GATE 2026 ST Question Paper with Solutions (Available)- Download Pdf

The question paper and solution PDF of the GATE 2026 ST (Statitstics) paper is available here for download. The exam ‌for the GATE 2026 ST paper was conducted on 8th February in Session 1 (9:30 AM to 12:30 PM).

The GATE 2026 ST exam happens for 100 marks, where 15 marks come from the general aptitude section, 13 marks from Engineering mathematics. The remaining 72 marks come from core subjects.

Based on the initial analysis, the GATE 2026 ST question paper was considered moderate to tough. To rank under 1000 in Instrumentation, you need to score 55-60+ marks out of 100.

GATE 2026 ST Question Paper with Solution PDF

GATE 2026 Statitstics (ST) Question Paper with Solution PDF	Download	Check Solutions

Question 1:

Let \( X \) be a random variable having discrete uniform distribution on \( \{1, 3, 5, 7, \dots, 99\} \). Then \( E(X \mid X is not a multiple of 15) \) equals

(A) \( \frac{2365}{47} \)
(B) \( \frac{2365}{50} \)
(C) 50
(D) 47

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Question 2:

In a testing of hypothesis problem, which one of the following statements is true?

(A) The probability of the Type-I error cannot be higher than the probability of the Type-II error
(B) Type-II error occurs if the test accepts the null hypothesis when the null hypothesis is actually false
(C) Type-I error occurs if the test rejects the null hypothesis when the null hypothesis is actually false
(D) The sum of the probability of the Type-I error and the probability of the Type-II error should be 1

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Question 3:

Let \( \{W(t)\}_{t \geq 0} \) be a standard Brownian motion. Which one of the following statements is NOT true?

(A) \( E[W(7)] = 0 \)
(B) \( E[W(5)W(9)] = 7 \)
(C) \( 2W(1) \) is normally distributed with mean 0 and variance 4
(D) \( E[W(5) \mid W(3) = 3] = 3 \)

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Question 4:

Two fair dice, one having red and another having blue color, are tossed independently once. Let \( A \) be the event that the die having red colour will show 5 or 6. Let \( B \) be the event that the sum of the outcomes will be 7 and let \( C \) be the event that the sum of the outcomes will be 8. Then which one of the following statements is true?

(A) \( A \) and \( B \) are independent as well as \( A \) and \( C \) are independent
(B) \( A \) and \( B \) are independent, but \( A \) and \( C \) are not independent
(C) \( A \) and \( C \) are independent, but \( A \) and \( B \) are not independent
(D) Neither \( A \) and \( B \) are independent, nor \( A \) and \( C \) are independent

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Question 5:

Let \( X \) be a random variable taking only two values, 1 and 2. Let \( M_X(t) \) be the moment generating function of \( X \). If the expectation of \( X \) is \( \frac{10}{7} \), then the fourth derivative of \( M_X(t) \) evaluated at 0 equals

(A) \( \frac{52}{7} \)
(B) \( \frac{67}{7} \)
(C) \( \frac{48}{7} \)
(D) \( \frac{60}{7} \)

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Question 6:

Let \( A \) be a \( 3 \times 3 \) real matrix and let \( I_3 \) be the \( 3 \times 3 \) identity matrix. Which one of the following statements is NOT true?

(A) If the row-reduced echelon form of \( A \) is \( I_3 \), then zero is not an eigenvalue of \( A \)
(B) If zero is not an eigenvalue of \( A \), then the row-reduced echelon form of \( A \) is \( I_3 \)
(C) If \( A \) has three distinct eigenvalues, then the row-reduced echelon form of \( A \) is \( I_3 \)
(D) If the system of equations \( Ax = b \) has a solution for every \( 3 \times 1 \) real column vector \( b \), then the row-reduced echelon form of \( A \) is \( I_3 \)

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Question 7:

A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube. The minimum number of such cuts required is

(A) 3
(B) 4
(C) 7
(D) 8

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GATE 2026 Question Paper

GATE Questions

1.
Consider two identical tanks with a bottom hole of diameter \( d \). One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column \( h \) is the same in both cases. The fluid exit velocity in the two tanks are \( V_1 \) and \( V_2 \). Neglecting all losses, which one of the following options is correct?

\( V_2>V_1 \)
\( V_2 = V_1 \)
\( V_2<V_1 \)
Insufficient data to definitively conclude the relationship between \( V_1 \) and \( V_2 \)

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2.
A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?
\[ {Given: } F = 1000\,{N} \]

\(BD\)
\(BC\)
\(BA\)
\(AD\)

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3.
During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, 85% of the power is absorbed within a circle of radius 5 mm while 65% is absorbed within an inner concentric circle of radius 3 mm. The power density in the shaded area is _________ W mm^-2 (rounded off to 2 decimal places).

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4.
The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.
Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]

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5.
Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is _______________ (rounded off to 2 decimal places).
Assume that solidification time follows Chvorinov's rule with an exponent of 2.

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6.
A vibrating system has a critical damping coefficient \(C_c = 350 \, \text{N}\cdot\text{s/m}\) and an actual damping coefficient \(C = 35 \, \text{N}\cdot\text{s/m}\). The logarithmic decrement of the system is approximately:

0.10
0.31
0.63
3.14

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GATE 2026 ST Question Paper with Solutions (Available)- Download Pdf

GATE 2026 ST Question Paper with Solution PDF

GATE 2026 Question Paper

GATE Questions

2.
A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?
\[ {Given: } F = 1000\,{N} \]

4.
The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.
Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]

6.
A vibrating system has a critical damping coefficient \(C_c = 350 \, \text{N}\cdot\text{s/m}\) and an actual damping coefficient \(C = 35 \, \text{N}\cdot\text{s/m}\). The logarithmic decrement of the system is approximately:

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GATE 2026 ST Question Paper with Solution PDF

GATE 2026 Question Paper

GATE Questions

2.A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?\[ {Given: } F = 1000\,{N} \]

4.The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]

6.A vibrating system has a critical damping coefficient \(C_c = 350 \, \text{N}\cdot\text{s/m}\) and an actual damping coefficient \(C = 35 \, \text{N}\cdot\text{s/m}\). The logarithmic decrement of the system is approximately:

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2.
A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?
\[ {Given: } F = 1000\,{N} \]

4.
The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.
Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]

6.
A vibrating system has a critical damping coefficient \(C_c = 350 \, \text{N}\cdot\text{s/m}\) and an actual damping coefficient \(C = 35 \, \text{N}\cdot\text{s/m}\). The logarithmic decrement of the system is approximately: