NTSE SAT Mathematics Papers 10

NTSE SAT Mathematics Papers 10

This is NTSE SAT Mathematics Papers 10 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The mean of n numbers \({x_1},\,\,{x_2},..............,\,\,{x_n}\)is M. If \({x_1}\)is replaced by ‘a’, the new mean is
  • A
    \(\frac{{nM - {x_1} + a}}{n}\)
    Correct
  • B
    \(\frac{{M - {x_1} + a}}{n}\)
  • C
    None of these
  • D
    \(\frac{{nM - a + {x_1}}}{n}\)
2
Which of the following is correct for the given data 55, 38, 69, 24, 89, ?
  • A
    Mean = median
    Correct
  • B
    None of these
  • C
    Mean = mode
  • D
    Median = mode
3
The mean of n numbers is M. if 1 is added to the first number, 2 is added to the second number, …………… N is added to the \({n^{th}}\)number then the new mean is
  • A
    \(M + \frac{n}{2}\)
  • B
    M + n
  • C
    \(M + \frac{{n + 1}}{2}\)
    Correct
  • D
    None of these
4
A bag contains 5 red and some blue balls. If the probability of drawing a blue ball is three times the probability of drawing a red ball then the number of blue balls in the bag is ____________
  • A
    8
  • B
    12
  • C
    15
    Correct
  • D
    10
5
\(\frac{{\tan x}}{{Secx - 1}} - \frac{{Sinx}}{{1 + Cosx}} = ................\)
  • A
    2 tanx
  • B
    2 Sinx
  • C
    2 Cotx
    Correct
  • D
    6 Cosx
6
Let N be the set of natural numbers and P be the set of prime integers in N. If \(A = n/n \in N,n\) is a multiple of some prime \(p \in p\), then N – A = \(\left[ {n \in N/n \notin A} \right]\)is
  • A
    A finite set of cardinality greater than 2
  • B
    Empty set
  • C
    Of cardinality 2
  • D
    A singleton set
    Correct
7
The sum of the first k natural numbers is A, for a certain k>1; the sum of their cubes is B, then \({\log _{\sqrt A }}B\) is:
  • A
    4
    Correct
  • B
    2
  • C
    3
  • D
    1
8
Given that P(x) and Q(x) are polynomials of degree 3 with real coefficients, which one of the following is not true?
  • A
    \(\deg \left[ {P(x) + Q(x)} \right] = 3\)
    Correct
  • B
    \(\deg \left[ {P(x) \times Q(x)} \right] = 6\)
  • C
    \(\deg \left[ {P(x) - Q(x)} \right] \leq 3\)
  • D
    \(\deg \left[ {{{\left[ {P(x)} \right]}^2} \times Q{{\left[ {(x)} \right]}^3}} \right] = 15\)
9
Suppose that a quadratic polynomial \({x^2} + bx + 1,\,\,b \in R\), has two zeros which are both real then which one of the following necessarily true?
  • A
    b has at most four distinct values
  • B
    b has a unique value
  • C
    b has at most two distinct values
  • D
    b can have infinitely many values
    Correct
10
It is given that there is no solution to the system \(x + 2y = 3,\,\,\,\,ax + by = 4\). Which one of the following is true?
  • A
    a has a unique value
  • B
    b has a unique value
  • C
    a has exactly two values
  • D
    a can have more than one value
    Correct
11
the unit digit in the chemical expansion of \({7^{25}}\)is:
  • A
    1
  • B
    5
  • C
    7
    Correct
  • D
    3
12
If the sum S of three consecutive even numbers is a perfect square between 200 and 400, then the square root of S is:
  • A
    16
  • B
    15
  • C
    18
    Correct
  • D
    19
13
The numbers are arranged in the descending order: 108, 94, 88, 82, x+7, x-7, 60, 58, 42, 39. If the median is 73, the value of x is:
  • A
    73
    Correct
  • B
    75
  • C
    72
  • D
    76
14
The mean of 16 numbers is 48. If each number is divided by 4 and diminished by 3, then the new mean is:
  • A
    12
  • B
    9
    Correct
  • C
    48
  • D
    52
15
A natural number k is chosen from the set {1, 2, 3, ................. , 100}. The probability that it is prime, is:
  • A
    \(\frac{{23}}{{100}}\)
  • B
    \(\frac{1}{4}\)
    Correct
  • C
    \(\frac{{19}}{{100}}\)
  • D
    \(\frac{1}{5}\)