NTSE SAT Mathematics Papers 01

NTSE SAT Mathematics Papers 01

This is NTSE SAT Mathematics Papers 01 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
In the adjacent figure, if \(\angle AOC = 110^\circ \), then the value of\(\angle D\) and \(\angle B\)respectively
Question 1 figure 1
  • A
    \(110^\circ ,25^\circ \)
  • B
    \(125^\circ ,55^\circ \)
  • C
    \(55^\circ ,110^\circ \)
  • D
    \(55^\circ ,125^\circ \)
    Correct
2
If \(a = \frac{9}{{\sqrt {11} - \sqrt 2 }};b = \frac{6}{{3\sqrt 3 }},\)then the relation between a and b is .....................
  • A
    \(a > b\)
    Correct
  • B
    \(a \leq b\)
  • C
    \(a + b > 1\)
  • D
    \(a < b\)
3
In a triangle XYZ, if the internal bisector of \(\angle X\) meets YZ at ‘P’, then .................
  • A
    \(\frac{{XY + XZ}}{{XZ}} = \frac{{YZ}}{{PZ}}\)
    Correct
  • B
    \(\frac{{XZ}}{{XY}} = \frac{{YP}}{{YZ}}\)
  • C
    \(\frac{{XY}}{{XZ}} = \frac{{PZ}}{{YP}}\)
  • D
    \(\frac{{XY}}{{PZ}} = \frac{{ZX}}{{YP}}\)
4
Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, the distance between their tops is .................
  • A
    14 m
  • B
    13 m
    Correct
  • C
    12 m
  • D
    11 m
5
If 'r' and 's' are the roots of the equation \(a{x^2} + bx + c = 0,\) then the value of \(\frac{1}{{{r^2}}} + \frac{1}{{{s^2}}}\) is…..
  • A
    \(\frac{{{b^2} - 4ac}}{{{c^2}}}\)
  • B
    \({b^2}-4ac\)
  • C
    \(\frac{{{b^2} - 2ac}}{{{c^2}}}\)
    Correct
  • D
    \(\frac{{{b^2} - 4ac}}{{2a}}\)
6
When the sum of the first ten terms of an A.P. is four times the sum of the first five terms. Then the k term is
  • A
    \(a\left( {2k - 1} \right)\)
    Correct
  • B
    \(2k + 1\)
  • C
    \(2k + 3\)
  • D
    \(a\left( {2k + 1} \right)\)
7
The value of \({\left[ {\sqrt[3]{{\sqrt[6]{{{a^9}}}}}} \right]^4}{\left[ {\sqrt[6]{{\sqrt[3]{{{a^9}}}}}} \right]^4}\)is ........................
  • A
    \({a^4}\)
    Correct
  • B
    \({a^{12}}\)
  • C
    \({a^8}\)
  • D
    \({a^{16}}\)
8
If the ratio of the legs of a right-angled triangle is 1:2, then the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex will be
  • A
    \(1:\sqrt 5 \)
  • B
    It is 1:4
    Correct
  • C
    It is 1:2
  • D
    \(1:\sqrt 2 \)
9
The sum of three numbers is 98. The ratio of the first to the second term is \(\frac{2}{3}\) and the ratio of the second to the third is \(\frac{5}{8}\) Then the second number is
  • A
    32
  • B
    30
    Correct
  • C
    20
  • D
    15
10
A cylindrical pencil of diameter 1.2 cm has one of its ends sharpened into a conical shape of height 1.4 cm. The volume of the material removed is (in cub. cms) .................
  • A
    it is 1.056
    Correct
  • B
    it is 42.24
  • C
    it is 4.224
  • D
    it is 10.56
11
If \(f:R \to R;g:R \to R\)are functions defined by \(f\left( x \right) = 3x - 1;g\left( x \right)\sqrt {x + 6} \)then the value of \(\left( {go{f^{ - 1}}} \right)\left( {2009} \right)\)is
  • A
    15
  • B
    16
  • C
    29
  • D
    26
    Correct
12
In the diagram, a squared ABCD has a side with a length of 6 cm. Circular arcs of radius 6 cm are drawn with centres B and D. What is the area of the shaded region in sq. cm?
Question 12 figure 1
  • A
    \(18\pi - 36\)
    Correct
  • B
    \(18\pi - 24\)
  • C
    \(18\pi \)
  • D
    \(36\pi \)
13
How many numbers between 3000 and 4000 can be formed from the digits 3, 4, 5, 6, 7 and 8; no digits being repeated in any number
  • A
    15 Nos.
  • B
    20 Nos.
  • C
    120 Nos.
  • D
    60 Nos
    Correct
14
If \({\log _{10}}2 = 0.3010,\) then the number of digits in \({256^{50}}\) is
  • A
    50
  • B
    121
    Correct
  • C
    256
  • D
    120
15
If sin A, cos A and tan A are in Geometric Progression, then \({\cot ^6}A - {\cot ^2}A\)is
  • A
    4
  • B
    2
  • C
    3
  • D
    1
    Correct