Question for USET Mathematical Science - Quiz / Questions / MCQ in English

To boost your performance in USET Mathematical Science exam, practice each question regularly and with focus. Every question tests your subject understanding, so solve them one at a time. Taking a quiz improves your speed and accuracy. Practicing topic-wise MCQs. Students benefit greatly from reviewing questions with answer keys, which help clarify concepts and strengthen Questions knowledge for success in USET Mathematical Science exams.

Latest USET Mathematical Science Exam Question (Objective Questions), MCQ in English

Subjects : Mathematical Science

Question Bank Uttarakhand SET Mathematical Science Exam - English

Mathematical Science

Q 1 :

The following schematic diagram represents a glaciated terrain with four different points A, B, C and D. The state at different points shown are X-Glacial Ice movement, Y-Glacial plucking, Z-Jointed bedrock, K-Abrasion and polishing. Find the correct match .

​

1. A.A - X; B - Z; C - Y; D - K
2. B.A - K; B - Y; C - Z; D - X
3. C.A - K; B - Z; C - X; D - Y
4. D.A - X; B - Y; C - Z; D - K

Show Answer

Q 2 :

The following schematic diagram shows velocities observed by a ground Doppler radar for two atmospheric phenomena. The solid lines indicate wind component towards the radar, the dashed lines indicate wind components away from the radar, and the dotted line indicates the zero isodop. Which of the following options correctly identifies the two phenomena ?

​

1. A.(i) Tornadic mesocyclone and (ii) Cold air downburst from a thunderstorm
2. B.(i) Sea-breeze and (ii) Mountain-valley winds
3. C.(i) Occluded front and (ii) Extra-tropical cyclone
4. D.(i) Butterfly effect and (ii) Coriolis effect

Show Answer

Q 3 :

Given profiles are schematic for the surface waters in northern temperate latitudes. Identify A, B, C and D parameters .

1. A.A – Nutrients, B – Phytoplankton, C –Zooplankton, D – Sunlight
2. B.A – Sunlight, B – Phytoplankton, C – Nutrients, D – Zooplankton
3. C.A – Zooplankton, B – Phytoplankton, C – Chlorophyll, D – Sunlight
4. D.A – Sunlight, B – Phytoplankton, C – Nutrients, D – Chlorophyll

Show Answer

Q 4 :

Find the value of f(0) if f(x+2) = (x + 1)³⁴ – (x + 1)³³ + 5 .

1. A.5
2. B.7
3. C.6
4. D.72

Show Answer

Q 5 :

The shortest distance between the parallel lines A and B in the following figure is :

1. B.2

Show Answer

Q 6 :

Two varieties A and B of rice cost Rs 30 and Rs 90 per kg, whereas two varieties C and D of pulases, Rs 100 and Rs 120 per kg, respectively. If at least one kg each of A and B and at least half a kg each of C and D have to be purchased, then the minimum and maximum costs of a total of 5 kg of these provisions are respectively .

1. A.Rs 150 and Rs 600
2. B.Rs 260 and Rs 530
3. C.RS 290 and Rs 470
4. D.Rs 370 and Rs 460

Show Answer

Q 7 :

One of four suspects A, B, C and D has committed a crime. A and D are always truthful, and B and C are always untruthful. C and D are identical twins and the interrogator does not know who is who. If A says "D is innocent", B says, "A is guilty and amoung C and D one say, “A is innocent” and the other says, "B is guilty", then which of the following is FALSE ?

1. A.D said "A is innocent"
2. B.D is innocent
3. C.B is innocent
4. D.C is innocent

Show Answer

Q 8 :

Which is an appropriate diagram to represent the relations between the following categories : quadruped, mammal, whale, house lizard ?

Show Answer

Q 9 :

A 7 m long tube having inner diameter of 2 cm is filled with water. The water is then poured into a cylindrical bucket having inner base area of 200 cm². What will be the approximate height (in cm) of water in the bucket ?

