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Objective Questions

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

Subjects : Mathematical Science

Question Bank Haryana SET Mathematical Science Exam - English
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Mathematical Science

Question 1Single Answer
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
Question 2Single Answer
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
Question 3Single Answer
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
Question 4Single Answer
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
Question 5Single Answer
The shortest distance between the parallel lines A and B in the following figure is :
  1. A
  2. B
    2
  3. C
  4. D
Question 6Single Answer
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
Question 7Single Answer
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
Question 8Single Answer
Which is an appropriate diagram to represent the relations between the following categories : quadruped, mammal, whale, house lizard ?
  1. A
  2. B
  3. C
  4. D
Question 9Single Answer
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
Question 10Single Answer
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
Question 11Single Answer
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 :
  1. A
  2. B
  3. C
  4. D
Question 12Single Answer
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
Question 13Single Answer
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
Question 14Single Answer
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
Question 15Single Answer
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
Question 16Single Answer
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
Question 17Single Answer
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
Question 18Single Answer
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 ?
  1. A
  2. B
  3. C
  4. D
Question 19Single Answer
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
Question 20Single Answer
Consider a parallelogram ABCD with centre O and E as the midpoint of side CD. The area of the triangle OAE, is :
  1. A
  2. B
  3. C
  4. D
Question 21Single Answer
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)
Question 22Single Answer
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°
Question 23Single Answer
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
Question 24Single Answer
Let (En) be a squence of subsets of  .
Define

Which of the following statements is true ?
  1. A
  2. B
     (x : x ∈ En for some n)
  3. C
     = (x : x ∈ En for all but finitely many n)
  4. D
      = (x : x ∈ En for infinitely many n)
Question 25Single Answer
 be a bounded function. Which of the following statements is NOT true ?
  1. A
  2. B
  3. C
  4. D
Question 26Single Answer
Which of the following statements is true ?
  1. A
    There are at most constably many continuous maps from  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
Question 27Single Answer
The series  converges
  1. A
    only for x = 0
  2. B
    uniformly only for x ∈ [−π, π]
  3. C
    uniformly only for x ∈  (nπ : n ∈ Z)
  4. D
    uniformly for all x ∈ 
Question 28Single Answer
Given (an)n ≥ 1 a sequence of real numbers, which of the following statements is true :
  1. A
  2. B
    There is a subsequence (ank)k≥1 such that  converges
  3. C
    There is a b such that  converges
  4. D
    There is a number b and a subsequence (ank)k≥1  such that converges
Question 29Single Answer
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)
Question 30Single Answer
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
Question 31Single Answer
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
Question 32Single Answer
If A = , then A20 euqals
  1. A
  2. B
  3. C
  4. D
Question 33Single Answer
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
Question 34Single Answer
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
Question 35Single Answer
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
Question 36Single Answer
Let  be the positively oriented circle in the complex plane given by . Then  equals :
  1. A
    3
  2. B
  3. C
    2
  4. D
Question 37Single Answer
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
Question 38Single Answer
Let  be the positively oriented circle in the complex plane given by . The line integral  equals :
  1. A
  2. B
  3. C
  4. D
Question 39Single Answer
Let p be a positie integer. Consider the closed curve r(t) = eit, 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
  2. B
  3. C
  4. D
Question 40Single Answer
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
Question 41Single Answer
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
Question 42Single Answer
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
Question 43Single Answer
For any two metric spaces (X, dX), (Y, dY) 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 {dX(x, x'), dY(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
Question 44Single Answer
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, ∞)
Question 45Single Answer
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 
Question 46Single Answer
The genral solution of the surface which are perpendicular to the family of surface
z2 = kxy, k ϵ
is :
  1. A
  2. B
  3. C
  4. D
Question 47Single Answer
The general solution of the equation
  1. A
  2. B
  3. C
  4. D
Question 48Single Answer
Let be an infinitely differentiable real valued function on a bounded inerval I. Take n ≥ 1 interpolation points (x0, xi­, ..., xn-1}. Take n additional interpolation points

where  is such that {x0, x1, ............... x2n-1} are distinct .
Let P2n-1 be the Lagrange interpolation polynomial of degree 2n - 1 with the interpolation points (x0, x1, ....., xn-1} for the function .
Let q2n-1 be the Hermite interpolation polynomial of degree 2n - 1 with the interpolation points {x0, x1, ...., xn-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 
Question 49Single Answer
The extremal of the function

is :
  1. A
  2. B
  3. C
  4. D
Question 50Single Answer
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)
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