GATE 2021 Mathematics (MA) Question Paper with Solutions is now available for downloading. GATE 2021 MA was organized by IIT Bombay on 13th February, 2021 in morning session. The question paper was a combination of 10 questions from the General Aptitude section and 55 questions from the core Mathematics section. Real Analysis & Calculus and ODE & PDE section holds most of the weightage in GATE 2021 MA.
GATE 2021 Mathematics (MA) Question Paper with Solutions
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The ratio of boys to girls in a class is 7 to 3. Among the options below, an acceptable value for the total number of students in the class is:
A polygon is convex if, for every pair of points inside the polygon, the line segment joining them lies completely inside or on the polygon. Which one of the following is NOT a convex polygon?
Consider the following sentences:
(i) Everybody in the class is prepared for the exam.
(ii) Babu invited Danish to his home because he enjoys playing chess.
Which of the following is the CORRECT observation about the above two sentences?
A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like \hspace{2cm}.
_____ is to surgery as writer is to _____ .
Which one of the following options maintains a similar logical relation in the above sentence?
We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is:
Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost.
The formula for Profit Percentage is:
Profit % = \frac{Selling Price - Cost}{Cost} \times 100
The discount on item Q, as a percentage of its marked price, is:
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is:
Given below are two statements 1 and 2, and two conclusions I ans II.
Statement 1: All bacteria are microorganisms.
Statement 2: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.
Based on the given statements and conclusions, which option is logically correct?
Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality. Which one of the following statements summarizes the passage?
Let A be a \(3 \times 4\) matrix and B be a \(4 \times 3\) matrix with real entries such that \( AB \) is non-singular. Consider the following statements:
P: Nullity of A is 0.
Q: \( BA \) is a non-singular matrix.
Then:
Let \( f(z) = u(x, y) + i v(x, y) \) for \( z = x + i y \in \mathbb{C} \), where \( x \) and \( y \) are real numbers, be a non-constant analytic function on the complex plane \( \mathbb{C} \). Let \( u_x, v_x \) and \( u_y, v_y \) denote the first order partial derivatives of \( u(x, y) = Re(f(z)) \) and \( v(x, y) = Im(f(z)) \) with respect to real variables \( x \) and \( y \), respectively. Consider the following two functions defined on \( \mathbb{C} \):
\[ g_1(z) = u_x(x, y) - i u_y(x, y) \quad for \quad z = x + i y \in \mathbb{C}, \quad g_2(z) = v_x(x, y) + i v_y(x, y) \quad for \quad z = x + i y \in \mathbb{C}. \]
Then,
Let \( T(z) = \frac{az + b}{cz + d}, ad - bc \neq 0 \), be the Möbius transformation which maps the points \( z_1 = 0, z_2 = -i, z_3 = \infty \) in the z-plane onto the points \( w_1 = 10, w_2 = 5 - 5i, w_3 = 5 + 5i \) in the w-plane, respectively. Then the image of the set \( S = \{ z \in \mathbb{C} : Re(z) < 0 \} \) under the map \( w = T(z) \) is
Let \( R \) be the row reduced echelon form of a \( 4 \times 4 \) real matrix \( A \) and let the third column of \( R \) be \[ \begin{bmatrix} 0
1
0
0 \end{bmatrix}. \]
Consider the following statements: \[ P: \quad If \quad \begin{bmatrix} \alpha
\beta
\gamma \end{bmatrix} is a solution of A x = 0, then \gamma = 0. \] \[ Q: \quad For all b \in \mathbb{R}^4, \quad rank[A | b] = rank[R | b]. \]
Then:
The eigenvalues of the boundary value problem \[ \frac{d^2y}{dx^2} + \lambda y = 0, \quad x \in (0, \pi), \quad \lambda > 0, \] \[ y(0) = 0, \quad y(\pi) - \frac{dy}{dx}(\pi) = 0 \]
are given by:
The family of surfaces given by \[ u = xy + f(x^2 - y^2), \quad where \, f : \mathbb{R} \to \mathbb{R} \, is a differentiable function, satisfies: \]
The function \( u(x, t) \) satisfies the initial value problem \[ \frac{\partial^2 u}{\partial t^2} = \frac{\partial^2 u}{\partial x^2}, \, x \in \mathbb{R}, \, t > 0, \] \[ u(x, 0) = 0, \, \frac{\partial u}{\partial t} (x, 0) = 4xe^{-x^2}. \]
Then \( u(5, 5) \) is:
Consider the fixed-point iteration \[ x_{n+1} = \varphi(x_n), \quad n \geq 0, \]
with \[ \varphi(x) = 3 + (x - 3)^3, \quad x \in (2.5, 3.5), \]
and the initial approximation \( x_0 = 3.25 \).
