NTSE SAT Mathematics Papers 04

NTSE SAT Mathematics Papers 04

This is NTSE SAT Mathematics Papers 04 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The angle of depression of a car moving with uniform speed towards the building as observed from the top of the building is found to be \(30^\circ \). The same angle of depression changes to \(60^\circ \)after 12 seconds. Then at what time it will reach the base.
  • A
    8 sec
  • B
    4 sec
  • C
    12 sec
  • D
    6 sec
    Correct
2
The value of \(S = \frac{1}{{2 \times 7}} + \frac{1}{{7 \times 12}} + \frac{1}{{12 \times 17}} + ...... + \frac{1}{{252 \times 257}}\)is
  • A
    \(\frac{{35}}{{2 \times 257}}\)
  • B
    \(\frac{{51}}{{2 \times 257}}\)
    Correct
  • C
    \(\frac{5}{{257}}\)
  • D
    \(\frac{{25}}{{2 \times 257}}\)
3
The lines \(x + \sqrt 3 \) y= 4 and \(\sqrt 3 x + y = 4\)are
  • A
    Equidistant from the origin
    Correct
  • B
    Perpendicular to each other
  • C
    Parallel to each other
  • D
    Identical
4
The radius of a cylindrical box is 8 cm and the height is 3 cm. The number of cm that may be added to either the radius or the height so that in either case the volume of the cylinder increases by same magnitude is
  • A
    \(7\frac{1}{2}\)
  • B
    1
  • C
    24
  • D
    \(5\frac{1}{3}\)
    Correct
5
The roots of the equation \(l{x^2} + nx + n = 0\)are in the ratio p:q. Then
  • A
    \(\sqrt {\frac{p}{q}} - \sqrt {\frac{q}{p}} - \sqrt {\frac{n}{1}} = 0\)
  • B
    \(\sqrt {\frac{p}{q}} - \sqrt {\frac{q}{p}} + \sqrt {\frac{n}{1}} = 0\)
  • C
    \(\sqrt {\frac{p}{q}} + \sqrt {\frac{q}{p}} + \sqrt {\frac{n}{1}} = 0\)
    Correct
  • D
    \(\sqrt {\frac{p}{q}} + \sqrt {\frac{q}{p}} + \sqrt {\frac{n}{1}} = 1\)
6
The straight line 3x + y=9 divides the segment joining the points (1,3) and (2,7) in the ration
  • A
    It is 4:3
  • B
    It is 3:4
    Correct
  • C
    It is 4:2
  • D
    It is 2:4
7
\(\sqrt {999 \times 1000 \times 1001 \times 1002 + 1} \)is
  • A
    1001001
  • B
    1000999
    Correct
  • C
    1001999
  • D
    1000989
8
Two dice are thrown at the same time. Then the probability of getting this total of at least 8 is
  • A
    \(\frac{5}{{36}}\)
  • B
    \(\frac{5}{6}\)
  • C
    0
  • D
    \(\frac{5}{{12}}\)
    Correct
9
The value of \(\tan 6^\circ .\tan 42^\circ .\tan 66^\circ .\tan 78^\circ \)is
  • A
    \(\frac{1}{2}\)
  • B
    0
  • C
    1
    Correct
  • D
    -1
10
The value of \(Cosec10^\circ - \sqrt 3 Sec10^\circ \)is
  • A
    2
  • B
    4
    Correct
  • C
    1
  • D
    \(\frac{1}{4}\)
11
A motor cycle and a scooter were sold for Rs. 12000 each. The motor cycle was sold at a loss of 20 percent of the cost and the scooter at a gain of 20 percent of the cost. The entire transaction resulted in:
  • A
    Loss of Rs 1000
    Correct
  • B
    Gain of Rs 1000
  • C
    Gain of Rs 2000
  • D
    No loss or gain
12
A man invested part of Rs 4500 at 4 percent interest and the rest at 6 percent interest per annum. If his annual return on each investment is the same, then the average rate of interest which he gets on the whole of Rs 4500 is
  • A
    4.6 percent
  • B
    5.2 percent
  • C
    4.8 percent
    Correct
  • D
    5 percent
13
A boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
  • A
    5.5 km/hr
  • B
    10 km/hr
  • C
    8 km/hr
  • D
    6 km /hr
    Correct
14
A person walked diagonally across a square plot. Approximately, what was the percentage saved by not walking along the edges ?
  • A
    30 percent
    Correct
  • B
    35 percent
  • C
    25 percent
  • D
    20 percent
15
If 9 times the 9th term in an arithmetic progression is equal to 15 times the 15th term in the arithmetic progression, what is the 24th term ?
  • A
    23
  • B
    0
    Correct
  • C
    15
  • D
    9