NTSE SAT Mathematics Papers 11

This is NTSE SAT Mathematics Papers 11 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

If \(A = \left( {\begin{array}{*{20}{c}} a&b \\ c&d \end{array}} \right)\)where \(a,\,\,b,\,\,c,\,\,d \in R\)such that AB = BA for each \(2 \times 2\)matrix B, then \({b^2} + {c^2}\):

A
0
B
1
Correct
C
Can have any positive value
D
2

If each side of a rectangle is increased by 20 percent then the percentage increase in its area is:

A
20 percent
B
44 percent
Correct
C
30 percent
D
40 percent

The perimeter and area of a sector are 10 cm and 20 sq. cm respectively. Then the length of the arc is:

A
10 cm or 4 cm
B
10 cm or 5 cm
C
10 cm or 8 cm
Correct
D
20 cm or 2 cm

If \(\sec \theta + \cos \theta = \sqrt 5 \), the value of \({\sec ^2}\theta + {\cos ^2}\theta \)is:

A
25
B
3
Correct
C
5
D
7

The value of \({\sin ^2} + 5^\circ + {\sin ^2}10^\circ + {\sin ^2}15^\circ + .....{\sin ^2}90^\circ \)is

A
8
B
9
C
\(9\frac{1}{2}\)
Correct
D
10

ABC is triangle with vertices A(1, 2), \(B\left( {\pi ,2} \right),\,\,C\left( {1,\pi } \right)\), then the orthocenter of the \(\Delta ABC\)has coordinates:

A
\(\left( {\frac{{\pi + 1}}{2},\frac{{2 + \pi }}{2}} \right)\)
B
\(\left( {\frac{\pi }{3},\frac{\pi }{3}} \right)\)
C
(1, 2)
Correct
D
\(\left( {\frac{{2 + \pi }}{3},\frac{{4 + \pi }}{3}} \right)\)

The circle S1 has centre at (1, 2) and radius 3; the circle S2 has centre at (9, 8) and radius 7. The circles S1 and S2 touch at the point whose coordinates are:

A
\(\left( {\frac{{17}}{{10}},\frac{{19}}{{10}}} \right)\)
B
\(\left( {\frac{{17}}{5},\frac{{19}}{5}} \right)\)
Correct
C
\(\left( {\frac{{33}}{{10}},\frac{{31}}{{10}}} \right)\)
D
\(\left( {\frac{{33}}{5},\frac{{31}}{5}} \right)\)

It is given that there are 6 straight lines in a plane so that no three of them are concurrent and no two are parallel. Then the number of points of intersection among the given six straight line is:

A
12
B
3
C
15
Correct
D
6

AB is a chord of a circle S subtending an angle of \(20^\circ \)at the centre. Suppose AB has length 1008 units and CD is another chord having length 1512 units, then the angle subtended by CD at the centre is:

A
\(30^\circ \)
Correct
B
\(40^\circ \)
C
\(25^\circ \)
D
\(60^\circ \)

If \(x = 3 + \sqrt 8 \), then \({x^4} + \frac{1}{{{x^4}}}\)is:

A
1056
B
1156
C
1154
Correct
D
1158

If the line segments joining the points (a, b) and (c, d) subtends a right angle at the origin, then which of the question is correct?

A
ab + cd = 0
B
ac + bd = 0
Correct
C
ac
D
ab

If the pair of linear equations \({a_1}x + {b_1}y + {c_1} = 0\) and \({a_2}x + {b_2}y + {c_2} = 0\) has infinite number of solutions then the correct condition is

A
\(\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{c_1}}}{{{c_2}}}\)
B
\(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} = \frac{{{c_1}}}{{{c_2}}}\)
Correct
C
\(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} \ne \frac{{{c_1}}}{{{c_2}}}\)
D
\(\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}}\)

If \(x = \frac{1}{{2 - \sqrt[{}]{3}}}\) then the value of \({x^2} - \frac{1}{{{x^2}}}\;\) is

A
12
Correct
B
\(8\sqrt 3 \)
C
14
D
\(12\sqrt 3 \)

In the triangle PQR, \(\frac{{2 - \sqrt 2 }}{2}\)\(MN\parallel QR\) and MN divides the triangle into two parts of equal areas, then \(\frac{{QM}}{{PQ}}\)

A
\(\frac{{2 - \sqrt 2 }}{2}\)
B
\(\frac{1}{{\sqrt 2 + 1}}\)
C
\(\frac{{\sqrt 2 - 1}}{{\sqrt 2 }}\)
Correct
D
\(\frac{1}{{\sqrt 2 - 1}}\)

The arithmetic mean of two given positive numbers is 2. If the larger number is increased by 1, the geometrical mean of the numbers becomes equal to the arithmetic mean of the given numbers. Then the harmonic mean of the given numbers is

A
\(\frac{3}{2}\)
Correct
B
\(\frac{2}{3}\)
C
\(\frac{1}{2}\)
D
2