Then, the order of convergence of the fixed-point iteration method is
Let \( \{ e_n : n = 1, 2, 3, \dots \} \) be an orthonormal basis of a complex Hilbert space \( H \). Consider the following statements:
P: There exists a bounded linear functional \( f: H \to \mathbb{C} \) such that \( f(e_n) = \frac{1}{n} \) for \( n = 1, 2, 3, \dots \)
Q: There exists a bounded linear functional \( g: H \to \mathbb{C} \) such that \( g(e_n) = \frac{1}{\sqrt{n}} \) for \( n = 1, 2, 3, \dots \)
Let \( f: \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \to \mathbb{R} \) be given by \( f(x) = \frac{\pi}{2} + x - \tan^{-1}x \). Consider the following statements:
P: \( |f(x) - f(y)| < |x - y| for all x, y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \).
Q: \( f \) has a fixed point.
Then:
Consider the following statements:
P: \( d_1(x,y) = \left| \log \left( \frac{x}{y} \right) \right| \) is a metric on \( (0, 1) \).
Q: \( d_2(x, y) = \begin{cases} |x| + |y|, & if x \neq y
0, & if x = y \end{cases} \) is a metric on \( (0, 1) \).
Then:
Let \( f: \mathbb{R}^3 \to \mathbb{R} \) be a twice continuously differentiable scalar field such that \( div(\nabla f) = 6 \). Let \( S \) be the surface \( x^2 + y^2 + z^2 = 1 \) and \( \hat{n} \) be the unit outward normal to \( S \). Then the value of \[ \iint_S (\nabla f \cdot \hat{n}) \, dS \]
is
Consider the following statements:
P: Every compact metrizable topological space is separable.
Q: Every Hausdorff topology on a finite set is metrizable.
Then,
Consider the following topologies on the set \( \mathbb{R} \) of all real numbers:
\( T_1 = \{ U \subset \mathbb{R} : 0 \notin U or U = \mathbb{R} \} \),
\( T_2 = \{ U \subset \mathbb{R} : 0 \in U or U = \emptyset \} \),
\( T_3 = T_1 \cap T_2 \).
Then the closure of the set \( \{1\} \) in \( (\mathbb{R}, T_3) \) is
Let \( f: \mathbb{R}^2 \to \mathbb{R} \) be differentiable. Let \( D_u f(0,0) \) and \( D_v f(0,0) \) be the directional derivatives of \( f \) at \( (0,0) \) in the directions of the unit vectors \( u = \left( \frac{1}{\sqrt{5}}, \frac{2}{\sqrt{5}} \right) \) and \( v = \left( \frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}} \right) \), respectively. If \( D_u f(0,0) = \sqrt{5} \) and \( D_v f(0,0) = \sqrt{5} \), then \[ \frac{\partial f}{\partial x} (0,0) + \frac{\partial f}{\partial y} (0,0) = \_\_\_\_\_. \]
Let \( \Gamma \) denote the boundary of the square region \( R \) with vertices \( (0,0), (2,0), (2,2), (0,2) \), oriented in the counter-clockwise direction. Then \[ \int_{\Gamma} (1 - y^2) dx + x \, dy = \_\_\_\_\_. \]
The number of 5-Sylow subgroups in the symmetric group \( S_5 \) of degree 5 is \( \_\_\_\_\_ \).
Let \( I \) be the ideal generated by \( x^2 + x + 1 \) in the polynomial ring \( R = \mathbb{Z}_3[x] \), where \( \mathbb{Z}_3 \) denotes the ring of integers modulo 3. Then the number of units in the quotient ring \( R/I \) is \( \_\_\_\_\_ \).
Let \( T: \mathbb{R}^3 \to \mathbb{R}^3 \) be a linear transformation such that \[ T \left( \begin{pmatrix} 1
1
1 \end{pmatrix} \right) = \begin{pmatrix} 1
-1
1 \end{pmatrix}, \quad T^2 \left( \begin{pmatrix} 1
1
1 \end{pmatrix} \right) = \begin{pmatrix} 1
1
1 \end{pmatrix}, \quad T^2 \left( \begin{pmatrix} 1
1
2 \end{pmatrix} \right) = \begin{pmatrix} 1
1
1 \end{pmatrix}. \]
Then the rank of \( T \) is ________ .
