Question 1 :
The 21st term of an A.P. whose first two terms are -3 and 4 is<br/>
Question 2 :
If the common difference of an A.P. is 5, then a<sub>18</sub> – a<sub>13</sub> is<br/>
Question 5 :
If A = {tex}\begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix} {/tex} , then A² = pA, then the value of p is<br/>
Question 6 :
If {tex}x\left[ \begin{matrix} 2 \\ 3 \end{matrix} \right] +y\left[ \begin{matrix} -1 \\ 0 \end{matrix} \right] =\left[ \begin{matrix} 10 \\ 6 \end{matrix} \right] {/tex} then the values of x and y are<br/>
Question 7 :
In an A.P., if d = -4, n = 7, a<sub>n</sub> = 4, then a is<br/>
Question 8 :
The points which divide the line segment joining the points (7, -6) and (3, 4) in the ratio 1 : 2 internally lies in the<br/>
Question 9 :
Which of the following equations has two distinct real roots ?<br/>
Question 10 :
In an A.P., if a = 1, a<sub>n</sub> = 20 and S<sub>n</sub> = 399, then n is<br/>
Question 11 :
In the given figure, {tex} \mathrm{O} {/tex} is the centre of the circle and {tex} \mathrm{GH} {/tex} is the tangent at {tex} \mathrm{D} {/tex}. If {tex} \angle \mathrm{EDF}=55^{\circ} {/tex} and {tex} \angle \mathrm{GDE}=101^{\circ} {/tex}, find {tex} \angle \mathrm{DFE} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e38dba5935f6cc6ee21"><br>
Question 12 :
In the given figure, {tex} \mathrm{O} {/tex} is the centre of the circle and {tex} \mathrm{LM} {/tex} is the tangent at {tex} \mathrm{K} {/tex}. If {tex} \angle \mathrm{JHK}=31^{\circ} {/tex} and {tex} \angle \mathrm{HJI}=44^{\circ} {/tex}, find {tex} \angle \mathrm{JHI} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e41dba5935f6cc6ee32"><br>(ii) {tex} \mathrm{BG}=2 \mathrm{GD} {/tex} for (i) above.
Question 13 :
In the given figure, {tex} \mathrm{O} {/tex} is the centre of the circle and the tangents {tex} \mathrm{BE} {/tex} and {tex} \mathrm{DE} {/tex} meet at point {tex} \mathrm{E} {/tex}. If {tex} \angle \mathrm{CDB}=49^{\circ}, {/tex} find {tex} \angle D E B {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e45dba5935f6cc6ee39"><br>
Question 14 :
In the given figure, $ER \& FR$ are tangents to the circle with centre $O$. Given {tex} \angle \mathrm{EOF}=131^{\circ}, {/tex} find {tex} \angle \mathrm{ERF} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e6b2282923f071fae56"><br>
Question 15 :
In the given figure, {tex} \mathrm{O} {/tex} is the centre of the circle and {tex} \mathrm{FH} {/tex} is the tangent at {tex} \mathrm{G} {/tex}. If {tex} \angle \mathrm{GHI}=45^{\circ}, \angle \mathrm{HGI}=34^{\circ}, {/tex} find {tex} \angle \mathrm{KGF} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e462282923f071fae22"><br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e46dba5935f6cc6ee3b">
Question 16 :
The distance between the centres of two circles is {tex} d {/tex}. If the radii are {tex} r_{1} {/tex} and {tex} r_{2}, {/tex} the length of their direct common tangent is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e31dba5935f6cc6ee16"><br>
Question 17 :
{tex} \mathrm{O} {/tex} is the centre of the circumcircle of {tex} \Delta \mathrm{CDE} {/tex}. Tangents at {tex} \mathrm{C} {/tex} and {tex} \mathrm{E} {/tex} intersect at {tex} \mathrm{F} {/tex}. If {tex} \angle \mathrm{CFE}=39.53^{\circ} {/tex}, find {tex} \angle \mathrm{EDC} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e49dba5935f6cc6ee41"><br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e492282923f071fae29">
Question 18 :
Which of the following statements are true?<br>If two circles touch externally, the square of the distance between their centres is the sum of the squares of a) their radii b) If two circles touch externally, the distance between their centres is the sum of their radii c) If two circles touch internally, the distance between their centres is the difference of their radii d) If two circles touch externally, their centres and the point of contact form an isosceles triangle e) If two circles touch internally, their centres and the point of contact form a scalene triangle If two circles touch internally, the square of the distance between their centres is the difference of the squares f) of their radii<br>
Question 19 :
