Q. If $si{n}^2(3x+45)+co{s}^2(2x+60)=1$ then $x=$ ...............

1. $30$
2. $60$
3. $15$
4. $0$

Q. To get the terminating decimal expansion of a rational number $\frac{p}{q}$. if $q=2^m{5}^n$ then $m$ and $n$ must belong to .................

1. $R$
2. $N\cup${$0$}
3. $N$
4. $Z$

Q. The probability of compliment event of impossible event is ..................

1. 0.5
2. 0.46
3. 0
4. 1

Q. If O(0, 0) and P(-8, 0) then co-ordinates of its midpoint are .............

1. (-4, 0)
2. (0, -4)
3. (4, 0)
4. (0, 0)

Q. In an isosceles right angled triangle $\Delta ABC$, r = ..................

1. 2
2. 1
3. $2-\sqrt{2}$
4. $1-\frac{1}{\sqrt{2}}$

Q. $(1,0),(0,1),(1,1)$ are the co-ordinates of vertices of a triangle. The triangle is ............. triangle.

1. Isosceles
2. Obtuse angled
3. Acute angled
4. Equilateral

Q. Find the probability of having 5 Sundays in the month of February in leap year 2004.

1. 0
2. 2/7
3. 1/7
4. 1

Q. The ratio of the radii of two cones having equal heights is $2:3$ then ratio of their volumes is ...................

1. $3:2$
2. $9:4$
3. $8:27$
4. $4:9$

Q. From the graph the value of $OA=$ ...................

1. $0$
2. $a^2+b^2$
3. $\sqrt{a^2+b^2}$
4. $\sqrt{a+b}$

Q. The graph of $p\left(x\right)=5x+3$, where x $\epsilon$ R is?

1. A parabola
2. A line
3. A ray
4. A line segment

Q. To find the length of a ladder making an angle $\theta$ with wall ................. trigonometric ratio is used.

1. $cosec\theta$
2. $tan\theta$
3. none
4. $cot\theta$

Q. From given figure tan A.tan C equals to:

1. 2
2. $\frac{1}{\sqrt{2}}$
3. $\sqrt{2}$
4. 1

Q. .................. is true for a tangent of a circle.
P: line intersect circle in one & only one point
Q: line and circle must be in same plane.
R: line passes from the centre of a circle.

1. $Q$ and $R$
2. Only $Q$
3. $P$ and $Q$
4. Only $P$

Q. In $\Delta ABC$, D, E and F are midpoints of $\overline{AB},\overline{BC}$ and $\overline{AC}$ respectively. If $A\left(\Delta ABC\right)=40$ then $A\left(\Delta DEF\right)=$ ..................

1. $10$
2. $20$
3. $\frac{40}{3}$
4. $5$

Q. For polynomial $p\left(x\right)=x^2-4x+3,\alpha +\beta =$ .................( where $\alpha and\beta$ are roots of polynomial.)

1. Positive fraction
2. Negative integer
3. Positive integer
4. Zero

Q. In given figure, co-ordinates of foot of perpendicular P are ..............

1. (5, 0)
2. (-5, 1)
3. (-1, 0)
4. (0, -1)

Q. If radius of circle is decreased by 10% then there is ................ decrease in its area.

1. 21%
2. 19%
3. 10%
4. 20%

Q. The conjugate surd of $2-\sqrt{3}$ is ..................

1. $2-(-\sqrt{3})$
2. $-2-\sqrt{3}$
3. $3+\sqrt{2}$
4. $\frac{1}{2-\sqrt{3}}$

Q. If $co{s}^2{45}^o-co{s}^2{30}^o=x.cos{45}^{o}sin{45}^o$ then $x=$ ................

1. -1/2
2. 2
3. 1/2
4. 3/4

Q. For the zeroes $\alpha$ & $\beta$ of polynomial $P\left(x\right)=a{x}^2+bx+c,\frac{1}{\alpha }+\frac{1}{\beta }=$ ....................

1. $-\frac{b}{c}$
2. $\frac{c}{a}$
3. none
4. $-\frac{b}{a}$

Q. Total area of the given closed figure will be ................. square units.

1. 45
2. 40
3. 31
4. 25

Q. In given figure, the minimum distance to reach from point "C" to point "A" will be ....................

1. $a^2$
2. 2
3. $\sqrt{2}$
4. 2a

Q. If the circumference of base of a hemisphere is 2$\pi$ then it volume is ................... cm${}^3$.

1. $\frac{2\pi }{3}{r}^3$
2. $\frac{8\pi }{3}$
3. $\frac{\pi }{12}$
4. $\frac{2\pi }{3}$

Q. The graph of polynomial $P\left(x\right)=ax-b$, where $a\ne 0;a,b\epsilon R$ intersect intersects $X-axis$ at

1. $(\frac{b}{a},0)$
2. $(0,\frac{b}{a})$
3. $(-\frac{b}{a},0)$
4. $(-\frac{a}{b},0)$

Q. Select the correct option given below:
From the figure, AB = ...................

1. $8$
2. $12$
3. $4$
4. $16$

Q. If the ratio of the height of tower and the length of its shadow is 1 : $\sqrt{3}$, then the angle of elevation of the sum has measure ................

1. 60${}^o$
2. 45${}^o$
3. 30${}^o$
4. 75${}^o$

Q. In the given cylinder the stick of maximum length ................. can be kept inside it.

1. 10
2. 12
3. 13
4. 17

Q. In the figure, from one handkerchief from four corners, sectors P, Q, R, S each of 2 cm are cut, whose sum is P + Q + R + S = $A_1$ and a circle of diameter 4 cm from the centre is cut whose area is $A_2$, then .................... is possible

1. $A_1\ne A$
2. $A_1<A_2$
3. $A_1=A_2$
4. $A_1>A_2$

Q. Formula to find area of sector is .............

1. $\frac{1}{2}rl$
2. $\frac{\pi r^2\theta }{180}$
3. $\frac{\pi r\theta }{360}$
4. $\pi r^2$

Q. From the given figure AD = ....................

1. $\sqrt{3}$
2. $2$
3. $2\sqrt{3}$
4. $\frac{\sqrt{3}}{2}$