NTSE SAT Mathematics Papers 23

This is NTSE SAT Mathematics Papers 23.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

A circle with area A \(c{m^2}\) is contained in the interior of a larger circle with area (A + B) \(c{m^2}\)and the radius of the larger circle is 4 cm. if A, B, A + B are in arithmetic progression, then the diameter (in cm) of the smaller circle is

A
\(\frac{{\sqrt 3 }}{2}\)
B
\(\frac{{8\sqrt 3 }}{3}\)
Correct
C
\(\frac{{4\sqrt 3 }}{3}\)
D
\(2\sqrt 3 \)

Each of the sides of a triangle is 8 cm less than the sum of its other two sides. Area of the triangle (in\(c{m^2}\)) is

A
16
B
8
C
\(16\sqrt 3 \)
Correct
D
\(8\sqrt 3 \)

If \(\cos ecx - \cot x = \frac{1}{3}\) , where \(x \ne 0\), then the value of \({\cos ^2}x - {\sin ^2}x\) is

A
\(\frac{9}{{25}}\)
B
\(\frac{{16}}{{25}}\)
C
\(\frac{7}{{25}}\)
Correct
D
\(\frac{8}{{25}}\)

A sector with acute central angle \(\theta \) is cut from a circle of diameter 14 cm. The area (in \(c{m^2}\) ) of the circle circumscribing the sector is

A
\(\frac{7}{2}{\sec ^2}\frac{\theta }{2}\)
B
\(\frac{{77}}{2}{\sec ^2}\frac{\theta }{2}\)
Correct
C
\(\frac{{77}}{2}{\sec ^2}\theta \)
D
\(\frac{{22}}{7}{\sec ^2}\frac{\theta }{2}\)

In the figure, PQSO is a trapezium in which \(PQ\parallel OS,\angle POS = 135^\circ \) and \(\angle OSQ = 90^\circ \). Point P, Q and R lie on a circle with centre O and radius 12 cm. The area of the shaded part, in \(c{m^2}\) , is

A
\(73\frac{2}{7}\)
B
\(73\frac{5}{7}\)
C
\(61\frac{2}{7}\)
D
\(61\frac{5}{7}\)
Correct

A solid sphere is cut into identical pieces by three mutually perpendicular planes passing through its centre. Increase in total surface area of all the pieces with respect to the total surface area of the original sphere is

A
250%
B
175%
C
125%
D
150%
Correct

A right circular cylinder has its height equal to two times its radius. It is inscribed in a right circular cone having its diameter equal to 10 cm and height 12 cm, and the axes of both the cylinder and the cone coincide. Then, the volume (in \(c{m^3}\) ) of the cylinder is approximately.

A
128.7
B
127.5
Correct
C
118.6
D
107.5

In the figure, ABCD is a square of side 1 dm and \(\angle PAQ = 45^\circ \). The perimeter (in dm) of the triangle PQC is

A
\(1 + \sqrt 3 \)
B
\(1 + \sqrt 2 \)
C
\(2\sqrt 2 - 1\)
D
2
Correct

In the figure, ABC is a triangle in with AD bisects \(\angle A\), AC = BC, \(\angle B = 72^\circ \) and CD = 1 cm. Length of BD (in cm) is

A
\(\frac{1}{2}\)
B
\(\frac{{\sqrt 5 - 1}}{2}\)
Correct
C
1
D
\(\frac{{\sqrt 3 + 1}}{2}\)

In the figure, BC is a chord of the circle with centre O and A is a point on the minor arc BC. Then, \(\angle BAC - \angle OAC\) is equal to

A
\(80^\circ \)
B
\(90^\circ \)
Correct
C
\(60^\circ \)
D
\(30^\circ \)

In the figure, \(\Delta APB\) is formed by three tangents to the circle with centre O. If \(\angle APB = 40^\circ \), then the measure of \(\angle BOA\)is

A
\(70^\circ \)
Correct
B
\(60^\circ \)
C
\(50^\circ \)
D
\(55^\circ \)

(5, –10), (–15, 15) and (5, 5) are the coordinates of vertices A, B and C respectively of \(\Delta ABC\) and P is a point on median AD such that AP : PD = 2 : 3. Ratio of the areas of the triangle PBC and ABC is

A
It is 3:5
Correct
B
It is 3:4
C
It is 2:3
D
It is 4:5

P is a point on the graph of y = 5x + 3. The coordinates of a point Q are (3, -2). If M is the mid-point of PQ, then M must lie on the line represented by

A
y = 5x – 7
Correct
B
y = 5x + 1
C
\(y = \frac{5}{2}x - \frac{7}{2}\)
D
\(y = \frac{5}{2}x + \frac{1}{2}\)

Three – digit numbers formed by using digits 0, 1, 2 and 5 (without repetition) are written on different slips with distinct number on each slip, and put in a bowl. One slip is drawn at random from the bowl. The probability that the slip bears a number divisible by 5 is

A
\(\frac{5}{9}\)
Correct
B
\(\frac{1}{3}\)
C
\(\frac{2}{3}\)
D
\(\frac{4}{9}\)

The mean of fifteen different natural numbers is 13. The maximum value for the second largest of these number is

A
53
B
52
C
51
Correct
D
46