NTSE SAT Mathematics Papers 21

NTSE SAT Mathematics Papers 21

This is NTSE SAT Mathematics Papers 21.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A solid metal sphere of surface area \({S_1}\)is melted and recast into a number of smaller spheres. \({S_2}\)is the sum of the surface areas of all the smaller spheres. Then
  • A
    \({S_1} = {S_2}\)
  • B
    \({S_1} > {S_2}\)
  • C
    \({S_2} > {S_1}\)
    Correct
  • D
    \({S_1} = {S_2}\) only if all the smaller spheres of equal radii
2
Which of the following is an irrational number?
  • A
    23.10100100010000…
    Correct
  • B
    23.232323
  • C
    \(\frac{{{{\left( {1 + \sqrt 3 } \right)}^3} - {{\left( {1 - \sqrt 3 } \right)}^3}}}{{\sqrt 3 }}\)
  • D
    \(\sqrt {41616} \)
3
Re. 1 and Rs 5 coins are available (as many required). Find the smallest payments which cannot be made by these coins, if not more than 5 coins are allowed.
  • A
    12
  • B
    8
  • C
    14
    Correct
  • D
    3
4
Median of a data number which has number of observations below and above it. The median set is a an equal below and of the data 1, 9, 4, 3, 7, 6, 8, 8, 12, 15 is
  • A
    8
  • B
    7
  • C
    Any number between 7 and 8
    Correct
  • D
    7.5
5
Read the following passage and answer the questions given after it. Ray Bradbury is regarded as one of the greats of 20th century science fiction along with Isaac Asimov and A.C. Clarke. He established himself at the age of thirty with The Martial Chronicle, which perhaps remains his best known work. The book celebrates space travel, but it is also critical of the social abuses that modern technology had made possible. Through other writers had represented science and technology as a mixed bag of blessings, his book had a great impact. Initially his audience was small as most readers had no patience with jargon. His popularity grew as he avoided technical words and expressed his ideas about the future in common language. Ray Bradbury became famous because
  • A
    Of the book The Martial Chronicle that he wrote.
    Correct
  • B
    He wrote in futuristic language.
  • C
    He was friends with Isaac Asimov and A.C. Clarke.
  • D
    He wrote in futuristic language.
6
If \(\phi \) is an acute angle such that \(\tan \phi = \frac{2}{3}\), then evaluate \(\left( {\frac{{1 + \tan \phi }}{{\sin \phi + \cos \phi }}} \right)\left( {\frac{{1 - \cot \phi }}{{\sec \phi + \cos ec\phi }}} \right)\)
  • A
    \( - \frac{1}{5}\)
    Correct
  • B
    \(\frac{1}{5}\)
  • C
    \(\frac{4}{{\sqrt {13} }}\)
  • D
    \(\frac{{ - 4}}{{\sqrt {13} }}\)
7
The value of the expression \(\frac{1}{{\sqrt {11 - 2\sqrt {30} } }} - \frac{3}{{\sqrt {7 - 2\sqrt {10} } }} - \frac{4}{{\sqrt {8 + 4\sqrt 3 } }}\) after simplification is
  • A
    1
  • B
    \(2\sqrt {10} \)
  • C
    \(\sqrt {30} \)
  • D
    0
    Correct
8
The minimum value of the polynomial \(p(x) = 3{x^2} - 5x + 2\) is
  • A
    \(\frac{1}{6}\)
  • B
    \(\frac{1}{{12}}\)
  • C
    \( - \frac{1}{{12}}\)
    Correct
  • D
    \( - \frac{1}{6}\)
9
For the equation \({\left| x \right|^2} + \left| x \right| - 6 = 0\),
  • A
    There are four roots
  • B
    The product of the roots is -6
  • C
    The sum of the roots is -1
  • D
    The product of the roots is -4
    Correct
10
In \(\Delta ABC\), D is a point on BC such that 3BD=BD. If each side of the triangle is 12 cm, then AD equals
  • A
    \(4\sqrt 6 cm\)
  • B
    \(4\sqrt 5 cm\)
  • C
    \(4\sqrt 7 cm\)
    Correct
  • D
    \(4\sqrt {11} cm\)
11
In \(\Delta ABC\), \(\overline {XY} \) is parallel to \(\overline {AC} \) and divides the triangle into the two parts of equal area. Then the \(\frac{{AX}}{{AB}}\) equals
Question 11 figure 1
  • A
    \(\frac{{2 - \sqrt 2 }}{2}\)
    Correct
  • B
    \(\frac{{\sqrt 2 - 1}}{2}\)
  • C
    \(\frac{{\sqrt 2 + 1}}{2}\)
  • D
    \(\frac{{2 + \sqrt 2 }}{2}\)
12
P is a point in the interior of an equilateral triangle with side a units. If \({p_1}\), \({p_2}\) and \({p_3}\) are the distances of P from the three sides of the triangle, them \({p_1} + {p_2} + {p_3}\)
  • A
    Equals \(\frac{{2a}}{3}\) units
  • B
    Equals \(\frac{{a\sqrt 3 }}{2}\) units
    Correct
  • C
    Cannot be determined unless the location of P is specified
  • D
    Is more than a units
13
In how many ways can a given square be cut into two congruent trapeziums?
  • A
    Exactly 12
  • B
    Exactly 8
  • C
    More than 12
    Correct
  • D
    Exactly 4
14
In how many ways can you partition 6 into ordered summands? (For example, 3 can be partitioned in 3 ways as : 1+2, 2+1, 1+1+1)
  • A
    29
  • B
    27
  • C
    33
  • D
    31
    Correct
15
The number of integers n (<20) for which \({n^2} - 3n + 3\) is a perfect square is
  • A
    0
    Correct
  • B
    1
  • C
    3
  • D
    2