1. A.22
2. B.44
3. C.9
4. D.11

Show Answer

Q 10 :

Water is being filled in a cone from the top at a constant volumetric rate. The rate of increase of the height of the water column :

1. A.is linearly dependent on time
2. B.depends on the apex angle of the cone
3. C.increases as cube-root of the volumetric rate
4. D.increases as square-root of the volumetric rate

Show Answer

Q 11 :

A square board is divided into 9 smaller identical squares by drawing lines. Three bullets are shot at the board randomly. The probability that at least 2 bullets hit the same small square is :

Show Answer

Q 12 :

A and B complete a work in 30 days. B and C complete the same work in 24 days wherea C and A complete the same work in 28 days. Based on these statements which of the following conclusions is correct ?

1. A.C is the most efficient and B is the least efficient
2. B.B is the most efficient but the least efficient one cannot be determined
3. C.C is the most efficient but, the least efficient one cannot be determined
4. D.C is the most efficient and A is the least efficient

Show Answer

Q 13 :

Clock A loses 4 minutes every hour, clock B always shows the correct time and clock C gains 3 minutes every hour. On a Monday, all the three clock showed the same time, 8pm. On the following Wednesday, when the clock C shows 2 pm, what time will clock A show ?

1. A.7 : 20 am
2. B.8 : 40 am
3. C.9 : 20 am
4. D.10 : 40 am

Show Answer

Q 14 :

In a class, there is one pencil for every two students, one eraser for every three students, and one ruler for every four students. If the total number of these stationery items required is 65 how many students are present in the class ?

1. A.55
2. B.60
3. C.65
4. D.70

Show Answer

Q 15 :

The given table shows the numbers of active and recovered case of a certain disease. Assuming that the lienear trend for both continues, on which days will recovered cases be twice that of the active cases ?​

Day	0	1	4	7	10
Active cases	990	1000	1030	1060	1090
Recovered cases	760	800	920	1040	1160

1. A.61
2. B.62
3. C.63
4. D.64

Show Answer

Q 16 :

A boat weights 60kg, and oarsmen A and B weight 80 and 90kg, respectively. Rowing at a constant power, the time required to complete a course is proportional to the total weight. Rowing alone, A and B complete the course in 1 and 1½ hours, respectively. Assuming that their powers add up, how long will they ake to complete the course if the row together ?

1. A.49.4 min
2. B.57.5 min
3. C.62.6 min
4. D.72.5 min

Show Answer

Q 17 :

The wavelength dependant absorbance of two compounds, A and B, is shown Absorbance of mixture is a linear function of the concentration of the two compounds. R is defined as a ratio of absorbance at 650nm to the abosrbance at 950 nm .



​If the mixture contains 95% of compound A then R must be :

1. A.95
2. B.5
3. C.1
4. D.Less than 1

Show Answer

Q 18 :

An epidemic is spreading in a population of size P. The rate of spread R of the disease at a given time is proportional to both, the number of people affected by the disease (N) and the number of people not yet affected by the disease. Which of the following graphs of R vs N is correct ?

Show Answer

Q 19 :

The figure shows temperature and salinity of four samples of water. Which one of the samples has the highest density ?

1. A.A
2. B.B
3. C.C
4. D.D

Show Answer

Q 20 :

Consider a parallelogram ABCD with centre O and E as the midpoint of side CD. The area of the triangle OAE, is :

Show Answer

Q 21 :

The sum of the first n even numbers is :

1. A.divisible by n and not by (n + 1)
2. B.divisible by (n + 1) and not by n
3. C.divisible by booth n and (n + 1)
4. D.neither divisible by n nor by (n + 1)

Show Answer

Q 22 :

A, B, C, D and E are the vertices of a regular pentagon as shown in the figure .​



The angle ∠ABC is :

1. A.48°
2. B.72°
3. C.54°
4. D.36°

Show Answer

Q 23 :

On a 200 m long straight road, maximum number of poles are fixed at 200 m interval. How many of the poles should be removed in order to have maximum number of poles at an interval of 40 m on the road ?

1. A.8
2. B.6
3. C.5
4. D.4

Show Answer

Q 24 :

Let (En) be a squence of subsets of  .
Define

Which of the following statements is true ?

1. B. (x : x ∈ E_n for some n)
2. C. = (x : x ∈ E_n for all but finitely many n)
3. D.  = (x : x ∈ E_n for infinitely many n)

Show Answer

Q 25 :

 be a bounded function. Which of the following statements is NOT true ?

Show Answer

Q 26 :

Which of the following statements is true ?

