Sample Paper Scholarship Test Worksheet With Answers - Dual/integrated Program For Two Year Page 7
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96
SP01/DIPTYIPTY/201618
79. a and b are the two sides adjacent to the right angle of a
86. A motor boat whose speed is 18 km/h in still water takes 1
right angled triangle and p is the perpendicular drawn to
hour more to go 24 km upstream than to return downs tream
2
the hypotenuse from the opposite vertex. Then p
is equal
to the same spot. Then the speed of the stream is
to
(1) 5
(2) 6
1
1
(3) 7
(4) 8
2
2
(1)
a
+
b
(2)
+
2
2
87. The ratio in which the yaxis divides the line segment
a
b
joining the points (5, –6) and (–1, –4)
2 2
a b
2
2
(3)
(4)
a
-
b
(1) 5 : 1
(2) 1 : 5
2
2
a
+
b
(3) 2 : 3
(4) 1 : 1
80. In a right angled triangle ABC right angled at A,
88. Two poles are erected on either bank of a river just
perpendicular D is drawn from A to the hypotenuse BC,
opposite to each other. One pole is 40 m high. From the
then which of the following is true
top and foot of this pole, the angles of elevation of top of
I.
D
ABD
~
D
CAD
the other pole are 30° and 60° respectively. Find the height
of the other pole (in m)
II.
D
ABD
@ D
CAD
(1) 60 3
III.
D
ADB
~
D
CAB
Of these statements the correctones are combination of
(2) 60
(1) I and II
(2) I and III
(3) 50
(3) II and III
(4) I, II and III
(4) 50 3
81. The sum of the third and seventh term of an A.P. is 8. Then
89. What is the area of circle with centre as O?
the sum of the first nine terms of this progression is
Statements:
(1) 24
(2) 32
A. Two chords AB and CD intersect at right angle to each
(3) 36
(4) Cannot be determined
other at E. AE = 16, EO = 6, AC = 8 5 .
sec
q -
1
=
?
B. Chord AB is the longest chord in the circle.
82. For any real values of q,
sec
q +
1
(1) The question cannot be answered even by using both
(1) cot q – cosec q
(2) sec q – tan q
statements together
(3) cosec q – cot q
(4) tan q – sec q
(2) The question can be answered only by using both the
statements together, but cannot be answered by using
83. The sum of length, breath and height of a cuboid is 19 cm
either statements alone
and its diagonal is 11 cm. Find the surface area of the
2
cuboid in cm
(3) The question can be answered by using either of the
statements alone
(1) 120
(2) 140
(4) The question can be answered by using one of the
(3) 160
(4) 240
statement's alone but cannot by using the other
84. If in a circle, a chord of length 5 2 cm makes a right angle
statement alone
at the centre, then the length of the radius of the circle is
90. The angle of elevation of a jet fighter from a point A on
(in cm)
the ground is 60°. After a flight of 15 seconds, the angle
(1) 10
(2) 4
of elevation changes to 30°. If the jet is flying at a height
(3) 6
(4) 5
of 1500 3 m, find the speed at which the jet is flying.
85. If x = a (sinq + cosq); y = b (sinq – cosq) then the value of
(1) 720 km/hr
2
2
x
y
(2) 620 km/hr
+
is
2
2
a
b
(3) 520 km/hr
(1) 0
(2) 1
(4) 820 km/hr
(3) 2
(4) –2
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