BCA-Semester-I First Mid Odd Semester Theory Examination 2024-25 Mathematics-I PDF

**BCA-Semester-I** **FIRST MID ODD SEMESTER THEORY EXAMINATION, 2024-25** **Mathematics-I** **Time: 01 Hour MM: 10** **Note : Both the sections (A & B) are compulsory.** +-----------------+-----------------+-----------------+-----------------+ | **Q. No.** | **Questions** | **Marks**...

**BCA-Semester-I** **FIRST MID ODD SEMESTER THEORY EXAMINATION, 2024-25** **Mathematics-I** **Time: 01 Hour MM: 10** **Note : Both the sections (A & B) are compulsory.** +-----------------+-----------------+-----------------+-----------------+ | **Q. No.** | **Questions** | **Marks** | | +=================+=================+=================+=================+ | 1 | A | A square matrix | 01 | | | | will be called | | | | | symmetric | | | | | matrix if... | | +-----------------+-----------------+-----------------+-----------------+ | | | *(a) A=A^T^ (b) | | | | | A= - A^T^* | | +-----------------+-----------------+-----------------+-----------------+ | | | \(c) *AA^T^ | | | | | =I* (d) None | | | | | of these | | +-----------------+-----------------+-----------------+-----------------+ | | B | [*n*]{.math | 01 | | | |.inline}^th^ | | | | | derivative of | | | | | [*cos*(*ax*)]{. | | | | | math | | | | |.inline} is... | | +-----------------+-----------------+-----------------+-----------------+ | | | *(a)* [\$cos(ax | | | | | + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} *(b)* | | | | | [\$a\^{n}cos(ax | | | | | + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} | | +-----------------+-----------------+-----------------+-----------------+ | | | (c) | | | | | [\$a\^{n}sin(ax | | | | | + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} (d) | | | | | [\$sin(ax + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} | | +-----------------+-----------------+-----------------+-----------------+ | 2 | **Solve the | 04 | | | | following | | | | | system of | | | | | linear | | | | | equations:** | | | | | | | | | | [2*x* − 4*y* +  | | | | | 3*z* = 10]{.mat | | | | | h | | | | |.inline} **;** | | | | | [*x* + 5*y* + 2 | | | | | *z* = 12]{.math | | | | |.inline} **;** | | | | | [*x* − 2*y* + 4 | | | | | *z* = 14]{.math | | | | |.inline}**.** | | | | | | | | | | by using Cramer | | | | | rule. | | | +-----------------+-----------------+-----------------+-----------------+ | | **OR** | | | +-----------------+-----------------+-----------------+-----------------+ | | **Find the | | | | | inverse of the | | | | | matrix** [\$A = | | | | | \\ | | | | | \\begin{bmatrix | | | | | } | | | | | 0 & 1 & 2 \\\\ | | | | | 1 & 2 & 3 \\\\ | | | | | 3 & 1 & 1 \\\\ | | | | | \\end{bmatrix}\ | | | | | $]{.math | | | | |.inline}**.** | | | +-----------------+-----------------+-----------------+-----------------+ | 3 | **If** [\$A = | 04 | | | | \\ | | | | | \\begin{bmatrix | | | | | } | | | | | 1 & 1 & 0 \\\\ | | | | | 1 & 1 & 1 \\\\ | | | | | 0 & 1 & 0 \\\\ | | | | | \\end{bmatrix}\ | | | | | $]{.math | | | | |.inline} | | | | | **and** [\$B = | | | | | \\ | | | | | \\begin{bmatrix | | | | | } | | | | | 2 & - 1 & 1 | | | | | \\\\ 0 & - 1 & | | | | | 2 \\\\ - 1 & 1 | | | | | & 3 \\\\ | | | | | \\end{bmatrix}\ | | | | | $]{.math | | | | |.inline} **, | | | | | then | | | | | find**[ *B*^′^* | | | | | A*^′^]{.math | | | | |.inline}**.** | | | +-----------------+-----------------+-----------------+-----------------+ | | OR | | | +-----------------+-----------------+-----------------+-----------------+ | | **Find the nth | | | | | differential | | | | | coefficient of | | | | | the y** | | | | | [ = *log*(*ax*  | | | | | + *b*).]