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A boat goes 32 km upstream and 36 km downstream in 7 hours. In 9 hours, it can go 40 km upstream and 48 km downstream. If x represents the speed of the boat in still water in km/hr and y represents the speed of the stream in km/hr, then_______.

A x + y = 12, x – y = 8
B x + y = 5, x – y = 11
C x + y = 6, x – y = 10
D x + y = 10, x – y = 6

A rectangular park is 100 m by 50 m. It is surrounded by semicircular flower beds all round. Find the cost of levelling the semicircular flower beds at 60 paise per m².

A ₹ 31425
B ₹ 28260
C ₹ 352.40
D ₹ 282.60

A sum of money is borrowed and paid back in two annual installments of Rs 882 each allowing 5% compound interest. The sum borrowed was _______.

ARs 1620
BRs 1640
CRs 1680
DRs 1700

In the given figure (not drawn to scale), OABC is a quadrilateral with ABC on horizontal ground and O is vertically above A. M is the mid-point of BC. If ∠BAC = 90°, AB = AC = 16 cm and OA = 12 cm, calculate the length of OB.



A25 cm
B15 cm
C20 cm
D28 cm

Find the value of if 1 + cot²θ =

A 2
B 3
C –2
D 1

A circle with area A₁ is contained in the interior of a larger circle with area A₁ + A₂. If the radius of the larger circle is 3 units and A₁, A₂, A₁ + A₂ are in A.P., then the radius of the smaller circle is _____.

A units
B 1 unit
C 2 units
D units

Read the following information carefully to answer the given question.
Fifty books belonging to different subjects, viz. History (8), Geography (7), Literature (13), Psychology (8) and Science (14), are placed on a shelf. They are arranged in an alphabetical order subject to the condition that no two books of the same subject are placed together so long as books of other subjects are available. Unless otherwise mentioned, all counting is done from the left.
Counting from the right end, the fifth book from the right of 39th book is ______.

AHistory
BPsychology
CGeography
DScience

Study the following information carefully to answer the given question.
M K K I D N E T T Q O B F H A A G T U U X W L S R I
Each of these letters gets a numerical value based on its position in the above arrangement, such as, 1 for M, 2 for K, 4 for I and so on.
Value of A is exactly equal to the total value of which of the following pairs?
(i) DO (ii) QE (iii) MH

AOnly (i)
BOnly (ii)
COnly (iii)
DBoth (i) and (ii)

Let f(x) = x² + bx + c where b, c are integers. If f(x) is a factor of both x⁴ + 6x² + 25 and 3x⁴ + 4x² + 28x + 5, then the value of f(1) is ______

A 1
B 2
C 3
D None of these