1. A.There are at most constably many continuous maps from â€‹ to ​
2. B.There are at most finitely many continuous surjective maps from  to ​
3. C.There are infinitely many continuous injective maps from  to ​
4. D.There are no continuous bijective maps from  to ​

Show Answer

Q 27 :

The series  converges

1. A.only for x = 0
2. B.uniformly only for x ∈ [−π, π]
3. C.uniformly only for x ∈ â€‹ (nπ : n ∈ Z)
4. D.uniformly for all x ∈ â€‹

Show Answer

Q 28 :

Given (a_n)_{n ≥ 1} a sequence of real numbers, which of the following statements is true :

1. B.There is a subsequence (a_nk)_k≥1 such that  converges
2. C.​There is a b such that  converges
3. D.There is a number b and a subsequence (a_nk)_k≥1  such that converges

Show Answer

Q 29 :

Given f, g are continuous function on [0,1] such that f(0) = f​(1) = 0 ; = g (1) = 1 and . Which of the following statements is true ?

1. A.There is no t ∈ [0,1] such that f(t) = g(t)
2. B.There is exactly one t ∈ [0,1] such that f(t) = g(t)
3. C.There are atleast two t ∈ [0,1] such that f​(t) = g(t)
4. D.There are always infinitely many t ∈ [0,1] such that f(t) = g (t)

Show Answer

Q 30 :

Let A be an n x n matrix such that the set of all its non-zero eigenvalues has exactly r elements. Which of the following statements is true ?

1. A.rank A ≤ r
2. B.If r = 0, then rank A < n − 1
3. C.rank A ≥ r
4. D.A² has r distinct non-zero eigenvalues

Show Answer

Q 31 :

Let A and B be 2 x 2 metries. Then which on the following is true ?

1. A.det (A+B) + det(A−B) = det A + det B
2. B.det (A+B) + det(A−B) = 2det A − 2det B
3. C.det (A+B) + det(A−B) = 2det A + 2det B
4. D.det (A+ B) − det(A−B) = 2det A − det B

Show Answer

Q 32 :

If A = , then A²⁰ euqals

Show Answer

Q 33 :

Let A be a 2 x 2 real matrix with det A = 1 and trace A = 3. What is the value of trace A² ?

1. A.2
2. B.10
3. C.9
4. D.7

Show Answer

Q 34 :

For a, b ∈ , let p (x, y) = a²x₁y₁ + abx₂y₁ + abx₁y₂+b²x₂y₂, x = (x₁, x₂) y = (y₁, y₂) ∈ 
For what values of a and b does p :  x  →  define an inner product ?

1. A.a > 0, b > 0
2. B.ab > 0
3. C.a = 0, b = 0
4. D.For no values of a, b

Show Answer

Q 35 :

Which of the following real quadratic froms on is positive definite ?

1. A.Q(X,Y) = XY
2. B.Q(X,Y) = X²− XY+ Y²
3. C.Q(X,Y) = X²− 2XY+ Y²
4. D.Q(X, Y) = X² + XY

Show Answer

Q 36 :

Let  be the positively oriented circle in the complex plane given by . Then  equals :

1. A.3
2. C.2

Show Answer

Q 37 :

For a positive integer p, consider the holomorphic function 
For which values of p does there exist a holomorphic function  such that f(z) = g' (z) for  ?

1. A.All even integers
2. B.All odd integers
3. C.All multiples of 3
4. D.All multiples of 4

Show Answer

Q 38 :

Let  be the positively oriented circle in the complex plane given by . The line integral  equals :

Show Answer

Q 39 :

​​Let p be a positie integer. Consider the closed curve r(t) = e^it, 0 ≤ t < 2π/. Let f be a function holomorphic in {z : |z| < 2 R} where R > 1. If f has a zero only at z₀, 0 < |z₀| < R, and it is of multiplicity q, then  equals

1. A.​

Show Answer

Q 40 :

Which of the following statements is true ?

