MCA Entrance Previous Year Question Bank

Given below are two statements:

one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A:

The system of equations

x + y + z = 4,

2x – y + 2z = 5,

x – 2y – z = –3 , has unique solution.

Reason R:

If A is 3 × 3 matrix and B is a 3 × 1 non-zero column matrix, then the equation AX = B has unique solution if A is non-singular.

In the light of the above statements, choose the most appropriate answer from the options given below:

If $(25{)}^{7.5}\times (5{)}^{2.5}÷(125{)}^{1.5}=(5{)}^x$ then $x=?$

Consider the system of linear equations as 2x + 2y + z = 1, 4x + ky + 2z = 2 and kx + 4y +z = 1 then choose the correct statement(/s) from below

(A) The system of equations has a unique solution if k ≠4 and k≠2

(B) The system of equations is inconsistent for every real number k

(C) The system of equations have infinite number of solution if k= 4

(D) The system of equations have infinite number of solution if k= 2

Choose the correct answer from the options given below

If $x=(2+\sqrt{3}{)}^{\frac{1}{8}}+(2+\sqrt{3}{)}^{-\frac{1}{8}}$ and $x^3-3x+k=0$, then the value of $k$ is:

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If she/he attempts all 60 questions and secures 130 marks, the number of questions she/he attempts wrongly, are?