MAKAUT Mathematics-IA (BS-M101) PYQ 2026 with Solutions

Q: What is the subject code for Mathematics-IA?

BS-M101 is the MAKAUT subject code for Mathematics-IA.

Q: Which exam is this Mathematics-IA question paper from?

The MAKAUT 2026 Mid Sem exam, semester 1. A student shared it, and it was checked before publishing.

Q: Which branches is this Mathematics-IA paper for?

It's a common paper for 2 B.Tech branches: Computer Science and Engineering and Information Technology. Every branch gets the same questions.

Q: Are there solutions for this paper?

Yes. Every question in the 2026 Mathematics-IA paper has a worked answer on this page, grouped like the paper. The first answer is free to read; sign in (it's free) to unlock the rest.

About this paper

The MAKAUT Mathematics-IA (BS-M101) 2026 Mid Sem previous year question paper, set in semester 1. Download the verified PDF or read it online, then check your answers against the worked solutions above.

Common paper for 2 branches

Every branch listed gets the same questions. Pick a branch to see its other papers.

Why solve Mathematics-IA PYQs?

Learn the exam patternSee how the MAKAUT Mid Sem paper is laid out: its groups, marks and choices.
Spot repeated questionsFind the topics in Mathematics-IA that come back year after year.
Practise against the clockAttempt a real paper in exam time to sharpen your pace.
Check your answersCompare your attempt with the worked solutions on this page.

Frequently asked questions

5 questions

What is the subject code for Mathematics-IA?

BS-M101 is the MAKAUT subject code for Mathematics-IA.

Which exam is this Mathematics-IA question paper from?

The MAKAUT 2026 Mid Sem exam, semester 1. A student shared it, and it was checked before publishing.

Which branches is this Mathematics-IA paper for?

It's a common paper for 2 B.Tech branches: Computer Science and Engineering and Information Technology. Every branch gets the same questions.

Where can I find more BS-M101 question papers?

On the Mathematics-IA subject page, which collects every year's papers along with notes and the syllabus.

Are there solutions for this paper?

Yes. Every question has a worked answer on this page, grouped like the paper. The first answer is free to read; sign in (it's free) to unlock the rest.

Solutions

Group AVery Short Answer Type Question · answer any 10 · 1 mark each

State whether the given system of equation have one, many or no solution: x−3y+5z+2=0x - 3y + 5z + 2 = 0x−3y+5z+2=0 3x−9y+15z−3=03x - 9y + 15z - 3 = 03x−9y+15z−3=0

Is Zero transformation a Linear Transformation? Give reason.

Is {(1, 1, 0), (0, 1, 1), (1, 0, 1)} basis of R3R^3R3 ? Justify.

Write the value of β(1/2,1/2)\beta(1/2, 1/2)β(1/2,1/2).

Is the function f(x)=log⁡(x+1)f(x) = \log (x + 1)f(x)=log(x+1) obeys L.M.V.T. in the interval [1,5][1,5][1,5] ?

Every square matrix A can be expressed as a sum of symmetric and skew symmetric matrix and it can be expressed as=

A non-null vector is linearly________.

What is eigen value of a square matrix? Explain with an example.

Define Beta and Gamma functions.

If f(x)=4x−x2f(x)=4x-x^2f(x)=4x−x2 satisfies Rolle's theorem in [0,4][0, 4][0,4] then c=c=c=?

Prove that the product of any matrix and its transpose is a symmetric matrix.

If T:V→WT:V \rightarrow WT:V→W is a Linear Transformation such that ker(T)={0}ker(T)=\{0\}ker(T)={0}. If dimension of VVV is rrr, then find dimension T(V)T(V)T(V).

Group BShort Answer Type Question · answer any 3 · 5 marks each

Check whether the vectors (2,6,−1,8)(2, 6, -1, 8)(2,6,−1,8), (0,10,4,3)(0, 10, 4, 3)(0,10,4,3), (0,0,−1,4)(0, 0, -1, 4)(0,0,−1,4) and (0,0,0,8)(0, 0, 0, 8)(0,0,0,8) are linearly independent in four-dimensional vector space R4R^4R4 or not. Is it a basis ? Justify.

Show that W={(x,y,z)∈R3:x+y+z=0,2x+y−z=0}W = \{(x,y,z) \in R^3: x + y + z = 0, 2x + y - z = 0\}W={(x,y,z)∈R3:x+y+z=0,2x+y−z=0} is a subspace of R3R^3R3. Find a basis of W. What is its dimension?

If possible diagonalise the matrix (10227)\begin{pmatrix} 10 & 2 \\ 2 & 7 \end{pmatrix}(102​27​).

