Q. 1 – Q. 5 carry one mark each.
Q.
A student is required to demonstrate a high level of comprehension of the subject, especially in the
social sciences.
The word closest in meaning to comprehension is
Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.
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Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above sentences?
If y = 5x2 + 3, then the tangent at x = 0, y = 3
A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q,
where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily
production of 100 tonnes?
(Important : you should answer only the numeric value)
Q. 6 – Q. 10 carry two marks each.
Q.
Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK
Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building
(the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered
floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors
below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor
immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the
following floor-person combinations is correct?
The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The
ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its
smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the
largest angle of the quadrilateral?
(Important : you should answer only the numeric value)
One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y
are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both
countries together, what is the percentage of people taller than 6 ft?
The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure.
Which of the following are true? (k percentile is the value such that k percent of the data fall below
that value)
(i) On average, it rains more in July than in December
(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be estimated with better confidence than February rainfall
(iv) In August, there is at least 500 mm of rainfall
Q. 11 – Q. 17 carry one mark each.
Q.
If 1, 0, and -1 are the eigenvalues of a 3x3 matrix A, then the trace of A2 + 5Ais equal to ________
(Important : you should answer only the numeric value)
Which of the following is a solution of the differential equation
x2 y''+ xy'+ y = 4sin(ln x), x > 0?
At z = 0 , the complex function
Ten chocolates are distributed randomly among three children standing in a row. The probability
that the first child receives exactly three chocolates is
Let the function f :[0, 5]→R be defined by
The number of points where f is not differentiable in (0, 5) , is ___________.
(Important : you should answer only the numeric value)
An integrating factor of the differential equation is
If a cubic polynomial passes through the points (0, 1), (1, 0), (2, 1) and (3, 10), then it also passes
through the point
Q. 18 – Q. 21 carry two marks each.
Q.
Let the function f :[0,∞)→ R be such that for x > 0 and f (0) = 1.Then f (1) lies in the interval
The perimeter of a rectangle having the largest area that can be inscribed in the ellipse
is _____________
(Important : you should answer only the numeric value)
If the work done in moving a particle once around a circle x2 + y2 = 4 under the force field then |a| is equal to _________.
(Important : you should answer only the numeric value)
Let r and s be real numbers. If then the system of linear equations AX = b has
Q. 22 – Q. 30 carry one mark each.
Q.
A dam with a curved shape is shown in the figure. The cross sectional area of the dam (shaded
portion) is 100 m2 and its centroid is at The vertical component of the hydrostatic force,
Fz , is acting at a distance xp . The value of xp is ____ m.
(Important : you should answer only the numeric value)
For an unsteady incompressible fluid flow, the velocity field is where
x , y are in meters and t is in seconds. Acceleration in m/s2 at the point x =10 m and y = 0 , as
measured by a stationary observer is
For an incompressible flow, the existence of components of acceleration for different types of flow
is described in the table below.
Which one of the following options connecting the left column with the right column is correct?
Velocity in a two-dimensional flow field is specified as: u = x2 y ; v = −y2 x . The magnitude of
the rate of angular deformation at a location ( x = 2 m and y = 1 m) is ____ s-1.
(Important : you should answer only the numeric value)
For a plane irrotational flow, equi-potential lines and streamlines are
Flow around a Rankine half-body is represented by the superposition of
It is required to carry out model studies on a boat having a characteristic length of 3.6 m and
travelling at a speed of 3 m/s. Assume the acceleration due to gravity as 10 m/s2 and neglect the
effects due to viscous and surface tension forces. The value of appropriate non-dimensional number
is ____
Which one of the following velocity profiles typically represents a fully developed incompressible,
turbulent flow in a pipe?
Consider an incompressible, laminar flow past a circular cylinder of diameter d . The flow is
uniform at the far upstream. Which one of the following figures typically represents the wake
velocity profile just downstream of the cylinder?