Let \( y(x) \) be the solution of the following initial value problem \[ x^2 \frac{d^2y}{dx^2} - 4x \frac{dy}{dx} + 6y = 0, \quad x > 0, \] \[ y(2) = 0, \quad \frac{dy}{dx}(2) = 4. \]
Then \( y(4) = \_\_\_\_\_\_ \).
Let \( f(x) = x^4 + 2x^3 - 11x^2 - 12x + 36 \) for \( x \in \mathbb{R}. \)
The order of convergence of the Newton-Raphson method \[ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}, \quad n \geq 0, \]
with \( x_0 = 2.1 \), for finding the root \( \alpha = 2 \) of the equation \( f(x) = 0 \) is ______ .
If the polynomial \[ p(x) = \alpha + \beta (x+2) + \gamma (x+2)(x+1) + \delta (x+2)(x+1)x \]
interpolates the data \[ \begin{array}{|c|c|} \hline x & f(x)
\hline -2 & 2
-1 & -1
0 & 8
1 & 5
2 & -34
\hline \end{array} \]
then \( \alpha + \beta + \gamma + \delta = \_\_\_\_\_\_ \).
Consider the Linear Programming Problem \( P \): \[ Maximize 2x_1 + 3x_2 \]
subject to \[ 2x_1 + x_2 \leq 6, \] \[ -x_1 + x_2 \leq 1, \] \[ x_1 + x_2 \leq 3, \] \[ x_1 \geq 0 \text{ and x_2 \geq 0. \]
\text{Then the optimal value of the dual of \( P \) is equal to ______.
Consider the Linear Programming Problem \( P \): \[ Minimize 2x_1 - 5x_2 \]
subject to \[ 2x_1 + 3x_2 + s_1 = 12, \] \[ -x_1 + x_2 + s_2 = 1, \] \[ -x_1 + 2x_2 + s_3 = 3, \] \[ x_1 \geq 0, x_2 \geq 0, s_1 \geq 0, s_2 \geq 0, \text{ and s_3 \geq 0. \]
If \[ \left[ \begin{array{c} x_1
s_1
s_2
s_3 \end{array} \right] \]
\text{is a basic feasible solution of \( P \), then \[ x_1 + s_1 + s_2 + s_3 = \_\_\_\_\_\_. \]
Let \( H \) be a complex Hilbert space. Let \( u, v \in H \) be such that \( \langle u, v \rangle = 2 \). Then \[ \frac{1}{2\pi} \int_0^{2\pi} \| u + e^{it} v \|^2 e^{it} dt = \_\_\_\_\_\_. \]
Let \( \mathbb{Z} \) denote the ring of integers. Consider the subring \[ R = \{ a + b\sqrt{-17} : a, b \in \mathbb{Z} \} \]
of the field \( \mathbb{C} \) of complex numbers. Consider the following statements:
P: \( 2 + \sqrt{-17} \) is an irreducible element.
Q: \( 2 + \sqrt{-17} \) is a prime element.
Then:
Consider the second-order partial differential equation (PDE) \[ \frac{\partial^2 u}{\partial x^2} + 4 \frac{\partial^2 u}{\partial x \partial y} + (x^2 + 4y^2) \frac{\partial^2 u}{\partial y^2} = \sin(x + y) \]
Consider the following statements:
P: The PDE is parabolic on the ellipse \( \frac{x^2}{4} + y^2 = 1 \).
Q: The PDE is hyperbolic inside the ellipse \( \frac{x^2}{4} + y^2 = 1 \).
Then:
If \( u(x, y) \) is the solution of the Cauchy problem \[ x \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} = 1, \quad u(x, 0) = -x^2, \quad x > 0, \]
then \( u(2, 1) \) is equal to
Let \( y(t) \) be the solution of the initial value problem \[ \frac{d^2 y}{dt^2} + a \frac{dy}{dt} + b y = f(t), \quad a > 0, \quad b > 0, \quad a \neq b, \quad a^2 - 4b = 0, \]
with initial conditions \( y(0) = 0 \), \( \frac{dy}{dt}(0) = 0 \), obtained by the method of Laplace transform. Then
The critical point of the differential equation \[ \frac{d^2y}{dt^2} + 2 \alpha \frac{dy}{dt} + \beta^2 y = 0, \quad \alpha > 0, \, \beta > 0, \]
is a
The initial value problem \[ \frac{dy}{dt} = f(t, y), \quad t > 0, \quad y(0) = 1, \]
where \( f(t, y) = -10 y \), is solved by the following Euler method: \[ y_{n+1} = y_n + h f(t_n, y_n), \quad n \geq 0, \quad with step-size \, h. \]
Then \( y_n \to 0 \) as \( n \to \infty \), provided
Consider the Linear Programming Problem P: \[ Maximize c_1x_1 + c_2x_2 \]
subject to: \[ a_{11x_1 + a_{12}x_2 \leq b_1, \] \[ a_{21}x_1 + a_{22}x_2 \leq b_2, \] \[ a_{31}x_1 + a_{32}x_2 \leq b_3, \] \[ x_1 \geq 0, \, x_2 \geq 0, \]
where a_{ij, b_i, c_j \text{ are real numbers (i = 1, 2, 3; j = 1, 2).
Let \[ \begin{bmatrix p
q \end{bmatrix} \]
be a feasible solution of P such that \( p c_1 + q c_2 = 6 \), and let all feasible solutions \[ \begin{bmatrix} x_1
x_2 \end{bmatrix} \]
of P satisfy \( -5 \leq c_1x_1 + c_2x_2 \leq 12 \).
Then, which one of the following statements is NOT true?
Let \( L^2[-1, 1] \) be the Hilbert space of real-valued square integrable functions on [-1, 1] equipped with the norm \[ \|f\| = \left( \int_{-1}^{1} |f(x)|^2 \, dx \right)^{1/2}. \]
Consider the subspace \[ M = \{ f \in L^2[-1, 1] : \int_{-1}^{1} f(x) \, dx = 0 \}. \]
For \( f(x) = x^2 \), define \[ d = \inf \{ \|f - g\| : g \in M \}. \]
Then
Let \( C[0, 1] \) be the Banach space of real valued continuous functions on [0, 1] equipped with the supremum norm. Define \( T: C[0, 1] \to C[0, 1] \) by \[ (Tf)(x) = \int_0^x t f(t) \, dt. \]
Let \( R(T) \) denote the range space of \( T \). Consider the following statements:
P: \( T \) is a bounded linear operator.
Q: \( T^{-1}: R(T) \to C[0, 1] \) exists and is bounded.
Let \( \ell^1 = \{ x = (x(1), x(2), \dots, x(n), \dots) : \sum_{n=1}^{\infty} |x(n)| < \infty \} \) be the sequence space equipped with the norm \( \|x\| = \sum_{n=1}^{\infty} |x(n)| \). Consider the subspace \[ X = \left\{ x \in \ell^1 : \sum_{n=1}^{\infty} |x(n)| < \infty \right\}, \]
and the linear transformation \( T: X \to \ell^1 \) given by \[ (Tx)(n) = n x(n) \quad for \quad n = 1, 2, 3, \dots. \]
Then:
Let \( f_n: [0, 10] \to \mathbb{R} \) be given by \( f_n(x) = n x^3 e^{-n x} \) for \( n = 1, 2, 3, \dots \). Consider the following statements:
P: \( (f_n) \) is equicontinuous on \( [0, 10] \).
Q: \( \sum_{n=1}^{\infty} f_n \) does NOT converge uniformly on \( [0, 10] \).
Then:
Let \( f: \mathbb{R}^2 \to \mathbb{R} \) be given by \[ f(x, y) = \begin{cases} \sqrt{x^2 + y^2} \sin\left( \frac{y^2}{x} \right) & if x \neq 0,
0 & if x = 0. \end{cases} \]
Consider the following statements:
P: \( f \) is continuous at \( (0, 0) \) but \( f \) is NOT differentiable at \( (0, 0) \).
Q: The directional derivative \( D_u f(0, 0) \) of \( f \) at \( (0, 0) \) exists in the direction of every unit vector \( u \in \mathbb{R}^2 \).
