Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-4)

Theory of Equation and Inequations

Total Questions: 50

31. Solve the following equation? [UKPSC Lecturer (Mains) 2020]

Correct Answer: (b) 53/49
Solution:

32. Solve the following equation? [UKPSC Lecturer (Mains) 2020]

 

Correct Answer: (b) 𝓍 >16
Solution:

33. The number of values of 'a' for which the system of equations [UKPSC Lecturer (Mains) 2020]

(a+1) 𝓍+8y = 4a
a𝓍+ (a+3) y = 3a - 1 has infinitely many solutions is :

Correct Answer: (b) 1
Solution:

For infinitely many solutions of the given system of linear equations we must have

34. The inequality 7𝓍²+11>𝓍³ +17𝓍 is satisfied for all values of 𝓍 which satisfy the following: [UKPSC Lecturer (Mains) 2020]

Correct Answer: (c) -∞<𝓍<1
Solution:

35. The number of values of k for which the linear equations 4𝓍+ky+2z = 0; k𝓍+4y+z = 0; 2𝓍+2y+z = 0 possess a non-zero solution is: [Haryana PGT 2019]

Correct Answer: (a) 2
Solution:

36. If the difference between the roots of the equation 𝓍²+a𝓍+1 = 0 is less than √5, then the set of possible values of 'a' is: [Haryana PGT 2019]

Correct Answer: (a) (-3,3)
Solution:

37. Solve the following equation? [Haryana TGT 2020]

Correct Answer: (a) 2
Solution:

38. The pair of equation y = 0 and y = 5 has solutions: [Haryana TGT 2020]

Correct Answer: (c) no solution
Solution:

The pair of equation y = 0 and y = 5 has no solution because they are parallel pair of lines.

39. If -2 and 3 are the zeroes of the quadratic polynomial 𝓍²+(a+1) 𝓍+b, then: [Haryana TGT 2020]

Correct Answer: (b) a = -2; b = -6
Solution:

40. If one of the zeros of the polynomial 𝓍³+ a𝓍²+ b𝓍 + c is -1, then the product of other two zeros is equal to: [Haryana TGT 2019]

Correct Answer: (a) b-a+1
Solution: