ISI Admission Test 2026 Question Paper M.Tech(CS), M.Tech(CrS) PCA

FOR ISI ADMISSION TEST EXAM PREPARATION

ISI Admission Test
2026
Question Paper ·
M.Tech(CS),
M.Tech(CrS) PCA
EXAM YEAR TYPE

ISI Admission Test 2026 Question Paper
SUBJECT

M.Tech(CS), M.Tech(CrS) PCA

Notes · Sample Papers · Previous Year Papers · Mock Tests

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• The symbol R denotes the set of all real numbers.

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• The symbol Q denotes the set of all rationals numbers.

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• The symbol Z denotes the set of all integers.
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• The symbol N denotes the set of all natural numbers.
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1. Which of the inferences are valid given the premises?

All birds have feathers.
(I1 ) Robins are birds.

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Therefore, robins have feathers.

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All insects need oxygen. m
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ag are insects.
(I2 ) Mosquitoes need oxygen.
Therefore, mosquitoes

All flowers need water.
(I3 ) Roses need water.
Therefore, roses are flowers.

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All mammals walk.
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(I4 ) Whales are mammals.

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Therefore, whales walk.

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ag (A) I1 , I2 and I4
(C) I1 , I2 and I3
(B) I1 and I4
(D) I1 and I3

2. The number of factors of 2025 (including 1 and itself) equals

(A) 15 (B) 25 (C) 35 (D) 45

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3. Suppose the function f is defined by the following pseudocode.
What will be printed when f(5) is called?

function f(x) {
if (x > 1) {
print(x);
f(x-2);
print(x);
}
}

(A) 5 5 3 3 (B) 5 3 5 3 (C) 5 5 5 5 (D) 5 3 3 5

4. Consider the following statements.

S1: In every country, there is a city through which a river
passes.
S2: There is no country in which every city has a river passing
through it.
S3: There is no country in which there is no city through which
a river passes.
S4: In every country, every river passes through a city.

Which of the above statements are equivalent to each other?

(A) S1 and S2 (B) S1 and S3 (C) S2 and S4 (D) S2 and S3

5. If the matrix " #
a 1
A=
2 3
has 1 as an eigenvalue, then det(A) equals

(A) 1 (B) 2 (C) 4 (D) 10

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6. Let A be the following 4 ⇥ 4 matrix:
2 3

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1 0 1 0

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6 7
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6 1 0 0 1 7

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6 7.

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A=6
e
7

s
4 0 1 1 0 5

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0 1 0 1

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The rank of A equals
a
a (A) 1 (B) 2 (C) 3 (D) 4

2025
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7. The remainder obtained when m! is divided by 18 is
m=1

(A) 7 (B) 9 (C) 12 (D) 16

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8. Consider the equation x + 4x + m
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la is
7 5 3
2x + x + 1 = 0. The number

(B) 3 a
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of real root(s) of this equation
(A) 1 (C) 5 (D) 7

9. Let Z be the number of heads obtained when Alice tossed an
unbiased coin 4 times. Then, Bob tossed the same coin a further

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Z times. Given that Bob got 2 heads, what is the probability

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that Z = 3?

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(B) 1/4 (C) 2/9

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ag 10. Let R be the region defined by
R = {(x, y) 2 R2 : x2 + y 2  50, x + y 0}.
The area of R equals
(A) 10⇡ (B) 15⇡ (C) 20⇡ (D) 25⇡

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11. For functions f, g : N ! R, we say that f is o(g) (in words, f is
f (n)
little-oh of g) if lim = 0. Then
n!1 g(n)

(A) n is o n1/2 (B) n 1/2 is o n 1/4
(C) n 1/4 is o(n 1/2 ) (D) 1 is o n 1/2

12. Let A be a 4 ⇥ 4 upper triangular matrix whose diagonal entries
1 1
are 1, 1, , . Then A 1 equals
2 2

(A) 5A 4A3 (B) 5A + 4A3

(C) 5A + 4A3 (D) 5A 4A3

13. If ↵, , are roots of x3 + ax + 1 = 0, then
↵ ↵
+ + + + +
↵ ↵
equals
(A) a (B) 3a (C) 1 (D) 3

14. Let f : [0, 1] ! [0, 1] be defined as follows. For x 2 [0, 1],
8 x
>
> if x is rational,
>
< 2
f (x) =
>
> x+1
>
: if x is irrational.
2

(A) f is a bijection.
(B) f is neither injective, nor surjective.
(C) f is injective, but not surjective.
(D) f is surjective, but not injective.

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15. Suppose f is a real-valued function defined on the set of real

m
numbers. Let

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sin x

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for x 6= 0, f (0) = a,
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f (x) =

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x

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where a is a real number. Let f be di↵erentiable at x = 0. Let
l a s
a s
l(A) 1
0
f (0) = b. Then a + b equals
ag
ag (B) 0 (C) 1 (D) 2

16. There are 10 points on a plane in such a way that 6 of these
points are collinear and other than these 6 points, no set of 3 or
more points are collinear. The number of triangles which can

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be formed with vertices among these 10 points equals

(C). 100
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(A) 10 (B) 60 (D) 120

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17. We call a function : R ! R a homomorphism if

(x + y) = (x) + (y) for all x, y 2 R.

Let
f (x) = 2x, g(x) = x + 1 and h(x) = 2x + 1.

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Which of the following statements is correct?

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(A) f is a homomorphism but g, h are not.

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(B) g is a homomorphism but f, h are not.

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ag (D) f, g, h are all homomorphisms.

18. Let L = (a + b)(a + b)⇤ a(a + b)⇤ be a regular language over
{a, b}. Which of the following strings does not belong to L?

(A) aaa (B) bba (C) abb (D) aab

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19. In the decimal system with digits in the set {0, . . . , 9}, a
notation like 234 stands for 2 ⇥ 102 + 3 ⇥ 10 + 4; but in a
di↵erent base r with digits in the set {0, . . . , r 1}, the notation
234 will stand for the number 2 ⇥ r2 + 3 ⇥ r + 4. If the relation
430 + 240 = 1000 holds when numbers are represented in a
certain base r, then r equals

(A) 5 (B) 6 (C) 7 (D) 8

20. Let R be the set of points (represented by the column vectors
(x1 x2 )T ) on the 2-dimensional vector space R2 , constituting the
rectangle shown in the figure on the left. Let T be a linear
transformation such that the parallelogram P shown in the figure
on the right is obtained by transforming all points in R by T .
In other words, P = {T x : x 2 R}.

Then, T can be represented by the matrix:
" # " #
1 0 0.5 1
(A) (B)
0 0.5 0 1
" # " #
0.5 1 1 1
(C) (D)
0 1 0 0.5

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21. There are 4 suspects, A, B, C and D, say, in a criminal case. At

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least one of them is guilty. If A is guilty then so is B. If A and

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D are innocent, then so is C, and if A or C is innocent, then so

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is B. Suppose the police found out that B is guilty. From the
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given information, the persons who can be certainly declared

a
l(A) A, B, C and D ag
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guilty

a (B) A, B and C
(C) B, C and D (D) A, B and D

22. Let f(x) be defined as follows:

function f(x) {

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count := 0;
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while (x > 0) {
x := floor(x/2);
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}
count := count + 1;
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return count;
}

where floor(y) is defined as the largest integer less than or
equal to y. Suppose, for a positive integer x, f(x) = 8. What
is the maximum possible value of x?
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gla 23. Twelve monkeys have collected a total of N bananas a
a where every
monkey has managed to collect at least one banana. What is the
maximum value of N for which you can guarantee that at least
two of the monkeys have gathered the same number of bananas?
(A) 72 (B) 77 (C) 84 (D) 88

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24. Five marbles of di↵erent sizes are to be coloured using the
three colours, namely red, yellow and blue, where each marble
is coloured with exactly one colour. The number of possible
colourings of all the marbles such that each colour is used to
colour at least one marble is

(A) 32 (B) 64 (C) 75 (D) 150

25. Consider the real-valued function
1
f (x) = x + , x > 0.
x
The tangents to the graph of f at the points (1/2, f (1/2)) and
(2, f (2)) intersect at the point (4/5, 8/5). The area of the region
enclosed by the graph of f and these two tangents equals
15 6
(A) 2 log 2 + (B) 2 log 2
8 5
15 3
(C) 2 log 2 + (D) 2 log 2
4 5

26. A coin with probability of head equal to 1/3 is repeatedly
tossed until at least one head and at least one tail is obtained.
The random experiment is stopped as soon as this condition
is satisfied. The probability that the experiment stops after
exactly 8 tosses equals
128 130 192 256
(A) (B) (C) (D)
6561 6561 6561 6561

27. Which of the following can be the degrees of the vertices of a
5-vertex undirected simple graph?

(A) 0, 1, 2, 3, 4 (B) 0, 3, 3, 4, 5
(C) 1, 1, 2, 2, 3 (D) 2, 2, 3, 3, 4

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28. Consider the set of all possible polynomials

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x 3 + a2 x 2 + a 1 x + a 0 ,

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. all of its roots are distinct positive integers in some s e
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with a0 , a1 , a2 integers and |a0 | 2 {0, . . . , 9}, such that for each

s e progression. The number of such polynomials is g l a
a
polynomial,

g l
geometric
a
a (A) 0 (B) 1 (C) 2 (D) 3

29. If two languages L1 and L2 are both non-regular, then which of
the following is always true?

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(A) L1 [ L2 is regular.

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(B) L1 \ L2 is finite.
(C) Both L1 and L2 are infinite.
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(D) L1 \ L2 is not regular. a
30. The complement of a simple graph G = (V, E) is defined as
Ḡ = (V, Ē) such that for all u, v 2 V , uv 2 E () uv 2
/ Ē.
Let G be a graph on n verties such that Ḡ is isomorphic to G.

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Then, which of the following is necessarily true?

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(A) n ⌘ 0 (mod 4) or n ⌘ 1 (mod 4)

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n ⌘ 0 (mod 4) or n ⌘ 2 (mod 4)
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(B)

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(C) n ⌘ 1 (mod 4) or n ⌘ 2 (mod 4)
(D) n ⌘ 2 (mod 4) or n ⌘ 3 (mod 4)

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