Then:
Let \( V \) be the solid region in \( \mathbb{R}^3 \) bounded by the paraboloid \( y = x^2 + z^2 \) and the plane \( y = 4 \). Then the value of \[ \iiint_V 15 \sqrt{x^2 + z^2} \, dV \]
is
Let \( f: \mathbb{R}^2 \to \mathbb{R} \) be given by \[ f(x, y) = 4xy - 2x^2 - y^4. \]
Then \( f \) has
The equation \[ xy - z \log y + e^{xz} = 1 \]
can be solved in a neighborhood of the point \( (0, 1, 1) \) as \( y = f(x, z) \) for some continuously differentiable function \( f \). Then
Consider the following topologies on the set \( \mathbb{R} \) of all real numbers. \[ T_1 is the upper limit topology having all sets (a, b) as basis. \] \[ T_2 = \{ U \subset \mathbb{R}: U is finite \} \cup \{\emptyset\}. \] \[ T_3 is the standard topology having all sets (a, b) as basis. \]
Then:
Let \( \mathbb{R} \) denote the set of all real numbers. Consider the following topological spaces. \[ X_1 = (\mathbb{R}, T_1), \quad where \, T_1 is the upper limit topology having all sets (a, b) as basis. \] \[ X_2 = (\mathbb{R}, T_2), \quad where \, T_2 = \{ U \subset \mathbb{R} : \mathbb{R} \setminus U is finite \} \cup \{\emptyset\}. \]
Then:
Let \( \langle \cdot, \cdot \rangle : \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R} \) be an inner product on the vector space \( \mathbb{R}^n \) over \( \mathbb{R} \). Consider the following statements:
P: \( |\langle u, v \rangle| \leq \frac{1}{2} \left( \langle u, u \rangle + \langle v, v \rangle \right) \) for all \( u, v \in \mathbb{R}^n \).
Q: If \( \langle u, v \rangle = \langle 2u, -v \rangle \) for all \( v \in \mathbb{R}^n \), then \( u = 0 \).
Then, which of the following is correct?
Let \( G \) be a group of order \( 5^4 \) with center having \( 5^2 \) elements. Then the number of conjugacy classes in \( G \) is ______ .
Let \( F \) be a finite field and \( F^{\times} \) be the group of all nonzero elements of \( F \) under multiplication. If \( F^{\times} \) has a subgroup of order 17, then the smallest possible order of the field \( F \) is ______ .
Let \( R = \{ z = x + iy \in \mathbb{C} : 0 < x < 1 and - 11 \pi < y < 11 \pi \} \) and \( r \) be the positively oriented boundary of \( R \). Then the value of the integral \[ \frac{1}{2 \pi i} \int_r \frac{e^z}{e^z - 2} \, dz \]
\text{is ______ .
Let \( D = \{ z \in \mathbb{C} : |z| < 2 \pi \} \) and \( f: D \to \mathbb{C} \) be the function defined by \[ f(z) = \begin{cases} \frac{3z^2}{1 - \cos z} & if z \neq 0,
6 & if z = 0. \end{cases} \]
If \[ f(z) = \sum_{n=0^{\infty} a_n z^n \quad for \quad z \in D, then 6a_2 = \_\_\_\_\_\_. \]
The number of zeros (counting multiplicity) of \( P(z) = 3z^5 + 2iz^2 + 7iz + 1 \) in the annular region \( \{ z \in \mathbb{C} : 1 < |z| < 7 \} \) is ________ .
Let \( A \) be a square matrix such that \[ det(xI - A) = x^4(x - 1)^2(x - 2)^3, \]
where \( \text{det(M) \) denotes the determinant of a square matrix \( M \).
If \[ \text{rank(A^2) < rank(A^3) = rank(A^4), \]
\text{then the geometric multiplicity of the eigenvalue 0 of \( A \) is ______ .
If \( y = \sum_{k=0}^{\infty} a_k x^k \), \( (a_0 \neq 0) \) is the power series solution of the differential equation
\[ \frac{d^2y}{dx^2} - 24x^2y = 0, then \frac{a_4}{a_0} = \_\_\_\_\_\_\_. \]
If \( u(x,t) = A e^{-t} \sin x \) solves the following initial boundary value problem:
\[ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}, \quad 0 < x < \pi, \quad t > 0, \] \[ u(0,t) = u(\pi,t) = 0, \quad t > 0, \] \[ u(x,0) = \begin{cases} 60, & 0 < x \leq \frac{\pi}{2},
40, & \frac{\pi}{2} < x < \pi, \end{cases} \]
then \( \pi A = \_\_\_\_\_\_ \).
