NTSE SAT Mathematics Papers 09

NTSE SAT Mathematics Papers 09

This is NTSE SAT Mathematics Papers 09 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
In an A.P, 5 times the 5th term is equal to 8 times the 8th term, then its 13th term is
  • A
    -13
  • B
    -1
  • C
    -12
  • D
    0
    Correct
2
If \(x + \frac{1}{x} = 5\), then \({x^3} - 5{x^2} + x + \frac{1}{{{x^3}}} - \frac{5}{{{x^2}}} + \frac{1}{x} = .............\)
  • A
    0
    Correct
  • B
    5
  • C
    -5
  • D
    10
3
The surface area of a cylindrical pipe, open at both ends is 628 sq. m. The difference between its radius and length is 15 m, the length being larger, if the pipe was closed at one end, the amount of water that it can hold is,
  • A
    None of these
  • B
    \(525\pi \,\,cu.\,m\)
  • C
    \(550\pi \,\,cu.\,m\)
  • D
    \(500\pi \,\,cu.\,m\)
    Correct
4
If a + b + c = 0 and \({a^2} + {b^2} + {c^2} = k\;({a^2} - b)\) then k =
  • A
    3
  • B
    1
  • C
    2
    Correct
  • D
    0
5
Given 5A9 + 3B7 + 2C8 = 1114, then the maximum value of C is
  • A
    7
  • B
    5
  • C
    8
  • D
    None of these
    Correct
6
Two fair die are thrown. The probability the sum of the numbers appearing is 6 is
  • A
    \(\frac{1}{{36}}\)
  • B
    \(\frac{1}{6}\)
  • C
    \(\frac{5}{{36}}\)
    Correct
  • D
    \(\frac{5}{6}\)
7
The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the axis is,
  • A
    It is 1:2
  • B
    It is 2:1
  • C
    It is 2:3
    Correct
  • D
    It is 3:2
8
If the co-ordinate of two opposite vertices of a square are (a, b) and (b, a) then the area of the square is
  • A
    \(2{\left( {a + b} \right)^2}\)
  • B
    \({\left( {a - b} \right)^2}\)
    Correct
  • C
    \(2{\left( {a - b} \right)^2}\)
  • D
    \({\left( {a + b} \right)^2}\)
9
If \(Sinx + Si{n^2}x = 1\)the \(Co{s^8}x + 2Co{s^6}x + Co{s^4}x = ...........\)
  • A
    1
    Correct
  • B
    0
  • C
    2
  • D
    -1
10
\(1 - \frac{{Si{n^2}y}}{{1 + Cosy}} + \frac{{1 + Cosy}}{{Siny}} - \frac{{Siny}}{{1 - Cosy}} = .............\)
  • A
    \(Siny\)
  • B
    0
  • C
    \(Cosy\)
    Correct
  • D
    1
11
A tower is \(100\sqrt 3 m\) high. The angle of elevation of its top from a point 100 m. away from its foot is __________
  • A
    \(22\frac{{1^\circ }}{2}\)
  • B
    \(60^\circ \)
    Correct
  • C
    \(30^\circ \)
  • D
    \(45^\circ \)
12
In a \(\Delta PRS,\,\,\angle PRS = 120^\circ \). A point Q is taken on PR such that PQ = QS and QR = RS then \(\angle QPS = .................\)
  • A
    \(30^\circ \)
  • B
    \(45^\circ \)
  • C
    \(15^\circ \)
    Correct
  • D
    \(12^\circ \)
13
A chord of a circle of radius 7 cm. subtends an angle of \(90^\circ \)at its centre. The ratio of areas of smaller and larger segment is
  • A
    It is 1:10
    Correct
  • B
    None of these
  • C
    It is 2:7
  • D
    It is 1:11
14
The length of a ladder is exactly equal to the height of the wall it is leaning against. If the lower end of the ladder is kept on a bench of height 3 m and the bench is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. The height of the wall is:
  • A
    15 m
    Correct
  • B
    11 m
  • C
    18 m
  • D
    12 m
15
A cone of height 7 cm and base radius 3 cm is carved from a rectangular block of wood of dimensions \(10\,cm\,\, \times \,\,5cm\,\, \times \,\,2cm\). The percentage of wood wasted is
  • A
    66 percent
  • B
    34 percent
    Correct
  • C
    46 percent
  • D
    54 percent