Question 1 :
The $288th$ term of the series $a, b, b, c, c, c, d, d, d, d,e, e, e, e, e, f, f, f, f, f, f,$ is 

Question 3 :
If a, b, c, d are any four consecutive coefficients in the expansion of $(1+x)^n$, then $\displaystyle\frac{a}{a+b}, \frac{b}{b+c}, \frac{c}{c+d}$ are in.

Question 4 :
The $8^{th}$ term of the sequence $1, 1, 2, 3, 5, 8, ....$ is

Question 5 :
If $a_{1}, a_{2}, a_{3}, ....$ are in A.P. such that $\dfrac {a_{4}}{a_{7}} = \dfrac {3}{2}$, then the $13^{th}$ of the A.P. is

Question 6 :
If the quadratic equation&#160;$\displaystyle x^{2}-mx-4x+1=0$ has real and distinct roots, then the values of $m$ are<br/>A. &#160;$\displaystyle (-\infty , -6)$<br/>B. &#160;$\displaystyle (-\infty,-3)$&#160;&#160;&#160;<div>C. &#160;$(-2,\infty )$&#160;&#160;</div><div>D. &#160;$\displaystyle \left ( 2,\infty &#160;\right )$<br/></div>

Question 7 :
Let for $a\neq a_1 \neq o$, $f(x)=ax^2+bx+C$, $g(x) = a_1x^2+b_1x+c_1$ and $P(x) =f(x)-g(x)$. If $P(x)=0$ only for $x=-1$ and $p(-2)=2$, then value of $P(2)$ is

Question 8 :
lf the equation $ax^{2}+2bx -3c=0$ has&nbsp;non-real roots and $\displaystyle \frac{3c}{4}&lt;a+b$, then $c$ is always<br>

Question 9 :
If&#160;$\displaystyle y^{2}&lt; x$ and&#160;$\displaystyle x\in \left ( -\infty ,0 \right )$ &#160;then $y$ must<br/>

Question 10 :
In $\Delta$ ABC, angle C&nbsp; is a right angle, then the value<br>of tan $A + tan B $is<br><br>

Question 11 :
<span>If in two triangles, one pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar by which similarity</span>

Question 12 :
SAS criterion is true when&#160;<span>&#160;In two triangles, a pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar.</span>

Question 13 :
The areas of two similar triangles are $16\ \text{cm}^2$ and $36\ \text{cm}^2$ respectively. If the altitude of the first triangle is $3\ \text{cm}$, then the corresponding altitude of the other triangle is:

Question 14 :
In $\triangle PQR,$ $PQ=4$ cm, $QR=3$ cm, and $RP=3.5$ cm. $\triangle DEF$ is similar to $\triangle PQR.$ If $EF=9$ cm, then what is the perimeter of $\triangle DEF\: ?$<br>

Question 15 :
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.

Question 16 :
If $\triangle ABC$ and $\triangle PQR$ are similar and $\dfrac {BC}{QR} = \dfrac {1}{3}$ find $\dfrac {area (PQR)}{area (BCA)}$

Question 17 :
Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion&#160;</td></tr><tr><td>2.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion&#160;</td></tr><tr><td>3.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion&#160;</td></tr><tr><td>4. In&#160;$\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>

Question 19 :
Point L, M and N lie on the sides AB, BC and CA of the triangle ABC such that $\ell (AL) :&nbsp;\ell (LB) =&nbsp;\ell (BM) :&nbsp;\ell (MC) =&nbsp;\ell (CN) :&nbsp;\ell (NA) = m : n$, then the areas of the triangles LMN and ABC are in the ratio

Question 20 :
Let $WXYZ$ be a square. Let $P,Q,R$ be the mid points of $WX, XY$ and $ZW$ respectively and $K,L$ be the mid-points of $PQ$ and $PR$ respectively. What is the value of $\cfrac { area\quad of\quad triangle\quad PKL }{ area\quad of\quad square\quad WXYZ } $?