1. A.Every even integer n ≥ 16 divides (n – 1)! +3
2. B.Every odd integer n ≥ 16 divides (n – 1)!
3. C.Every even integer n ≥ 16 divides (n – 1)!
4. D.For every integer n ≥ 16, n² divides n! + 1

Show Answer

Q 41 :

Let X be a non-empty set and P(X) be the set of all subsets of X. On P(X) defines two operations * and Δ as follows :
for A, B  P(X), A * B = A B ;
A Δ B = (A  B) (A  B) .
Which of the following statements is true ?

1. A.P(X) is a group under * as well as under Δ
2. B.P(X) is a group under *, but not under Δ
3. C.P(X) is a group under Δ, but not under *
4. D.P(X) is neither a group under * nor under Δ

Show Answer

Q 42 :

Let φ(n) be the cardinality of the set {a|1 ≤ a ≤ n, (a, n ) = 1} where (a, n) denotes the gcd of a and n. Which of the following is NOT true ?

1. A.There exist infinitely many n such that φ(n) > φ(n+1)
2. B.There exist infinitely many n such that φ(n) < φ(n+1)
3. C.There exists N ϵ such that N > 2 and for all n > N, φ(N) < φ(n)
4. D.The set  has finitely many limite points

Show Answer

Q 43 :

For any two metric spaces (X, d_X), (Y, d_Y) a map  is said to be a closed map if whenever F is closed in X, then (F) is closed in Y. For any subset B of a metric space, B is given the induced metric. The metric on X x Y is given by d((x, y), (x', y')) = max {d_X(x, x'), d_Y(y, y')}. Which of the following are true ?

1. A.For any subset A  X in the inclusion map i : A → X is closed
2. B.The projection map p₁ : X x Y → X given by p₁ (x, y) = x is closed
3. C.Suppose that  : X → Y, g : Y → Z are continuous maps. If g o : X → Z is a closed map then g|_f(x) : (X) → Z is closed. Here g|_f(x) means the map g restricted to (X)
4. D.If takes closed balls into closed sets then is closed

Show Answer

Q 44 :

Let k be a positive integer. Consider the differential equation

Which of the following statements is true ?

1. A.It has a unique solution which is continuously differentiable on (0, ∞)
2. B.It has at most two solutions which are continuously differentiable on (0, ∞)
3. C.It has infinitely many solutions which are contiuously differentiable on (0, ∞)
4. D.It has no continuously differentiable solution on (0, ∞)

Show Answer

Q 45 :

Let y₀ > 0, Z₀ > 0 and α > 1 .
Consider the following tow differential equations :

We say that the solution to a differential equation exists globally if it exists for all t > 0 .
which of the following statements is true ?

1. A.Both (*) and (**) have global solutions
2. B.None of (*) and (**) have global solutions
3. C.There exists a global solution for (*) and there exists a T < ∞ such that 
4. D.There exists a global solution for (*) and there exists a T < ∞ such that 

Show Answer

Q 46 :

The genral solution of the surface which are perpendicular to the family of surface
z² = kxy, k ϵ ​
is :

Show Answer

Q 47 :

The general solution of the equation

Show Answer

Q 48 :

Let be an infinitely differentiable real valued function on a bounded inerval I. Take n ≥ 1 interpolation points (x₀, x_i­, ..., x_n-1}. Take n additional interpolation points

where  is such that {x₀, x₁, ............... x_2n-1} are distinct .
Let P_2n-1 be the Lagrange interpolation polynomial of degree 2n - 1 with the interpolation points (x₀, x₁, ....., x_n-1} for the function ​.
Let q_2n-1 be the Hermite interpolation polynomial of degree 2n - 1 with the interpolation points {x₀, x₁, ...., x_n-1} for the function . In the  limit, the quantity
​

1. A.does not necessarily converge
2. B.converges to 
3. C.converges to 0
4. D.converges to 

Show Answer

Q 49 :

The extremal of the function

is :

Show Answer

Q 50 :

The solution of the Fredholm integral equation
y(s) = s + 2  is :

1. A.y(s) = −(50s + 40s²)
2. B.y(s) = (30s + 15s²)
3. C.y(s) = −(30s + 40s²)
4. D.y(s) = (60s + 50s²)

Show Answer

USET Mathematical Science Exam Online Question Bank Package

Buy USET Mathematical Science Important Questions, MCQ, question answer in Hindi & English. It will help you to score high marks in USET Mathematical Science question bank 2026 in Online, PDF & Print study material.