Evaluate ∫0πsin⁡4xcos⁡5x dx\int_0^{\pi} \sin^4 x \cos^5 x \, dx∫0π​sin4xcos5xdx

Expand sin⁡x\sin xsinx in a Maclaurin's series with nth remainder.

Group CLong Answer Type Question · answer any 3 · 15 marks each

The line segment x+y=1,0≤y≤1x + y = 1, 0 \le y \le 1x+y=1,0≤y≤1 is revolved about y-axis to generate a cone. Find the lateral surface area of the cone.

Find the maxima and minima of the function f(x)=x5−5x4+5x3−1f(x)= x^5 - 5x^4 + 5x^3 - 1f(x)=x5−5x4+5x3−1

Find a Linear Transformation T:R3→R3T: R^3 \rightarrow R^3T:R3→R3 whose kernel is generated by (1,2,3,4)(1, 2, 3, 4)(1,2,3,4) and (0,1,1,1)(0, 1, 1, 1)(0,1,1,1).

Using Gauss-Jordan Elimination method solve the system of equation x+y+z=9x + y + z = 9x+y+z=9 2x−3y+4z=132x - 3y + 4z = 132x−3y+4z=13 3x+4y+5z=403x + 4y + 5z = 403x+4y+5z=40

Prove that ∫0∞1(1+x2)5dx=35π/256\int_0^\infty \frac{1}{(1+x^2)^5} dx = 35\pi/256∫0∞​(1+x2)51​dx=35π/256

Obtain the evolute of the parabola y2=4axy^2 = 4axy2=4ax.

Define Inner product space with an example. Use Gram-Schmidt process to convert the basis {(1,2,−2),(2,0,1),(1,1,0)}\{(1, 2, -2), (2, 0, 1), (1, 1, 0)\}{(1,2,−2),(2,0,1),(1,1,0)} of R3R^3R3 into an orthogonal basis and next to an orthonormal basis.

About this paper

Why solve Mathematics-IA PYQs?

Frequently asked questions

What is the subject code for Mathematics-IA?

Which exam is this Mathematics-IA question paper from?

Which branches is this Mathematics-IA paper for?

Where can I find more BS-M101 question papers?

Are there solutions for this paper?

Have notes or the answer key for Mathematics-IA?

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State whether the given system of equation have one, many or no solution: $x - 3y + 5z + 2 = 0$ $3x - 9y + 15z - 3 = 0$

Is {(1, 1, 0), (0, 1, 1), (1, 0, 1)} basis of $R^3$ ? Justify.

Write the value of $\beta(1/2, 1/2)$ .

Is the function $f(x) = \log (x + 1)$ obeys L.M.V.T. in the interval $[1,5]$ ?

If $f(x)=4x-x^2$ satisfies Rolle's theorem in $[0, 4]$ then $c=$ ?

If $T:V \rightarrow W$ is a Linear Transformation such that $ker(T)=\{0\}$ . If dimension of $V$ is $r$ , then find dimension $T(V)$ .

Check whether the vectors $(2, 6, -1, 8)$ , $(0, 10, 4, 3)$ , $(0, 0, -1, 4)$ and $(0, 0, 0, 8)$ are linearly independent in four-dimensional vector space $R^4$ or not. Is it a basis ? Justify.

Show that $W = \{(x,y,z) \in R^3: x + y + z = 0, 2x + y - z = 0\}$ is a subspace of $R^3$ . Find a basis of W. What is its dimension?

If possible diagonalise the matrix $\begin{pmatrix} 10 & 2 \\ 2 & 7 \end{pmatrix}$ .

Evaluate $\int_0^{\pi} \sin^4 x \cos^5 x \, dx$

Expand $\sin x$ in a Maclaurin's series with nth remainder.

The line segment $x + y = 1, 0 \le y \le 1$ is revolved about y-axis to generate a cone. Find the lateral surface area of the cone.

Find the maxima and minima of the function $f(x)= x^5 - 5x^4 + 5x^3 - 1$

Find a Linear Transformation $T: R^3 \rightarrow R^3$ whose kernel is generated by $(1, 2, 3, 4)$ and $(0, 1, 1, 1)$ .

Using Gauss-Jordan Elimination method solve the system of equation $x + y + z = 9$ $2x - 3y + 4z = 13$ $3x + 4y + 5z = 40$

Prove that $\int_0^\infty \frac{1}{(1+x^2)^5} dx = 35\pi/256$

Obtain the evolute of the parabola $y^2 = 4ax$ .

Define Inner product space with an example. Use Gram-Schmidt process to convert the basis $\{(1, 2, -2), (2, 0, 1), (1, 1, 0)\}$ of $R^3$ into an orthogonal basis and next to an orthonormal basis.