{.math | | | | |.inline} | | | +-----------------+-----------------+-----------------+-----------------+ **BCA-Semester-I** **FIRST MID ODD SEMESTER THEORY EXAMINATION, 2024-25** **Mathematics-I** **Time: 01 Hour MM: 10** **Note : Both the sections (A & B) are compulsory.** +-----------------+-----------------+-----------------+-----------------+ | **Q. No.** | **Questions** | **Marks** | | +=================+=================+=================+=================+ | 1 | A | A square matrix | 01 | | | | will be called | | | | | symmetric | | | | | matrix if... | | +-----------------+-----------------+-----------------+-----------------+ | | | *(a) A=A^T^ (b) | | | | | A= - A^T^* | | +-----------------+-----------------+-----------------+-----------------+ | | | \(c) *AA^T^ | | | | | =I* (d) None | | | | | of these | | +-----------------+-----------------+-----------------+-----------------+ | | B | [*n*]{.math | 01 | | | |.inline}^th^ | | | | | derivative of | | | | | [*cos*(*ax*)]{. | | | | | math | | | | |.inline} is... | | +-----------------+-----------------+-----------------+-----------------+ | | | *(a)* [\$cos(ax | | | | | + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} *(b)* | | | | | [\$a\^{n}cos(ax | | | | | + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} | | +-----------------+-----------------+-----------------+-----------------+ | | | (c) | | | | | [\$a\^{n}sin(ax | | | | | + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} (d) | | | | | [\$sin(ax + | | | | | \\frac{\\text{n | | | | | π}}{2})\$]{.mat | | | | | h | | | | |.inline} | | +-----------------+-----------------+-----------------+-----------------+ | 2 | **Solve the | 04 | | | | following | | | | | system of | | | | | linear | | | | | equations:** | | | | | | | | | | [2*x* − 4*y* +  | | | | | 3*z* = 10]{.mat | | | | | h | | | | |.inline} **;** | | | | | [*x* + 5*y* + 2 | | | | | *z* = 12]{.math | | | | |.inline} **;** | | | | | [*x* − 2*y* + 4 | | | | | *z* = 14]{.math | | | | |.inline}**.** | | | | | | | | | | by using Cramer | | | | | rule. | | | +-----------------+-----------------+-----------------+-----------------+ | | **OR** | | | +-----------------+-----------------+-----------------+-----------------+ | | **Find the | | | | | inverse of the | | | | | matrix** [\$A = | | | | | \\ | | | | | \\begin{bmatrix | | | | | } | | | | | 0 & 1 & 2 \\\\ | | | | | 1 & 2 & 3 \\\\ | | | | | 3 & 1 & 1 \\\\ | | | | | \\end{bmatrix}\ | | | | | $]{.math | | | | |.inline}**.** | | | +-----------------+-----------------+-----------------+-----------------+ | 3 | **If** [\$A = | 04 | | | | \\ | | | | | \\begin{bmatrix | | | | | } | | | | | 1 & 1 & 0 \\\\ | | | | | 1 & 1 & 1 \\\\ | | | | | 0 & 1 & 0 \\\\ | | | | | \\end{bmatrix}\ | | | | | $]{.math | | | | |.inline} | | | | | **and** [\$B = | | | | | \\ | | | | | \\begin{bmatrix | | | | | } | | | | | 2 & - 1 & 1 | | | | | \\\\ 0 & - 1 & | | | | | 2 \\\\ - 1 & 1 | | | | | & 3 \\\\ | | | | | \\end{bmatrix}\ | | | | | $]{.math | | | | |.inline} **, | | | | | then | | | | | find**[ *B*^′^* | | | | | A*^′^]{.math | | | | |.inline}**.** | | | +-----------------+-----------------+-----------------+-----------------+ | | OR | | | +-----------------+-----------------+-----------------+-----------------+ | | **Find the nth | | | | | differential | | | | | coefficient of | | | | | the y** | | | | | [ = *log*(*ax*  | | | | | + *b*).]{.math | | | | |.inline} | | | +-----------------+-----------------+-----------------+-----------------+