NTSE SAT Mathematics Papers 22

NTSE SAT Mathematics Papers 22

This is NTSE SAT Mathematics Papers 22.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
For positive x and y, the LCM is 225 and HCF is 15. There
  • A
    Is exactly one such pair
  • B
    Are exactly four such pair
  • C
    Are exactly two such pair
    Correct
  • D
    Are exactly three such pair
2
In the figure, a semi-circle with centre O is drawn on AB. The ratio of the larger shaded area to the smaller shaded area is
Question 2 figure 1
  • A
    \(\frac{{4\pi - 2\sqrt 3 }}{{2\pi - 2\sqrt 3 }}\)
  • B
    \(\frac{{3\pi - 2\sqrt 3 }}{{2\pi - 2\sqrt 3 }}\)
  • C
    \(\frac{{4\pi - 3\sqrt 3 }}{{3\pi - 3\sqrt 3 }}\)
  • D
    \(\frac{{4\pi - 3\sqrt 3 }}{{2\pi - 3\sqrt 3 }}\)
    Correct
3
In\(\Delta ABC\), angle B is obtuse. The smallest circle which covers the triangle is the
  • A
    Circle with BC as diameter
  • B
    Circumcircle
    Correct
  • C
    Circle with AC as diameter
  • D
    Circle with AB as diameter
4
Which of the number can be expressed as the sum of square of two positive integers, as well three positive integers?
  • A
    250
    Correct
  • B
    75
  • C
    100
  • D
    192
5
If P is a point inside the scalene triangle ABC such that \(\Delta ABC\), \(\Delta BPC\) and \(\Delta CPA\) have the same area, then P must be
  • A
    In centre of \(\Delta ABC\)
  • B
    Circum centre of \(\Delta ABC\)
  • C
    Centroid of \(\Delta ABC\)
    Correct
  • D
    Ortho centre of \(\Delta ABC\)
6
If the line segments joining the midpoints of the consecutive side of a quadrilateral ABCD form a rectangle then ABCD must be a
  • A
    Rhombus
  • B
    All of these
    Correct
  • C
    Square
  • D
    Kite
7
\({C_1}\) and \({C_2}\) are two circles in a plane. If N is the total number of common tangents, then which of the following is wrong?
  • A
    N=4 when \({C_1}\) and \({C_2}\) are disjoint
  • B
    N can never be more than 4
  • C
    When \({C_1}\) and \({C_2}\) touch then N must be 3
    Correct
  • D
    N=2 when \({C_1}\) and \({C_2}\) interest but do not touch
8
The sides of a triangle are of lengths 20, 21 and 29 units. The sum of the lengths of altitudes will be
  • A
    70 units
  • B
    \(\frac{{1609}}{{21}}\) units
  • C
    \(\frac{{1609}}{{19}}\) units
    Correct
  • D
    49 units
9
If a, b, c be the 4th, 7th and 10th term of an AP respectively, then the sum of the roots of the equation \(a{x^2} - 2bx + c = 0\)
  • A
    is \( - \frac{b}{a}\)
  • B
    is \(\frac{{c + a}}{a}\)
    Correct
  • C
    cannot be determined unless some more information is given about the AP
  • D
    is \( - \frac{{2b}}{a}\)
10
PQRS is the smallest square whose vertices are on the respective sides of the square ABCD. The ration of the area of PQRS to ABCD is
  • A
    it is 2:3
  • B
    it is 1:3
  • C
    \(1:\sqrt 2 \)
  • D
    it is 1:2
    Correct
11
LCM of two numbers x and y is 720 and the LCM of numbers 12x and 5y is also 720. The number y is
  • A
    144
    Correct
  • B
    90
  • C
    180
  • D
    120
12
When a natural number x is divided by 5, the remainder is 2. When a natural number by is divided by 5, the remainder is 4. The remainder is z when x + y is divided by 5. The value of \(\frac{{2z - 5}}{3}\) is
  • A
    -1
    Correct
  • B
    -2
  • C
    2
  • D
    1
13
If the zeroes of the polynomial \(64{x^3} - 144{x^2} + 92x - 15\) are in A.P., then the difference between the largest and the smallest zeroes of the polynomial is
  • A
    \(\frac{3}{4}\)
  • B
    1
    Correct
  • C
    \(\frac{1}{2}\)
  • D
    \(\frac{7}{8}\)
14
x and y are two non–negative numbers such that 2x + y = 10. The sum of the maximum and minimum values of (x + y) is
  • A
    6
  • B
    15
    Correct
  • C
    9
  • D
    10
15
The number of integral solutions of the equation \(7\left( {y + \frac{1}{y}} \right) - 2\left( {{y^2} + \frac{1}{{{y^2}}}} \right) = 9\) is
  • A
    1
    Correct
  • B
    2
  • C
    0
  • D
    3