Q.1
Which of the following rational has terminating decimal expansion ?
  • \(\frac{64}{445}\)
  • \(\frac{13}{3125}\)
  • \(\frac{29}{343}\)
  • \(\frac{77}{210}\)
Q.2
\(3.\overline{27}\) is
  • an integer
  • a rational number
  • a natural number
  • 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
  • \(x^2+qx+p\)
  • \(x^2-px+q\)
  • \(qx^2+px+1\)
  • \(px^2+qx+1\)
Q.4
If zeros of the polynomial \(f\left( x \right) =x^3-3px^2+qx-r \) are in AP then
  • \(2p^3=pq-r\)
  • \(2p^3=pq+r\)
  • \(p^3=pq-r\)
  • \(p^3=pq+r\)
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
  • 10
  • 6
  • 3
  • 1
Q.6
The value of \(\sqrt{6+\sqrt{6+\sqrt{6+........}}}\) is
  • 4
  • 3
  • .2
  • 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 \(ab = ?\)
  • –3
  • 3.5
  • 6
  • 3
Q.8
If \(\frac{1}{x+2}\), \(\frac{1}{x+3}\), \(\frac{1}{x+5}\) are in A.P. then \(x = ?\)
  • 5
  • 3
  • 1
  • 2
Q.9
If the sum of 1st n terms of an A.P. is \(3n^2+n\) then its common difference is
  • 6
  • 4
  • 14
  • 10
Q.10
Sides of two similar triangles are in the ratio \(4 : 9\). Areas of these triangles are in the ratio -
  • \(2 : 3\)
  • \(4 : 9\)
  • \(81 : 16\)
  • \(16 : 81\)
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
  • 100 m
  • 120 m
  • 25 m
  • 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 \(a^3 + b^3 + c^3 = ?\)
  • \(abc\)
  • \(0 \)
  • \(a + b + c\)
  • \(3abc\)
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
  • \((2,4)\)
  • \((3,5)\)
  • \((4,2)\)
  • \((5,3)\)
Q.14
If \(\sin \theta + \sin^2 \theta = 1\), then \(\cos^{12} \theta + 3 \cos^{10} \theta + 3 \cos^8 \theta + \cos^6 \theta + 2 \cos^4 \theta + 2 \cos^2 \theta -2= ?\)
  • 1
  • 2
  • 3
  • 0
Q.15
The value of \(\sin^2 29^0 + \sin^2 61^0\) is
  • \(2\sin^2 29^0\)
  • \(2\sin^2 61^0\)
  • 0
  • 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
  • \(50^0\)
  • \(60^0\)
  • \(70^0\)
  • \(80^0\)
Q.17
The length of the diameter of a circle whose area and circumference are numerically equal, is
  • \(\frac{\pi}{2}\)
  • \(2\pi\)
  • 2
  • 4
Q.18
The mean of first n natural number isThen \(n = ?\)
  • 15
  • 30
  • 14
  • 29
Q.19
The median of first 10 prime number is
  • 11
  • 12
  • 13
  • 14
Q.20
Which of the following cannot be the probability of an event ?
  • 2.3
  • -1.5
  • 0.8
  • 0.5
0 h : 0 m : 1 s