Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-3)

Theory of Equation and Inequations

Total Questions: 50

21. If Ξ± and Ξ² are the roots of the equation 3𝓍²+4𝓍-3 = 0, then the values of Ξ± + Ξ² and Ξ±Ξ² are respectively: [OAVS TGT 2018]

Correct Answer: (b)
Solution:

22. To add or subtract a positive number from both sides of any inequality without any change in the equality sign is called the: [OAVS TGT 2018]

Correct Answer: (a) Additive Property of Inequality
Solution:

We know that if we add or subtract a positive number from both sides of any inequality without any change in the equality sign is called the additive property of inequality.

23. For a, b ∈ R; a β‰  0, bβ‰  0, a > b imply: [OAVS TGT 2018]

Correct Answer: (d)
Solution:

In inequality
If a > b & a β‰  0, b β‰  0
Then (1/a) < (1/b)

24. If in a general quadratic equation, b = 0, then it is called a: [OAVS TGT 2018]

Correct Answer: (c) Pure Quadratic equation
Solution:

25. When |𝓍+y| = |𝓍| + |y|, 𝓍,y ∈ R, if: [OAVS TGT 2018]

Correct Answer: (b) 𝓍yβ‰₯ 0
Solution:

If 𝓍y β‰₯ 0, then
|𝓍+y| = |𝓍| + |y|, 𝓍,y ∈ R

26. If a specific 𝓍 = 2 is substituted variable 𝓍 in the polynomial such that the value is 0, then 𝓍 = 2 is said to be : [OAVS TGT 2018]

Correct Answer: (b) Zero of the Polynomial
Solution:

If any 𝓍 = a satisfy any equation, then, 𝓍 = a will be zero of eqn.
Then, 𝓍 = 2 will be zero of the polynomial.

27. The expected value or ________ of a random variable is the centre of its distribution. [OAVS TGT 2018]

Correct Answer: (a) Mean
Solution:

We know that the expected value or mean of a random variable is the centre of its distribution.

28. If two variables, 𝓍 and y, are involved in a linear equation, then the equation is:

Correct Answer: (c) a𝓍 + by = c
Solution:

We know that linear equation of two variable will be of the form a𝓍 + by = c

29. Solve the following equation? [OAVS TGT 2017]

Correct Answer: (d) 4,-4
Solution:

30. The degree of the polynomial obtained by the proΔ‘uct (𝓍² +4𝓍 + 3) (2𝓍² -9𝓍 +7) is: [OAVS TGT 2017]

Correct Answer: (b) 4
Solution:

We know that the degree of the polynomial is highest posiΘ›ive integer power of variable.
Hence, degree of (𝓍²+4𝓍+3) (2𝓍²-9𝓍+7) is 4.