NTSE SAT Mathematics Papers 14

NTSE SAT Mathematics Papers 14

This is NTSE SAT Mathematics Papers 14 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Find the area of the shaded region 1 the radius of each circle is 1 cm:
Question 1 figure 1
  • A
    None of the above
  • B
    \(\left( {2 - \pi x\sqrt 3 } \right)c{m^2}\)
  • C
    \(\left( {5 - \pi x\sqrt 3 } \right)c{m^2}\)
  • D
    \(\left( {4 - \pi } \right)c{m^2}\)
    Correct
2
Three Positive integers \({a_1},{a_2},{a_3}\)are in AP such that:\({a_1},{a_2},{a_3} = 33\)and \({a_1}{\text{ }}x{\text{ }}{a_2}{\text{ }}x{\text{ }}{a_3} = 1155\)values of \({a_1},{a_2},{a_3}\)are:
  • A
    9, 8, 16
  • B
    7, 11, 15
    Correct
  • C
    10, 11, 12
  • D
    8, 11, 14
3
If \(A\left( {{x_1},{y_1}} \right),B\left( {{x_2}{y_2}} \right)\)and \(C\left( {{x_3},{y_3}} \right)\)are the vertices of \(\Delta ABC\)then the co-ordinates of the centroid of the triangle are:
  • A
    \(\left( {3\left( {{x_1} + {x_2} + {x_3}} \right),3\left( {{y_1} + {y_2} + {y_3}} \right)} \right)\)
  • B
    \(\left( {\frac{{{x_1}^2 + {x_2}^2 + {x_3}^2}}{3},\frac{{{y_1}^2 + {y_2}^2 + {y_3}^2}}{3}} \right)\)
  • C
    None of these
  • D
    \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3}} \right)\)
    Correct
4
If \(\alpha ,\beta ,\gamma ,\left( {\alpha + \beta + \gamma } \right),\left( {\beta + \gamma - \alpha } \right)\)and \(\left( {\gamma + \alpha - \beta } \right)\)be acute angles such that:\(\sin \left( {\alpha + \beta - \gamma } \right)\frac{1}{2},\cos \left( {\beta + \gamma - \alpha } \right) = \frac{1}{2},\tan \left( {\gamma + \alpha - \beta } \right) = 1\)value of \(\gamma \)is:
  • A
    105\(^\circ \)
  • B
    \(52\frac{1}{2}^\circ \)
    Correct
  • C
    \(37\frac{1}{2}^\circ \)
  • D
    45\(^\circ \)
5
Evaluate: \(\frac{{{{\sec }^2}54^\circ - {{\cot }^2}36^\circ }}{{\cos e{c^2}57^\circ - {{\tan }_2}33^\circ }} + 2{\sin _2}38^\circ .{\sec _2}52^\circ - {\sin ^2}45^\circ \)
  • A
    \(\frac{1}{2}\)
  • B
    2
  • C
    \(\frac{5}{2}\)
    Correct
  • D
    \(\frac{7}{5}\)
6
Equivalent of \(\frac{6}{{20}}\)is
  • A
    26 percent
  • B
    6 percent
  • C
    30 percent
    Correct
  • D
    20 percent
7
How many surfaces in solid cylinder-
  • A
    2
  • B
    3
    Correct
  • C
    4
  • D
    1
8
The order of any matrix is \(3 \times 2\)then no. of element it are-
  • A
    3
  • B
    6
    Correct
  • C
    5
  • D
    2
9
If (x-2) is factor of polynomial \({x^3} + 2{x^2} - kx + 10\). Then the value of k will be
  • A
    13
    Correct
  • B
    10
  • C
    9
  • D
    16
10
From a pack of playing cards all cards whose numbers are multiple of 3 are removed. A card is now drawn at random. Then the probability that the card drawn is an even number is red card-
  • A
    \(\frac{{10}}{{52}}\)
  • B
    \(\frac{1}{5}\)
    Correct
  • C
    \(\frac{1}{4}\)
  • D
    \(\frac{3}{{13}}\)
11
Median of 4, 5, 10, 6, 7, 14, 9 and 15 will be-
  • A
    9
  • B
    6
  • C
    7
  • D
    8
    Correct
12
Mean proportion of 64 and 225 will be-
  • A
    120
    Correct
  • B
    90
  • C
    60
  • D
    30
13
If the points (-2, -5), (2, -2) and (8, a) are collinear then value of a will be-
  • A
    \(\frac{1}{2}\)
  • B
    \( - \frac{5}{2}\)
  • C
    \(\frac{3}{2}\)
  • D
    \(\frac{5}{2}\)
    Correct
14
If the number 13, 15, 17, 18 and n are arranged in ascending order and their arithmetic mean and median are equal then value of n will be-
  • A
    27
  • B
    None of these
  • C
    28
  • D
    22
    Correct
15
\({\log _{10}}1 = ?\)
  • A
    0
    Correct
  • B
    1000
  • C
    100
  • D
    10