NTSE SAT Mathematics Papers 05

This is NTSE SAT Mathematics Papers 05 .. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

Graph drawn from the equation \(y = {x^2} - 3x - 4\)will be-

A
Straight line
B
Parabola
Correct
C
Circle
D
Hyperbola

For which values of ‘a’ and ‘b’ does the following pair of linear equations and infinite number of solutions- 2x + 3y = 7, (a – b)x + (a + b)y = 3a + b - 2

A
a = 2, b = 4
B
a = 4, b = 2
C
a = 1, b = 5
D
a = 5, b = 1
Correct

If \({b^2} - 4ac \geq \)then the roots of quadratic equation \(a{x^2} + bx + c = 0\)is-

A
\(\frac{b}{{2a}} \pm \frac{{\sqrt {{b^2} - 4ac} }}{{2a}}\)
B
\( - \frac{b}{{2a}} \pm \frac{{\sqrt {{b^2} - 4ac} }}{{2a}}\)
C
\(\frac{b}{{2a}} \pm \frac{{\sqrt {{b^2} + 4ac} }}{{2a}}\)
Correct
D
\( - \frac{b}{{2a}} \pm \frac{{\sqrt {{b^2} + 4ac} }}{{2a}}\)

The sum of the third and seventh terms of an A.P. is 6 and their product then common difference is-

A
\( \pm 1\)
B
\( \pm 2\)
C
\( \pm \frac{1}{2}\)
Correct
D
\( \pm \frac{1}{4}\)

In a given figure in trapezium ABCD if \(AB\parallel CD\)then value of x is-

A
\(\frac{8}{{29}}\)
B
20
Correct
C
\(\frac{{29}}{8}\)
D
\(\frac{1}{{20}}\)

If points (x, 0), (0, y) and (1, 1) are Collinear then the relation is-

A
x + y = xy
Correct
B
x + y + xy = 0
C
x + y + 1 = 0
D
x + y =1

If \(Sin(A + B) = \frac{{\sqrt 3 }}{2},\,\,Cos\left( {A - B} \right) = \frac{{\sqrt 3 }}{2}\) and \(0 < A + B \leq 90^\circ \), A>B then the value of A and B are-

A
\(A = 30^\circ ,\,\,B = 0^\circ \)
B
\(A = 45^\circ ,\,\,B = 15^\circ \)
Correct
C
\(A = 60^\circ ,\,\,B = 30^\circ \)
D
\(A = 0^\circ ,\,\,B = 30^\circ \)

If the angle of elevation of sun increases from \(0^\circ \;\,to\,\,90^\circ \)then the changes in length of shadow of Tower will be-

A
Length of shadow will be zero
Correct
B
Length of shadow decreases
C
Length of shadow increases
D
No changes in length of shadow

The perimeter of square and circumference of Circle are equal, the area of square is \(121{m^2}\)then the area of Circle is-

A
\(14\pi {m^2}\)
B
\(21\,\pi \,{m^2}\)
C
\(49\,\pi \,{m^2}\)
Correct
D
\(7\pi {m^2}\)

A drinking glass is in the shape of a frusturm of a cone of height 14 cm. The diameter of its two circular ends are 4 cm. and 2 cm. then the capacity glass is-

A
\(101\frac{1}{3}c{m^3}\)
B
\(101\frac{2}{3}c{m^3}\)
C
\(102\frac{1}{3}c{m^3}\)
D
\(102\frac{2}{3}c{m^3}\)
Correct

The median and mode of a frequency distribution are 525 and 500 then mean of same frequency distribution is-

A
527.5
B
75
C
537.5
Correct
D
107.5

The author of the book “The Book on games of chances” based on probability theory is-

A
P. D. Pherma
B
J. Cardon
Correct
C
R. S. Woodwards
D
P. S. Laplace

Rationalizing the denominator of \(\frac{5}{{\sqrt 3 - \sqrt 5 }}\)is-

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

Value of \(\frac{{{2^{100}}}}{2}\)is

A
\({5^{100}}\)
B
\({2^{50}}\)
C
1
D
\({2^{99}}\)
Correct

The number of Straight line drawn from one point to any other point are-

A
2
B
3
C
4
D
1
Correct