NTSE SAT Mathematics Papers 07

NTSE SAT Mathematics Papers 07

This is NTSE SAT Mathematics Papers 07 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If the heights and radii of a cone and a hemisphere are same then the ratio of their volumes is
  • A
    It is 2:3
  • B
    It is 1:2
    Correct
  • C
    It is 1:1
  • D
    It is 1:3
2
The lengths of two parallel chords of a circle are 6 cm and 8 cm. if the smaller chord is at distance 4 cm from the centre, then the distance of the other chord from the centre is
  • A
    3 cm
    Correct
  • B
    5 cm
  • C
    4 cm
  • D
    2 cm
3
In the figure given below, ABC is an equilateral triangle. D, E, F, G, H and I are the trisector points of the sides as shown. If the side of the triangle ABC is 6 cm, then the area of the regular hexagon DEFGHI is
Question 3 figure 1
  • A
    \(5\sqrt 3 \,c{m^2}\)
  • B
    \(6\sqrt 3 \,c{m^2}\)
    Correct
  • C
    \(4\sqrt 3 \,c{m^2}\)
  • D
    \(3\sqrt 3 \,c{m^2}\)
4
In the given, figure, \(\angle DBC = 22^\circ \) and \(\angle DCB = 78^\circ \)then \(\angle BAC\)is equal to
Question 4 figure 1
  • A
    \(78^\circ \)
  • B
    \(22^\circ \)
  • C
    \(80^\circ \)
    Correct
  • D
    \(90^\circ \)
5
In the given figure, ABC is an equilateral triangle whose side is \(2\sqrt 3 \). A circle is drawn which passes through the midpoints D, E and F of its sides. The area of shaded region is
Question 5 figure 1
  • A
    \(\frac{1}{4}\left( {3\pi - \sqrt 3 } \right)c{m^2}\)
  • B
    \(\frac{1}{4}\left( {4\pi - 3\sqrt 3 } \right)c{m^2}\)
    Correct
  • C
    \(\frac{1}{4}\left( {2\pi - \sqrt 3 } \right)c{m^2}\)
  • D
    \(\frac{1}{4}\left( {\pi - 3\sqrt 3 } \right)c{m^2}\)
6
If a cylinder of radius 3 cm and height of 10 cm is melted and recast into the shapes of small spheres of diameter 1 cm, then the number of spheres so formed is
  • A
    270
  • B
    135
  • C
    540
    Correct
  • D
    1080
7
The graph of y = p(x) is given below. The number of zeroes of polynomial p(x), is
Question 7 figure 1
  • A
    0
  • B
    1
  • C
    3
    Correct
  • D
    2
8
The center of a circle passing through the points (7, -5), (3, -7) and (3, 3) is
  • A
    (3, -2)
    Correct
  • B
    (5, -6)
  • C
    (5, -1)
  • D
    (3, 2)
9
In the given figure, \(\Delta ODC \sim \Delta OBA,\,\,\angle BOC = 115^\circ \)and \(\angle COD = 80^\circ \). Then \(\angle OAB\)is equal to
Question 9 figure 1
  • A
    \(65^\circ \)
  • B
    \(35^\circ \)
    Correct
  • C
    \(45^\circ \)
  • D
    \(80^\circ \)
10
\(\tan 43^\circ \tan 45^\circ \tan 47^\circ \)is equal to
  • A
    2
  • B
    1
    Correct
  • C
    \(\frac{1}{{\sqrt 3 }}\)
  • D
    \(\sqrt 3 \)
11
If \(\frac{a}{{a + b}} = \frac{{17}}{{23}}\), what is \(\frac{{a + b}}{{a - b}}\)equal to?
  • A
    \(\frac{{23}}{{17}}\)
  • B
    \(\frac{{23}}{{11}}\)
    Correct
  • C
    \(\frac{{11}}{{23}}\)
  • D
    \(\frac{{17}}{{32}}\)
12
If the annual decrease in the population of a town by 5 percent and the present population be 68590, what was the population three years ago?
  • A
    86000
  • B
    65000
  • C
    60000
  • D
    80000
    Correct
13
If the number 82\(*\)091 is divisible by 11, then the digit in the place of star-mark (\(*\)) will be
  • A
    7
  • B
    6
  • C
    9
  • D
    8
    Correct
14
The average of x numbers is 3x. If (x-1) is subtracted from each given number, what will be the new average?
  • A
    3(x-1)
  • B
    2x+1
    Correct
  • C
    2x-1
  • D
    Data inadequate
15
A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coins are in the ration 2:3:5 respectively. The number of 2 rupees coins is
  • A
    76
  • B
    52
  • C
    60
    Correct
  • D
    85