Explore topic-wise MCQs in Mathematics.

This section includes 15 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, x4 + 4x3 + 6ax2 + 6bx + c is divisible by x3 + 3x2 + 9x + 3. Then, what is the value of a + b + c?

A. 4
B. 6
C. 7
D. 10
Answer» D. 10
Discussion
2.

Let S denotes the set of all real values of the parameter a for which every solution of the inequality log1/2 x2 log1/2 (x + 2) is the solution of the inequality 49x2 4a4 0. What is the value of S?

A. (- , - 7) ( 7, )
B. (- , - 7] [ 7, )
C. (- 7, 7)
D. [- 7, 7]
Answer» C. (- 7, 7)
Discussion
3.

A real number a is called a good number if the inequality (2x2 2x 3) / (x2 + x + 1) a is satisfied for all real x. What is the set of all real numbers?

A. (- , 10/3]
B. (10/3, )
C. [10/3, )
D. [-10/3, )
Answer» D. [-10/3, )
Discussion
4.

For what value of , 1 lies between the roots of the quadratic equation 3x2 3sin x 2cos2 = 0?

A. 2n + /6 < < 2n + 5 /6
B. 2n + /3 < < 2n + 5 /3
C. 2n + /6 2n + 5 /6
D. 2n + /3 2n + 5 /3
Answer» B. 2n + /3 < < 2n + 5 /3
Discussion
5.

What is the set of values of p for which the roots of the equation 3x2 + 2x + p(p 1) = 0 are of opposite sign?

A. (- , 0)
B. (0, 1)
C. (1, )
D. (0, )
Answer» C. (1, )
Discussion
6.

Which one is the complete set of values of x satisfying log x2 (x + 1) > 0?

A. (1, )
B. (-1, 0) {0}
C. (-1, 1) {0}
D. (1, 0) (1, )
Answer» E.
Discussion
7.

Which is the largest negative integer which satisfies (x2 1)/(x 2)(x 3)?

A. -4
B. -3
C. -1
D. -2
Answer» E.
Discussion
8.

What is the number of solution(s) of the equation | x 2| + x( x 4) + 2 = 0?

A. 2
B. 4
C. No solution
D. Infinitely many solutions
Answer» B. 4
Discussion
9.

What will be the sum of the real roots of the equation x2 + 5|x| + 6 = 0?

A. Equal to 5
B. Equal to 10
C. Equal to -5
D. Does not exist
Answer» E.
Discussion
10.

What will be the value of f(x) if, 2A, A + B, C are integers and f(x) = Ax2 + Bx + C = 0?

A. Natural Number
B. Unpredictable
C. Integer
D. Complex Number
Answer» D. Complex Number
Discussion
11.

What is the value of x if (a + 2b 3c)x2 + (b + 2c 3a)x + (c + 2a 3b) = 0 where a, b, c are in A.P?

A. 1/2
B. 1/4
C. 2/3
D. 3/4
Answer» C. 2/3
Discussion
12.

If x1, x2 are real roots of ax2 x + a = 0. Then, find the set of all values of parameter a for which |x1 x1| < 1?

A. (1 5a)/ a<sup>2</sup> &lt; 0
B. (1 5a)/ a<sup>2</sup> = 0
C. (1 5a)/ a<sup>2</sup> &gt; 0
D. (1 5a)/ a &lt; 0
Answer» B. (1 5a)/ a<sup>2</sup> = 0
Discussion
13.

If, (a + 1)x2 + 2(a+1)x + (a 2) = 0, then, for what parameter of a the given equation have imaginary roots?

A. (- , -1)
B. (-1, )
C. (-1, 1)
D. (- , )
Answer» B. (-1, )
Discussion
14.

If, (a + 1)x2 + 2(a+1)x + (a 2) = 0, then, for what parameter of a the given equation have equal roots?

A. (- , -1)
B. [-1, )
C. (0, 1)
D. Not possible
Answer» E.
Discussion
15.

If, (a + 1)x2 + 2(a+1)x + (a 2) = 0, then, for what parameter of a the given equation have real and distinct roots?

A. (- , )
B. (-1, )
C. [-1, )
D. (-1, 1)
Answer» C. [-1, )
Discussion