Explore topic-wise MCQs in Mathematics.

This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

What is the relation between the two determinants f(x) = ( begin{vmatrix} a^2 & ab & ac ab & -b^2 & bc ac & bc & -c^2 end {vmatrix} ) and g(x) = ( begin{vmatrix}0 & c & b c & 0 & a b & a & 0 end {vmatrix} )?

A. f(x) = g(x)
B. f(x) = (g(x))<sup>2</sup>
C. g(x) = 2f(x)
D. g(x) = (f(x))<sup>2</sup>
Answer» C. g(x) = 2f(x)
Discussion
2.

What will be the value of x if ( begin{vmatrix}2-x & 2 & 3 2 & 5-x & 6 3 & 4 & 10-x end {vmatrix} ) = 0?

A. 8 37
B. -8 37
C. 8 35
D. -8 35
Answer» B. -8 37
Discussion
3.

Which one is correct, the following system of linear equations 2x 3y + 4z = 7, 3x 4y + 5z = 8, 4x 5y + 6z = 9 has?

A. No solutions
B. Infinitely many solutions
C. Unique Solution
D. Can t be predicted
Answer» C. Unique Solution
Discussion
4.

The co-ordinates of the vertices of a triangle are [m(m + 1), (m + 1)], [(m + 1)(m + 2), (m + 2)] and [(m + 2)(m + 3), (m + 3)]. Then which one among the following is correct?

A. The area of the triangle is dependent on m
B. The area of the triangle is independent on m
C. Answer cannot be predicted
D. Data inadequate
Answer» C. Answer cannot be predicted
Discussion
5.

Which one among the following is correct if x, y, z are eliminated from, ( ( frac{bx}{y+z} ) = a, ( frac{cy}{z+x} ) = b, ( frac{az}{x+y} ) = c)?

A. a<sup>2</sup>b + b<sup>2</sup>c + c<sup>2</sup>a + abc = 0
B. a<sup>2</sup>b b<sup>2</sup>c + c<sup>2</sup>a + abc = 0
C. a<sup>2</sup>b + b<sup>2</sup>c + c<sup>2</sup>a + 2abc = 0
D. a<sup>2</sup>b b<sup>2</sup>c c<sup>2</sup>a abc = 0
Answer» B. a<sup>2</sup>b b<sup>2</sup>c + c<sup>2</sup>a + abc = 0
Discussion
6.

Let, and be real. Find the set of all values of for which the system of equation x + sin *y + cos *z = 0, x + cos * y + sin * z = 0 , -x + sin *y cos * z = 0 has a non-trivial solution. For = 1 what are all values of ?

A. 2 = 2n /2 + /2
B. 2 = 2n /2 + /4
C. 2 = 2n /4 + /4
D. 2 = 2n /4 + /2
Answer» D. 2 = 2n /4 + /2
Discussion
7.

If, Si = ai + bi + ci then what is the value of ( begin{vmatrix}S0 & S1 & S2 S1 & S2 & S3 S2 & S3 & S4 end {vmatrix} )?

A. (a + b)<sup>2</sup>(b c)<sup>2</sup>(c a)<sup>2</sup>
B. (a b)<sup>2</sup>(b c)<sup>2</sup>(c + a)<sup>2</sup>
C. (a b)<sup>2</sup>(b c)<sup>2</sup>(c a)<sup>2</sup>
D. (a b)<sup>2</sup>(b + c)<sup>2</sup>(c a)<sup>2</sup>
Answer» D. (a b)<sup>2</sup>(b + c)<sup>2</sup>(c a)<sup>2</sup>
Discussion
8.

What will be the value of f(x) = ( begin{vmatrix}p & 2 i & i + 1 2 + i & q & 3 + i 1 i & 3 i & r end {vmatrix} )?

A. Real
B. Imaginary
C. Zero
D. Can t be predicted
Answer» B. Imaginary
Discussion
9.

If f(x) = ( begin{vmatrix}1 & a & bc 1 & b & ca 1 & c & ab end {vmatrix} ) = ( begin{vmatrix}1 & a & a^2 1 & b & b^2 1 & c & c^2 end {vmatrix} ) then which one among the following is correct?

A. (a b)(b c)(c a)
B. a, b, c are in G.P
C. b, c, a are in G.P
D. a, c, b are in G.P
Answer» C. b, c, a are in G.P
Discussion