Explore topic-wise MCQs in Mathematics.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

If α, β are the roots of the equation ax2 + bx + c = 0, then the equation whose roots are \(\alpha + \dfrac{1}{\beta }\) and \(\beta + \dfrac{1}{\alpha }\) is:

A. ac x2 + (a + c) bx + (a + c)2 = 0
B. ab x2 + (a + c) bx + (a + c)2 = 0
C. ac x2 + (a + b) cx + (a + c)2 = 0
D. None of these
Answer» B. ab x2 + (a + c) bx + (a + c)2 = 0
Discussion
2.

If α and β are the roots of the equation x2 - px + q = 0, then \(\sum {{(\alpha ^2 + \beta^2)}} \) is

A. p2 + 2q
B. p + 2q
C. p2 - 2q
D. p - 2q
Answer» D. p - 2q
Discussion
3.

If f(x) = 3x2 - 5x + p and f(0) and f(1) are opposite in sign, then which of the following is correct?

A. -2 < p < 0
B. -2 < p < 2
C. 0 < p < 1
D. 3 < p < 5
Answer» D. 3 < p < 5
Discussion
4.

If one root of 5x2 + 26x + k = 0 is reciprocal of the other, then what is the value of k?

A. 2
B. 3
C. 5
D. 8
Answer» D. 8
Discussion
5.

If α and β are the roots of the equation 4x2 + 2x - 1 = 0, then which one of the following is correct?

A. β = -2α2 - 2α
B. β = 4α2 - 3α
C. β = α2 - 3α
D. β = -2α2 + 2α
Answer» B. β = 4α2 - 3α
Discussion
6.

If cot α and cot β are the roots of the equation x2 + bx + c = 0 with b ≠ 0, then the value of cot (α + β) is

A. \(\frac{{{\rm{c}} - 1}}{{\rm{b}}}\)
B. \(\frac{{1 - {\rm{c}}}}{{\rm{b}}}\)
C. \(\frac{{\rm{b}}}{{{\rm{c}} - 1}}\)
D. \(\frac{{\rm{b}}}{{1 - {\rm{c}}}}\)
Answer» C. \(\frac{{\rm{b}}}{{{\rm{c}} - 1}}\)
Discussion
7.

If k is one of the roots of the equation x(x + 1) + 1 = 0, then what is its other root?

A. 1
B. -k
C. k2
D. -k2
Answer» D. -k2
Discussion
8.

If cot α and cot β are the roots of the equation x2 - 3x + 2 = 0, then what is cot (α + β) equal to ?

A. 1 / 2
B. 1 / 3
C. 2
D. 3
Answer» C. 2
Discussion