NTSE SAT Mathematics Papers 13

This is NTSE SAT Mathematics Papers 13 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

\(\sqrt {81} + \sqrt {0.81} = 10.09 - x,\)then \(x\)is equal to:

A
0.019
B
0.00019
C
0.19
Correct
D
0.0019

The greatest number among \({2^{50}},{3^{40}},{4^{30}},{5^{20}}\)is:

A
\({5^{20}}\)
B
\({3^{40}}\)
Correct
C
\({2^{50}}\)
D
\({4^{30}}\)

X takes 3 hours more than Y to walk 30 km, but if X doubles his pace, he is ahead of Y by \(1\frac{1}{2}\)hour. The speed of Y is:

A
2.5 km/hr
B
3.33 km/hr
C
10 km/hr
D
5 km/hr
Correct

Value of x is:

A
\(\frac{{ac}}{{b + c}}\)
Correct
B
\(\frac{{b + c}}{{ac}}\)
C
\(\frac{{cb}}{{b + c}}\)
D
\(\frac{{b + a}}{{b + c}}\)

If \({3^{(2{x^2}-{9x})}}= {81^{ - 1}}\) then\(x\)is:

A
2, 1/4
B
2, 1
C
4, 1/2
Correct
D
Both 1 and 2

If \(x\)is \(z\% \)of y, then y will be how much percent of x?

A
\(\frac{{1000}}{{{z^2}}}\)
B
\(\frac{{1000}}{z}\)
C
\(\frac{{100}}{{{z^2}}}\)
D
\(\frac{{10000}}{z}\)
Correct

If \(a\cos \theta - b\sin \theta = c,\)then \(a\sin \theta + b\cos \theta = ?\)

A
\( \pm \sqrt {{a^2} + {b^2} - {c^2}} \)
Correct
B
\( \pm \sqrt {{a^2} + {b^2} + {c^2}} \)
C
None of these
D
\( \pm \sqrt {{c^2} - {a^2} - {b^2}} \)

Diameter of moon is approximately one fourth of the diameter of earth. What fraction of the volume of the earth is the volume of moon?

A
1/8
B
1/64
Correct
C
64/1
D
1/4

Which one is false?

A
\(d = \frac{{{t_{n + 1}} - {t_{n - 1}}}}{2}\)
B
\(d = {a_n} - {a_{n - 1}}\)
C
\(d = {S_{n - 2}} - {S_{n - 1}}\)
Correct
D
\({t_n} = {S_n} - {S_{n - 1}}\)

In the given figure a circle is inscribed in a \(\Delta PQR\)with \(PQ = 10\)cm, \(QR = 12\)cm, Length of PL is:

A
3cm
B
10cm
C
5cm
D
7cm
Correct

A student obtains 75 percent 80 percent and 85 percent marks in three subjects. If the marks of any other subject is added, then his average cannot be less than:

A
65 percent
B
60 percent
Correct
C
70 percent
D
80 percent

The angle of elevation of a cloud from a point 60 m above a lake is \(30^\circ \)and angle of depression of the reflection of cloud in the lake is \(60^\circ \). The height of the cloud is

A
60 m
B
50 m
C
120 m
Correct
D
140 m

If \(\sqrt {19 + \sqrt {30 + \sqrt {32 + x} } } = 5\)then the value of x is:

A
4
Correct
B
3
C
5
D
2

If \(f\left( x \right) = \frac{{{x^3} + 6{x^2} + 9x + 12}}{{{x^2} + 2x + 7}}\)then \({\left( {f\left( 3 \right)} \right)^2} - f\left( 2 \right)f\left( 1 \right)\)will be:

A
\(\frac{{164972}}{{9075}}\)
Correct
B
\(\frac{{165575}}{{10000}}\)
C
\(\frac{{164875}}{{9000}}\)
D
None of these

With the money I have I can buy 50 pens or 150 pencils. I keep 10 percent of it aside for taxi fare and with the remaining money I purchase 54 pencils and 'p' pens. The value of 'p' is

A
29
B
32
C
30
D
27
Correct