Let \( V = \{ p : p(x) = a_0 + a_1 x + a_2 x^2, a_0, a_1, a_2 \in \mathbb{R} \} \) be the vector space of all polynomials of degree at most 2 over the real field \( \mathbb{R} \). Let \( T: V \to V \) be the linear operator given by
\[ T(p) = (p(0) - p(1)) + (p(0) + p(1)) x + p(0) x^2. \]
Then the sum of the eigenvalues of \( T \) is ________ .
The quadrature formula \[ \int_0^2 x f(x) \, dx \approx \alpha f(0) + \beta f(1) + \gamma f(2) \]
is exact for all polynomials of degree \( \leq 2 \). Then \( 2 \beta - \gamma = \_\_\_\_ \).
For each \( x \in (0, 1) \), consider the decimal representation \( x = d_1 d_2 d_3 \cdots d_n \cdots \). Define \( f: [0, 1] \to \mathbb{R} \) by \( f(x) = 0 \) if \( x \) is rational, and \( f(x) = 18n \) if \( x \) is irrational, where \( n \) is the number of zeroes immediately after the decimal point up to the first nonzero digit in the decimal representation of \( x \). Then the Lebesgue integral \[ \int_0^1 f(x) \, dx = \_\_\_\_. \]
Let \( \tilde{x} = \begin{bmatrix} 11/3
2/3
0 \end{bmatrix} \) be an optimal solution of the following Linear Programming Problem P:
Maximize \( 4x_1 + x_2 - 3x_3 \)
subject to \[ 2x_1 + 4x_2 + ax_3 \leq 10, \] \[ x_1 - x_2 + bx_3 \leq 3, \] \[ 2x_1 + 3x_2 + 5x_3 \leq 11, \] \[ x_1 \geq 0, \quad x_2 \geq 0, \quad x_3 \geq 0, \quad where \quad a, b are real numbers. \]
If \( \tilde{y} = \begin{bmatrix} p
q
r \end{bmatrix} \) is an optimal solution of the dual of P, then \( p + q + r = _____ \text{ (round off to 2 decimal places).
Quick Links:
GATE 2021 MA Paper Analysis
- IIT Bombay introduced MSQs (Multiple Select Questions) in GATE 2021 examinations, but none of the MSQs appeared in GATE 2021 MA
- 65% percentage of the total weightage was carried by MCQs
- NATs (Numerical Answer Types) questions were responsible for the remaining 35% weightage
- Overall Difficulty level- Easy to moderate
- Difficulty level of General Aptitude- Easy
- Difficulty level of core Mathematics- Moderate
Go through the below-mentioned table to see the complete analysis of the appeared MCQs and NATs in GATE 2021 MA-
| Question Types | No. Of Questions Asked | Carried Marks |
|---|---|---|
| 1 Mark MCQs | 19 | 19 |
| 2 Marks MCQs | 23 | 46 |
| 1 Mark MSQs | - | - |
| 2 Marks MSQs | - | - |
| 1 Mark NATs | 11 | 11 |
| 2 Marks NATs | 12 | 24 |
GATE 2021 MA section wise weightage
Real Analysis & Calculus and ODE & PDE were accountable for almost 28% of the total questions appearing in GATE 2021 MA.
Follow the below-mentioned table to get the details of number of questions appeared as per the sections-
| Section | No. Of Questions Asked | Difficulty Level |
|---|---|---|
| Real Analysis & Calculus | 10 | Moderate |
| General Aptitude | 10 | Easy |
| ODE & PDE | 8 | 5 were easy |
| LPP ODE PDE NA | 5 | 4 were easy |
| Linear Algebra | 5 | 3 were easy |
| Abstract Algebra | 5 | 3 were easy |
| Numerical Analysis | 5 | Moderate |
| Functional Analysis | 5 | 5 were easy |
| Topology | 4 | Easy |
| Complex Analysis | 3 | Easy |
Also Check:
GATE 2021 Marking Scheme and Exam Pattern
- The exam was conducted online via CBT (Computer Based Test) mode
- Students were entitled to pay a penalty of 1 mark for every wrong MCQ
- No marks would be deducted for wrong MSQs and NATs
GATE Previous Year Question Papers:
| GATE 2022 Question Papers | GATE 2021 Question Papers | GATE 2020 Question Papers |
| GATE 2019 Question Papers | GATE 2018 Question Papers | GATE 2017 Question Papers |
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