Question 21 :
If the area of two similar triangles are equal then they are

Question 22 :
If the three sides of a triangle are proportional to the corresponding three sides of another triangle then their corresponding angles are

Question 23 :
A man of height 1.8 metre is moving away from a lamp post at the&nbsp; rate of 1.2 m/sec . If the height of the lamp post be 4.5 metre , then the rate at which the shadow of the&nbsp;&nbsp;man is lengthening is&nbsp;

Question 24 :
The areas of two similar triangles $\triangle{ABC}$ and $\triangle{DEF}$ are $144\ cm^{2}$ and $81\ cm^{2}$ respectively. If the longest side of larger $\triangle{ABC}$ be $36\ cm$, then, the largest side of the similar triangle $\triangle{DEF}$ is

Question 26 :
When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x+y is divided by 5. The value of $\dfrac { 2z-5 }{ 3 } $ is

Question 27 :
Express the following in the form&nbsp;$\frac{p}{{q,}}$ where $p$ and $q$ are integers and&nbsp;$q \ne 0.$

Question 28 :
Lines are drawn through the point P(-2, -3) to meet the circle ${ x }^{ 2 }+{ y }^{ 2 }-2x-10y+1=0$. The length of the line segment PA.A being the point on the circle where the line meets the circle at coincident points, is

Question 29 :
The number of tangents that can be drawn to a circle at a given point on it is

Question 30 :
There cannot be more than two tangents to a circle parallel to a given secant.

Question 31 :
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the&nbsp;centre is 25 cm. The radius of circle is :<br>

Question 32 :
A pair of tangents are drawn from a point $P$ to the circle $x^{2} + y^{2} = 1$. If the tangents make an intercept of $2$ on the line $x = 2$, the locus of $P$ is

Question 33 :
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q, so that $OQ=12$ cm. Length of PQ is :

Question 34 :
If $5x-12y+10=0$ and $12y-5x+16=0$ are two tangents<br/>to a circle then radius of the circle is<br/>

Question 35 :
lf the tangent at $\mathrm{P}$ on the circle $\mathrm{x}^{2}+\mathrm{y}^{2}=\mathrm{a}^{2}$ cuts two parallel tangents of the circle at $\mathrm{A}$ and $\mathrm{B}$ then $\mathrm{P}\mathrm{A}.\ \mathrm{P}\mathrm{B}=$<br>

Question 36 :
The radius of the circle touching the straight lines $x-2y-1=0$ and $3x-6y+7=0$ is

Question 37 :
If roots of cubic equation are in G.P. , $ ax^3 + bx^2 + cx + d $ then :<br/>

Question 38 :
If $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }-5x+4=0$ then ${ \left( { \alpha &nbsp;}^{ 3 }+{ \beta &nbsp;}^{ 3 }+{ \gamma &nbsp;}^{ 3 } \right) &nbsp;}^{ 2 }=$

Question 39 :
Given&nbsp;$l{x^2} - mx + 5 = 0$ does not have distinct real roots then minimum value of $5l+m$ is&nbsp;

Question 40 :
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = x^2 - (\sqrt{5} -1)x -(\sqrt{5} + 1)$, then the value of $\displaystyle \frac{1}{\alpha^2} + \frac{1}{\beta^2}$ is ____________.

Question 41 :
The number of integers $n$ for which $3x^3-25x+n=0$ has three real roots is$?$<br/>

Question 42 :
Suppose $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }+{ x }^{ 2 }+2x+3=0$. If $f(x)=0$ is a cubic polynomial equation whose roots are $\alpha +\beta ,\beta +\gamma ,\gamma +\alpha $ then $f(x)=$

Question 43 :
The number of different possible values for the sum $x+y+z$, where $x,y,z$ are real numbers such that ${x}^{4}+4{y}^{4}+16{z}^{4}+64=32xyz$ is

