NTSE SAT Mathematics Papers 20

This is NTSE SAT Mathematics Papers 20.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

An open box is made from a square lamina of side 12 cm, by cutting equal squares at the corners and folding up the remaining flaps. The volume of this box cannot be

A
115 c.c.
B
130 c.c.
Correct
C
120 c.c.
D
125 c.c.

A has a pair of triangles corresponding sides proportional, and B has a pair of pentagon with corresponding sides proportional, \({S_1}\)= A’s triangles must be similar \({S_2}\)= B’s pentagons must be similar Which of the following statement is correct?

A
\({S_2}\) is true, but \({S_1}\) is not true
B
Both \({S_1}\) and \({S_2}\) are true
C
\({S_1}\) is true but \({S_2}\) is not true
Correct
D
Neither \({S_1}\) and \({S_2}\) is true

\(\Delta ABC\)is an equilateral triangle of side \(2\sqrt 3 cms\). P is any point in the interior of \(\Delta ABC\). If x, y, z are the distances of P from the sides of the triangle, then x + y + z =

A
\(2 + \sqrt 3 cms\)
B
3 cms
Correct
C
4 cms
D
5 cms

Which of the following numbers is the fourth power of a natural number?

A
6765207
B
6765206
C
6765209
D
6765201
Correct

The square of an odd integer must be of the form:

A
8n + 1
Correct
B
6n + 2
C
6n + 1
D
4n + 1 but may not be 8n + 1

ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let \(\delta \)be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of \(\delta \)is :

A
\(\frac{{\pi {a^2}}}{4}\)
B
\({a^2}(1 - \pi )\)
C
\({a^2}(\pi - 1)\)
D
\({a^2}\left( {\frac{{(4 - \pi )}}{4}} \right)\)
Correct

The value of \(\tan 1^\circ \tan 2^\circ \tan 3^\circ ....\tan 89^\circ \)

A
0
B
2
C
4
D
1
Correct

\({\text{a}}{{\text{x}}^2} + {\text{ bx}} + {\text{c}} = 0\), where a, b, c are real, has real roots if :

A
ac > 0 and b is zero
B
\({b^2} > 3ac\)
C
a, b, c are integers
D
c = 0
Correct

An open box A is made from a square piece of tin by cutting equal squares S at the corners and folding up the remaining flaps. Another open box B is made similarly using one of the squares S. If U and V are the volumes of A and B respectively, then which of the following is not possible?

A
V > U
B
Minimum value of U > maximum value of V
Correct
C
U = V
D
U > V

Which of the following statements holds always?

A
Every parallelogram is a trapezium
Correct
B
Every rectangle is a square
C
Every parallelogram is a rectangle
D
Every rhombus is a square

Which of the following polygons are uniquely determined when all the sides are give?

A
pentagon
B
hexagon
C
triangle
Correct
D
quadrilateral

There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total numbers of feet are 77. Then the number of dogs is:

A
4
B
5
Correct
C
Not determinable due to insufficient data
D
6

All the arcs in the following diagram are semi-circles. This diagram shows two paths connecting A to B. Path I is the single large semi-circle and Path II consists of the chain of small semi- circles.

A
Path I is of the same length as Path II. Only if the number of semi circles is not more than 4
B
Path I of the same length of Path II
Correct
C
Path I is longer than Path II
D
Path I is shorter than Path II

One integer is chosen out of 1, 2, 3, …., 100. What is the probability that it is neither divisible by 4 nor by 6.

A
0.59
B
0.41
C
0.33
D
0.67
Correct

\(\sqrt {{{\left( {a - b} \right)}^2}} + \sqrt {{{\left( {b - a} \right)}^2}} \) is:

A
Never zero
B
Positive if and only if a>b
C
Positive only if \(a \ne b\)
Correct
D
Always zero