In the given figure, {tex} \mathrm{O} {/tex} is the centre of the circle and {tex} \mathrm{HI} {/tex} is the tangent at {tex} \mathrm{E} {/tex}. If {tex} \angle \mathrm{OFE}=33^{\circ}, {/tex} find {tex} \angle \mathrm{IEF} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e43dba5935f6cc6ee36"><br>
Question 20 :
In the given figure, O is the centre of the circle. If ∠AOB = 90° and ∠ABC = 30°, then ∠CAO is equal to<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e6d6150ce6eb5a146f1"/>
Question 21 :
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is<br/>
Question 22 :
The volume of the greatest sphere cut off from a circular cylindrical wood of base radius 1 cm and height 6 cm is<br/>
Question 23 :
If a solid of one shape is converted to another, then the surface area of the new solid<br/>
Question 24 :
The volume of the largest right circular cone that can be carved out from a cube of edge 4.2 cm is<br/>
Question 25 :
If the diameter of the base of cone is 10 cm and its height is 12 cm, then its curved surface area is<br/>
Question 26 :
If a cone, a hemisphere and a cylinder have equal bases and have same height, then the ratio of their volumes is<br/>
Question 27 :
If two cylinders of the same lateral surface have their radii in the ratio 4 : 9, then the ratio of their heights is<br/>
Question 28 :
If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5 cm and height 6 cm, then the volume of water that flows out of the cylindrical cup is<br/>
Question 29 :
The total surface area of a cone whose radius is {tex} \frac { r }{ 2 } {/tex} and slant height 2l is<br/>
Question 30 :
If the diameter of the base of a cone is 12 cm and height is 20 cm, then its volume is ,<br/>
Question 31 :
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is<br/>
Question 32 :
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that {tex}\\ \frac { 1 }{ 8 } {/tex} space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is<br/>
Question 33 :
If the base radius of a cone is 5.00 cm and L.S.A is 161.86 sq.cm, its base area is
Question 34 :
A solid metallic cylinder of base radius 12.00 cm and height 23.00 cm is melted to form cones each of height 1.00 cm and radius 1.00 cm . Find the number of complete cones formed
Question 35 :
If the base radius of a cone is 9.00 cm and L.S.A is 340.56 sq.cm, its slant height is
Question 36 :
A well of diameter 20.00 mt is dug to a depth of 16.00 mt and the soil from digging is evenly spread out to form a platform of base dimensions 25.00 mt✕31.00 mt . Find the height of the platform
Question 37 :
If the base radius of a cone is 10.00 cm and slant height is 12.21 cm, its L.S.A. is
Question 38 :
If the vertical height of a cone is 10.00 cm and volume is 261.90 cu.cm, its L.S.A. is
Question 39 :
If the slant height of a cone is 8.60 cm and L.S.A is 189.20 sq.cm, its T.S.A is
Question 40 :
If the slant height of a cone is 13.45 cm and vertical height is 10.00 cm, its L.S.A. is
Question 41 :
The radii of the ends of a frustum of a right circular cone 14.00 cm high are 10.00 cm and 7.00 cm. Its slant height is
Question 42 :
An open cylindrical vessel of internal diameter 29.00 cm and height 11.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 14.50 cm and height 11.00 cm and filled with water. If the cone is replaced by another cone whose height is 6.60 cm and base radius is 2.17 cm, find the drop in the water level.
Question 43 :
If the slant height of a cone is 9.22 cm and vertical height is 6.00 cm, its base area is
Question 44 :
If the base radius of a cone is 5.00 cm and T.S.A is 254.26 sq.cm, its base area is
Question 45 :
If the slant height of a cone is 7.07 cm and vertical height is 5.00 cm, its T.S.A is
Question 46 :
The radii of the ends of a frustum of a right circular cone 8.00 cm high are 11.00 cm and 3.50 cm. Its total surface area is
Question 47 :
If the base radius of a cone is 6.00 cm and volume is 188.57 cu.cm, its base area is
Question 48 :
If the base radius of a cone is 6.00 cm and vertical height is 5.00 cm, its slant height is
Question 49 :
If the base radius of a cone is 9.00 cm and volume is 509.14 cu.cm, its vertical height is
Question 50 :
The radii of the ends of a frustum of a right circular cone 9.00 cm high are 13.50 cm and 9.00 cm. Its total surface area is