NTSE SAT Mathematics Papers 12

NTSE SAT Mathematics Papers 12

This is NTSE SAT Mathematics Papers 12 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If the quotient obtained on dividing \(({x^4} + 10{x^3} + 35{x^2} + 50x + 29)\) by (x + 4) is \({x^2} - a{x^2} + bx + 6,\;\)then the value of \(\frac{{a + b}}{{a - b}}\) is
  • A
    \(\frac{{53}}{{25}}\)
  • B
    \(\frac{{ - 5}}{{17}}\)
    Correct
  • C
    \(\frac{{25}}{{33}}\)
  • D
    \(\frac{{17}}{5}\)
2
The value of \(\cos {1^0}\;\;\cos {2^{0\;\;}}\cos {3^0}\;.......\;\cos {179^0}\) is
  • A
    1
  • B
    -1
  • C
    \(\frac{1}{{\sqrt 2 }}\)
  • D
    0
    Correct
3
If the equations \({x^2} + ax + b = 0\) and \({x^2} + bx + a = 0\) have a common root, then the value of a + b is
  • A
    1
  • B
    -1
  • C
    2
    Correct
  • D
    0
4
A person walked diagonally across a square plot. Approximately, what was the percentage saved by not walking along the edges?
  • A
    35 percent
  • B
    30 percent
    Correct
  • C
    20 percent
  • D
    25 percent
5
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
    0
    Correct
  • B
    23
  • C
    15
  • D
    9
6
If x, 2y, 3z are in arithmetic progressions, where the distinct numbers x, y, z are in geometric progression, then the common ratio of the geometric progression is
  • A
    \(\frac{1}{2}\)
  • B
    2
  • C
    3
  • D
    \(\frac{1}{3}\)
    Correct
7
Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in \(A \cup B\)?
  • A
    6
    Correct
  • B
    18
  • C
    9
  • D
    3
8
3 balls drawn randomly form a beg containing 3 black, 5 red and 4 blue balls. What is the probability that the balls drawn contains balls of different colours?
  • A
    \(\frac{3}{{11}}\)
    Correct
  • B
    \(\frac{2}{{11}}\)
  • C
    \(\frac{1}{3}\)
  • D
    \(\frac{1}{2}\)
9
The smallest number which when increased by 17 is exactly divisible by both 520 and 468 is
  • A
    4697
  • B
    4663
    Correct
  • C
    4680
  • D
    4656
10
The area of a square inscribed inside a circle of radius 6 cm is
  • A
    36 square cm
  • B
    108 square cm
  • C
    144 square cm
  • D
    72 square cm
    Correct
11
If the sum of an arithmetic progression is the same for p terms as for the q terms, find the sum for (p + q ) terms.
  • A
    1
  • B
    0
    Correct
  • C
    2
  • D
    4
12
If \(^{12}{P_r}\; = {\;^{11}}{P_6} + {6.^{11}}{P_5}\;,\) then r is equal to
  • A
    11
  • B
    5
  • C
    6
    Correct
  • D
    7
13
In a graph the order of the nodes A, B, C and D are respectively 5, 3,6, and 2. Then the number of arcs and regions are respectively
  • A
    8, 4
  • B
    4, 8
  • C
    8, 6
    Correct
  • D
    6, 8
14
If 3 equal circles of radius 3 cm each touch each other, then area of the shaded portion is
Question 14 figure 1
  • A
    \(\frac{{\sqrt 3 }}{2}(2 - \pi )sq\;cm\)
  • B
    \(\frac{9}{2}(\sqrt 3 - \pi )sq\;cm\)
  • C
    \(\frac{9}{2}(2\sqrt 3 - \pi )\;sq\;cm\)
    Correct
  • D
    \(\frac{3}{2}(\sqrt 3 - \pi )\,sq\;cm\)
15
25 buses are running between two places P and Q. What is the total number of way that a person can travel from P to Q and return by a different bus?
  • A
    600
    Correct
  • B
    675
  • C
    576
  • D
    625