Question 44 :
If $\cos{\cfrac{\pi}{7}},\cos{\cfrac{3\pi}{7}},\cos{\cfrac{5\pi}{7}}$ are the roots of the equation $8{x}^{3}-4{x}^{2}-4x+1=0$<br>The value of $\sec{\cfrac{\pi}{7}}+\sec{\cfrac{3\pi}{7}}+\sec{\cfrac{5\pi}{7}}=$

Question 45 :
Total number of polynomials of the form ${ x }^{ 3 }+a{ x }^{ 2 }+bx+c$ that are divisible by ${ x }^{ 2 }+1$, where $a,b,c\in \left\{ 1,2,3,......10 \right\} $ is equal to&nbsp;

Question 46 :
Number of intergers&nbsp;in the range of 'a' so that the equation ${ x }^{ 3 }-3x+a=0$ has all its&nbsp; roots real and distinct,is

Question 47 :
A cylinder is with in the cube touching all the vertical faces . A cone is inside the cylinder. If their heights are same with the same base . If the ratio of their volumes is x : y : z . (HCF of x , y , z = 1) , then x + y + z =

Question 48 :
If the radii of the circular ends of a bucket $24$ cm high are $5$ cm and $15$ cm respectively, find the inner surface area of the bucket (i.e., the area of the metal sheet required to make the bucket)&#160;<div>(Take $\pi = 3.14$)</div>

Question 49 :
A right circular cone and a sphere have equal volumes. If the radius of the base of the cone is $2x$ and the radius of the sphere is $3x$, find the height of the cone in terms of $x$.

Question 50 :
A solid is in the&#160;form of a cone mounted on a right circular cylinder both having same radii of&#160;their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm, respectively, and the height of the cylindrical part of the solid is 3.5 cm, the volume of the solid is equal to

Question 51 :
What length of the solid cylinder that is $2$ cm in diameter must be taken to cast into a hollow cylinder of external diameter $12$ cm, $0.25$ cm thick, and $15$ cm long?

Question 52 :
<span>The interior of a&#160;building is in the form of a right circular cylinder of a diameter 4.2 m and&#160;height&#160; 4 m, surmounted by a cone. The&#160;vertical height of the cone is 2.1 m. Find the outer surface area and volume of&#160;the building.(Take $\pi$ = 22/7)</span>

Question 53 :
A spherical ball of lead $5 \,cm$ in diameter is melted and recast into three spherical balls. The diameters of two of these balls are $2 \,cm$ and $2(14.5)^{1/3}\, cm$. Find the diameter of the third ball.

Question 54 :
<span>A solid toy is in the&#160;form of a right circular cylinder with a hemispherical shape of one end and a&#160;cone at the other end. Then common diameter is $4.2 cm$ and the heights of the&#160;cyndrical and conical portions are $12 cm$ and $7 cm$, respectively. Find the volume of the solid. (Take $\pi$ = 22/7)</span>

Question 55 :
A rectangular sheet of paper $22$cm long and $12$cm broad can be&#160; curved to form the lateral surface of a right circular cylinder in two ways. Taking $\pi= \dfrac{22}{7}$. Difference in the&#160;volumes of the two cylinders thus formed is<br/>

Question 56 :
The centre of a circle passing through the points (0 , 0), (1 , 0) and touching the circle $x^2 + y^2$ = 9&nbsp;

Question 57 :
If four points are $A(6,3),B(-3,5),C(4,-2)$ and $P(x,y),$ then the ratio of the areas of $\triangle PBC$ and $\triangle ABC$ is:

Question 58 :
If the area of the triangle formed by the line -y = 0, x + y = 0 and x - c = 0 is 16 units, c is

Question 59 :
The centroid and two vertices of a triangles are (4,-8), (-9,7), (1,4) then the area of the triangle is&nbsp;

Question 60 :
If $m_1$ and $m_2$ are the roots of the equation $x^2 +(\sqrt 3 +2) x + \sqrt 3 - 1 = 0 $, then the area of the triangle formed by the lines $y=m_1x,y=-m_2x$ and $y=1$ is: