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NTSE
Ntse Assam Question Paper 2019
Sat
Quiz 3
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Q.1
Which of the following rational has terminating decimal expansion ?
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\(\frac{64}{445}\)
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\(\frac{13}{3125}\)
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\(\frac{29}{343}\)
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\(\frac{77}{210}\)
Q.2
\(3.\overline{27}\) is
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an integer
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a rational number
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a natural number
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an irrational number
Q.3
If \(\alpha\) and \(\beta\) are the zeros of the polynomial \(f\left( x \right) =x^2+px+q\),then a polynomial having \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) as its zero is
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\(x^2+qx+p\)
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\(x^2-px+q\)
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\(qx^2+px+1\)
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\(px^2+qx+1\)
Q.4
If zeros of the polynomial \(f\left( x \right) =x^3-3px^2+qx-r \) are in AP then
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\(2p^3=pq-r\)
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\(2p^3=pq+r\)
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\(p^3=pq-r\)
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\(p^3=pq+r\)
Q.5
The value of \(K\) for which the system of equations \(x + 2y – 3 = 0\) and \(5x + ky + 7 = 0\) has no solution, is
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10
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6
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3
0%
1
Q.6
The value of \(\sqrt{6+\sqrt{6+\sqrt{6+........}}}\) is
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4
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3
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.2
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3.5
Q.7
If \(x = 1\) is a common root of the equations \(ax^2 + ax + 3 = 0\) and \(x^2 + x + b = 0\), then \(ab = ?\)
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–3
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3.5
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6
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3
Q.8
If \(\frac{1}{x+2}\), \(\frac{1}{x+3}\), \(\frac{1}{x+5}\) are in A.P. then \(x = ?\)
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5
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3
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1
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2
Q.9
If the sum of 1st n terms of an A.P. is \(3n^2+n\) then its common difference is
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6
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4
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14
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10
Q.10
Sides of two similar triangles are in the ratio \(4 : 9\). Areas of these triangles are in the ratio -
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\(2 : 3\)
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\(4 : 9\)
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\(81 : 16\)
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\(16 : 81\)
Q.11
A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is
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100 m
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120 m
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25 m
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200 m
Q.12
If the centroid of the triangle formed by the points \((a,b)\), \((b,c)\) and \((c,a)\) is at the origin then \(a^3 + b^3 + c^3 = ?\)
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\(abc\)
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\(0 \)
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\(a + b + c\)
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\(3abc\)
Q.13
The co-ordinates of the point P dividing the line segment joining the points \(A(1,3)\) and \(B(4,6)\) in the ratio \(2 : 1\) are
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\((2,4)\)
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\((3,5)\)
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\((4,2)\)
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\((5,3)\)
Q.14
If \(\sin \theta + \sin^2 \theta = 1\), then \(\cos^{12} \theta + 3 \cos^{10} \theta + 3 \cos^8 \theta + \cos^6 \theta + 2 \cos^4 \theta + 2 \cos^2 \theta -2= ?\)
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1
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2
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3
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0
Q.15
The value of \(\sin^2 29^0 + \sin^2 61^0\) is
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\(2\sin^2 29^0\)
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\(2\sin^2 61^0\)
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0
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1
Q.16
If tangents \(PA\) and \(PB\) from a point \(P\) to a circle with centre \(O\) are inclined to each other at an angle of \(80^0\) then \(\angle POA\) is equal to
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\(50^0\)
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\(60^0\)
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\(70^0\)
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\(80^0\)
Q.17
The length of the diameter of a circle whose area and circumference are numerically equal, is
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\(\frac{\pi}{2}\)
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\(2\pi\)
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2
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4
Q.18
The mean of first n natural number isThen \(n = ?\)
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15
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30
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14
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29
Q.19
The median of first 10 prime number is
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11
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12
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13
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14
Q.20
Which of the following cannot be the probability of an event ?
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2.3
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-1.5
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0.8
0%
0.5
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