Question 1 :
If the sum of the series $2+5+8+11.....$ is $60100$, then the number of terms are
Question 2 :
Find the number of terms common to the two A,P's $3,7,11,.....,407$ and $2,9,16,..........,709$
Question 3 :
If $(1 + 3 + 5+...+p) + (1 + 3 + 5+...+q) =(1 + 3 + 5 + ... + r)$ where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of $p + q + r$, (where $p > 6$) is
Question 4 :
$M$ is a set of six consecutive even integers. When the least three integers of set $M$ are summed, the result is $x$. When the greatest three integers of set $M$ are summed, the result is $y$. Mark the true equation.
Question 5 :
If the sum of first p terms, first q terms and first r terms of an A.P . be a, b and c respectively, then $\dfrac {a}{p}(q-r)+\dfrac {b}{q}(r-p)+\dfrac {c}{r}(p-q) $ is equal to
Question 6 :
The tangents drawn at the ends of a diameter of a circle are ?
Question 7 :
There is no tangent to a circle passing through a point lying ..... the circle.
Question 8 :
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 9 :
If radius of circle is 5 cm and distance from centre to the point of intersection of 2 tangents in 13 cm. Find length of tangent.
Question 10 :
Tangents PA and PB drawn to $x^2+y^2=9$ from any arbitrary point 'P' on the line $x+y=25$. Locus of midpoint of chord AB is<br>
Question 11 :
If two similar triangles have a scale factor of $a:b$, then the ratio of their areas is:
Question 12 : <p>If two similar triangles have a scale factor of $a:b$<em>,</em>then the ratio of their perimeters is <i>....</i></p>
Question 13 :
The areas of two similar triangles are $45$ sq. cm and $80$ sq. cm. The sum of their perimeters is $35$ cm. Find the perimeter of each triangle in cm.
Question 14 :
A shuttle cock used for playing badminton has the shape of the combination of<br>
Question 15 :
How many bricks, each measuring $25\ cm\times 11.25\ cm\times 6\ cm$, will be needed to build a wall $8\ m$ long, $6\ m$ high and $22.5\ cm$ thick?
Question 16 : <p>The slant heightof a frustum of a flower pot is 2 mm and the perimeters of its circular endsare 12 mm and 4 mm. Find the curved surface area of the flower pot.</p>
Question 17 :
The curved surface area of frustum cone is 400 $m^2$The diameter of a cone is 0.5 and 2 m.Find the slant height. (Use $\pi$ = 3.14).
Question 18 :
A vessel is in the form of a frustum of a cone.Its radius at top end is 8 cm and the bottom end is 12 cm. Its height is 21 cm.Find the volume of the frustum cone.
Question 23 :
Find the mean of the following data: Range of first $n$ natural numbers range of negative integers from $-n$ to $-1$ (where $-n < - 1$), range of first $n$ positive even integers and range of first $n$ positive odd integers
Question 24 :
I: If $a,b,c$ are real, the roots of $(b-c)x^{2}+(c-a)x+(a-b)=0$ are real and equal, then $a, b, c$ are in A.P.<br>II: If $a, b, c$ are real andthe roots of$(a^{2}+b^{2})x^{2}-2b(a+c)x+b^{2}+c^{2}=0$ are real and equal, then $a, b,c$ are in H.P.<br>Which of the above statement(s) is(are) true?<br>
Question 25 :
The set of values of k for which the given quadratic equation has real roots<br/>$2x^2$ + 3x + k = 0 are k $\leq \dfrac{9}{8}$
Question 26 :
For what value of k will$\displaystyle x^{2}-\left ( 3k-1 \right )x+2k^{2}+2k=11$ have equal roots?
Question 27 :
Hypotenuse length is$\displaystyle3\sqrt { 10 }$. Base length istripled and perpendicular doubles, new length of hypotenuse will be$\displaystyle 9\sqrt { 5 }$. Find the length of base.
Question 28 :
The coefficient of $x$ in the equation $x^2+px+q=0$ was wrongly written as $17$ in place of$13$ and the roots thus found was $-2$ and $-15$.<br>Then the roots of the correct equation are
Question 29 :
If the altitude of the sun is $60^{\circ}$, the height of a tower which casts a shadow of length 30 m is :<br/>
Question 30 :
A kite is flying with the string inclined at$\displaystyle 45^{\circ}$ to the horizontal If the string is straight and 50 m long the height at which the kite is flying is
Question 31 :
A ladder is placed against a vertical tower. If the ladder makes an angle of $\displaystyle 30^{\circ}$ with the ground and reaches up to a height of $15\ m$ of the tower; find length of the ladder in cm.
Question 32 :
From the top of a tower $80$ metres high, the angles of depression of two points $P$ and $Q$ in the same vertical plane with the tower are $45^{0}$ and $75^{0}$ respectively, $PQ=$<br>
Question 33 :
Horizontal distance between two pillars of different height is 60 m. it was observed that the angular elevation form form the top of the shorter pillar to the top of the taller pillar is$\displaystyle 45^{\circ}$ if the height of taller pillar is 130 m, the height of the shorter pillar
