Q. The tenth term of an A.P. : $\sqrt{2},3\sqrt{2},5\sqrt{2},7\sqrt{2}$, ..... is:

1. $12$
2. $10\sqrt{2}$
3. $19\sqrt{2}$
4. $11\sqrt{2}$

Q. If $M$ is the foot of the perpendicular drawn from $P(-5,2)$ on X-axis then the co-ordinates of $M$ are ______.

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

Q. If $(1,4)$ is the centroid of the triangle having the vertices $(a,3),(4,b)$ and $(-3,2)$ then $a=$ _______ and $b=$ _______.

1. $-7,-2$
2. $2,7$
3. $-2,-7$
4. $-4,2$

Q. If the angle of elevation of the sun at $$8:00$$ Oclock is $$\alpha$$ and at $$10:00$$ Oclock is $$\beta$$ then ______ holds.

Q. The angle of elevation of the sum when the length of the shadow of a tower is equal to its height is:

1. ${60}^o$
2. ${30}^o$
3. ${45}^o$
4. ${90}^o$

Q. Which of the following is true for the points $X$ and $Y$ if the co-ordinates of the mid-points $P$ of $\overline{XY}$ are $(-2,3)$?

1. $X(-4,-2)$ and $Y(0,4)$
2. $X(-4,3)$ and $Y(2,2)$
3. $X(-6,2)$ and $Y(2,4)$
4. $X(0,2)$ and $Y(-2,4)$

Q. The cost of a pen is $Rs.15$. If its cost decreases by $Rs.x$ then the number of pens purchased of $Rs.600$ is _______.

1. $\frac{15+x}{600}$
2. $\frac{600}{15+x}$
3. $\frac{600}{15-x}$
4. $\frac{15-x}{600}$

Q. If $\theta$ is the measure of an acute angle and $\sqrt{3}\sin \theta =\cos \theta$ then $\theta =$ _________.

1. ${45}^{\circ }$
2. ${90}^{\circ }$
3. ${60}^{\circ }$
4. ${30}^{\circ }$

Q. Which of the following equations, is not a quadratic equation?

1. $4x^2-7x+3=0$
2. $2x-7=0$
3. $3x^2-4x+1=0$
4. $4x^2-3=0$

Q. The length of the minor arc of $\odot (0,6)$ is _______.

1. More than $6\pi$
2. Less than $6\pi$
3. $6\pi$
4. $10\pi$

Q. In the given figure $l\parallel \overleftrightarrow{AB}$ and $l$ intersects $\overline{AC}$ and $\overline{BC}$ at $P$ and $Q$ respectively. If $CP=3,PA=4,QB=6$ then $BC=$ ________.

1. $12.5$
2. $10.5$
3. $7.5$
4. $4.5$

Q. ________ lies on X-axis.

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

Q. Which of the following is true for a line $l$ lying in the same plane and intersecting $△ABC$ but not perpendicular to $\overline{BC}$?

1. $l$ intersects $\overline{AB}$ or $\overline{AC}$
2. $l$ intersects $\overline{AC}$
3. $l$ does not intersects $\overline{AB}$ or $\overline{AC}$
4. $l$ intersects $\overline{AB}$

Q. $\tan 5^{\circ }\cdot \tan {25}^{\circ }\cdot \tan {45}^{\circ }\cdot \tan {65}^{\circ }\cdot \tan {85}^{\circ }=$ ________.

1. $1$
2. $2$
3. $5$
4. $0$

Q. In $△ABC,\angle A$ is a right angle. If $AD\perp BC$ and $DϵBC$ then which of the following statements are true?
1. $A{D}^2=BD\cdot DC$
2. $B{C}^2=AD\cdot DC$
3. $A{B}^2=BD\cdot BC$
4. $A{C}^2=CD\cdot BD$.

1. Statements $1$ and $4$ are true
2. Statements $1$ and $3$ are true
3. Statements $1,3$ and $4$ are true
4. Statements $1$ and $2$ are true

Q. For a quadratic equation if $D<0$ then which of the following is true?

1. Real roots do not exist
2. Roots are real and equal
3. Roots are rational and distinct
4. Roots are real and distinct

Q. The mid-points of the sides of any quadrilateral are the vertices of ________.

1. Parallelogram
2. Trapezium
3. Rectangle
4. Rhombus

Q. If the roots of the quadratic equation $5x^2-2kx+20=0$ are real and equal then the value of $k$ is ________.

1. $20$
2. $10$
3. $-10$
4. $10$ or $-10$

Q. The area of the shaded region in the figure is _________.

1. $4\pi$
2. $6\pi$
3. $9\pi$
4. $3\pi$

Q. If a tangent $l$ of $\odot (P,10)$ touches the circle at $A$, then $PA=$ _______.

1. $10$
2. $5$
3. $8$
4. $20$

Q. The radius of a semi-circular garden is $35m$. One has to walk ______ $m$ to make a trip along its boundary.

1. $175$
2. $165$
3. $180$
4. $110$

Q. For an arithmetic progression; $5,\frac{11}{2},6,\frac{13}{2},.....$ then $T_{40}-T_{20}=$ _________.

1. $15$
2. $10$
3. $5$
4. $20$

Q. If the length of the median of an equilateral triangle is $3\sqrt{3}$ then the length of a side of the triangle of _______.

1. $9$
2. $6$
3. $7.5$
4. $3$

Q. If $({\cos }^2\theta +\frac{1}{cose{c}^2\theta })+4=x$ then what is the value of $x$?

1. $3$
2. $5$
3. $6$
4. $4$

Q. The angle of elevation of the top of the tower from the point a meter away from the base of the tower is ${60}^{\circ }$. The height of the tower is _______ meter.

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

Q. For $△ABC,\cos \left(\frac{B+C}{2}\right)=$ ________.

1. $\cos \frac{A}{2}$
2. $\cos A$
3. $\sin \frac{A}{2}$
4. $\sin A$

Q. The discriminant of quadratic equation $3x^2-4x-1=0$ is _______.

1. $28$
2. $0$
3. $4$
4. $12$

Q. As shown in the diagram if $AB=11,BC=13$ and $AC=15$ then $x+y+z=$ _____.

1. $19.5$
2. $17$
3. $17.5$
4. $39$

Q. In $△ABC$ if $m\angle B={90}^{\circ }$ and $AB=BC$ then $AC:BC=$ ____.

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

Q. If the $n^{th}$ term of an arithmetic progression is $15n+10$ then its fifth term is _______.

1. $25$
2. $75$
3. $55$
4. $85$