 5600, then
the value of x is
Integer Type
![Page 25: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/25.jpg)
Q24. The coefficient of x50 in (1 + x)41 (1 - x + x2)40 is
Integer Type
![Page 26: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/26.jpg)
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
![Page 27: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/27.jpg)
Q26. If the number of integral solutions (x, y, z) of the equation
xyz = 18 is t, then the value of is
Integer Type
![Page 28: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/28.jpg)
Q27. The smallest possible natural number n, for which the equation x2 - nx + 2014 = 0 has integral roots, is
Integer Type
![Page 29: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/29.jpg)
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
![Page 30: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/30.jpg)
Q29. The value of is (where i is iota)
Integer Type
![Page 31: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/31.jpg)
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
![Page 32: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/32.jpg)
Algebra Assignment solutions - NTA Abhyas
![Page 33: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/33.jpg)
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
![Page 34: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/34.jpg)
Solution :
![Page 35: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/35.jpg)
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
![Page 36: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/36.jpg)
Solution :
![Page 37: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/37.jpg)
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
![Page 38: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/38.jpg)
Solution :
![Page 39: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/39.jpg)
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
![Page 40: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/40.jpg)
Solution :
![Page 41: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/41.jpg)
Q5. The coefficient of the term independent of x in is
A
B
D
C 6
![Page 42: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/42.jpg)
Solution :
![Page 43: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/43.jpg)
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
![Page 44: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/44.jpg)
Solution :
![Page 45: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/45.jpg)
Q7. The first integral term in the expansion of , is the
A
B
D
C
2nd term
3rd term
5th term
4th term
![Page 46: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/46.jpg)
Solution :
![Page 47: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/47.jpg)
Q8. In the expansion of , the coefficient of the 8th and 19th
terms are independent of x is given by
A
B
D
C
![Page 48: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/48.jpg)
Solution :
![Page 49: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/49.jpg)
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
![Page 50: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/50.jpg)
Solution :
- -
![Page 51: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/51.jpg)
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
![Page 52: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/52.jpg)
Solution :
![Page 53: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/53.jpg)
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
![Page 54: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/54.jpg)
Solution :
![Page 55: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/55.jpg)
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
![Page 56: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/56.jpg)
Solution :
![Page 57: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/57.jpg)
Q13. If x is rational and then the product
of all possible values of x is
A
B
D
C
4
3
1
2
![Page 58: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/58.jpg)
Solution :
![Page 59: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/59.jpg)
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
![Page 60: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/60.jpg)
Solution :
![Page 61: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/61.jpg)
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, ∞)
![Page 62: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/62.jpg)
Solution :
![Page 63: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/63.jpg)
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
![Page 64: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/64.jpg)
Solution :
![Page 65: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/65.jpg)
Q17. z ∈ C satisfies the condition |z| ≥ 3. Then the least value of
is
A
B
D
C
![Page 66: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/66.jpg)
Solution :
![Page 67: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/67.jpg)
Q18. If z is a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be
A
B
D
C
![Page 68: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/68.jpg)
Solution :
![Page 69: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/69.jpg)
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
![Page 70: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/70.jpg)
Solution :
![Page 71: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/71.jpg)
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
![Page 72: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/72.jpg)
Solution :
![Page 73: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/73.jpg)
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
![Page 74: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/74.jpg)
Solution :
![Page 75: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/75.jpg)
Q22. If , then the value of is
Integer Type
![Page 76: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/76.jpg)
Solution :
![Page 77: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/77.jpg)
Q23. If the 6th term in the expansion of is 5600, then
the value of x is
Integer Type
![Page 78: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/78.jpg)
Solution :
![Page 79: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/79.jpg)
Q24. The coefficient of x50 in (1 + x)41 (1 - x + x2)40 is
Integer Type
![Page 80: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/80.jpg)
Solution :
![Page 81: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/81.jpg)
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
![Page 82: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/82.jpg)
Solution :
![Page 83: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/83.jpg)
Q26. If the number of integral solutions (x, y, z) of the equation
xyz = 18 is t, then the value of is
Integer Type
![Page 84: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/84.jpg)
Solution :
![Page 85: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/85.jpg)
Q27. The smallest possible natural number n, for which the equation x2 - nx + 2014 = 0 has integral roots, is
Integer Type
![Page 86: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/86.jpg)
Solution :
![Page 87: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/87.jpg)
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
![Page 88: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/88.jpg)
Solution :
![Page 89: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/89.jpg)
Q29. The value of is (where i is iota)
Integer Type
![Page 90: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/90.jpg)
Solution :
![Page 91: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/91.jpg)
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
![Page 92: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/92.jpg)
Solution :
![Page 93: Algebra Assignment - NTA Abhyas](https://reader033.vdocument.in/reader033/viewer/2022041413/6251e322057a3a61e668ea86/html5/thumbnails/93.jpg)
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