Question 1 :
If the radius of a hemisphere is 5 cm, then its volume is<br/>
Question 2 : The shape of a gilli, in the the game of gilli- danda, is a combination of<br/> <img style='object-fit:contain' src="> (b) a cone and a cylinders<br/> (c) two cones and a cylinder<br/> (d) two cylinders and a cone<br/>
Question 3 :
If the diameter of a sphere is 16 cm, then its surface area is<br/>
Question 4 :
In a cylinder, if the radius is doubled &nd height is halved then its curved surface area will be<br/>
Question 5 :
If the radius of a sphere is 2r, then its volume will be<br/>
Question 6 :
The total surface area of a cone whose radius is {tex} \frac { r }{ 2 } {/tex} and slant height 2l is<br/>
Question 7 :
If the diameter of the base of a cone is 12 cm and height is 20 cm, then its volume is ,<br/>
Question 8 :
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 9 :
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 10 :
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 11 :
If the slant height of a cone is 12.04 cm and L.S.A is 340.56 sq.cm, its base area is
Question 12 :
If the slant height of a cone is 12.81 cm and T.S.A is 716.89 sq.cm, its L.S.A. is
Question 13 :
If the base radius of a cone is 9.00 cm and vertical height is 10.00 cm, its T.S.A is
Question 14 :
If the base radius of a cone is 10.00 cm and L.S.A is 444.40 sq.cm, its volume is
Question 15 :
If the slant height of a cone is 12.21 cm and T.S.A is 698.03 sq.cm, its vertical height is
Question 16 :
If A = {tex}\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} {/tex} , then A² =<br/>
Question 17 :
The slope of the line passing through the points (0, -4) and (-6, 2) is<br/>
Question 18 :
The list of numbers – 10, – 6, – 2, 2, … is<br/>
Question 19 :
The list of number {tex} \frac { 1 }{ 9 } {/tex} , {tex} \frac { 1 }{ 3 } {/tex}, 1, – 3,… is a<br/>
Question 20 :
If the mid-point of the line segment joining the points P (a, b – 2) and Q (-2, 4) is R (2, -3), then the values of a and b are<br/>
Question 21 :
If the first term of an A.P. is -5 and the common difference is 2, then the sum of its first 6 terms is<br/>
Question 22 :
The third proportional to {tex}6 \frac { 1 }{ 4 } {/tex} and 5 is<br/>
Question 23 :
If the sum of the GP., 1, 4, 16, … is 341, then the number of terms in the GP. is<br/>
Question 24 :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is<br/>
Question 25 :
If {tex} \frac { 1 }{ 2 } {/tex} is a root of the equation x<sup>2</sup> + kx – {tex} \frac { 5 }{ 4 } {/tex} = 0, then the value of k is<br/>
Question 26 :
If on dividing 4x<sup>2</sup> – 3kx + 5 by x + 2, the remainder is -3 then the value of k is<br/>
Question 27 :
If x ∈ W, then the solution set of the inequation 5 – 4x ≤ 2 – 3x is<br/>
Question 28 :
If x ∈ W, then the solution set of the inequation 3x + 11 ≥ x + 8 is<br/>
Question 29 :
Which term of the A.P. 21, 42, 63, 84,… is 210?<br/>
Question 30 :
The 30th term of the A.P. 10, 7, 4, … is<br/>
Question 31 :
If on dividing 2x<sup>3</sup> + 6x<sup>2</sup> – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is<br/>
Question 32 :
The roots of the equation x<sup>2</sup> – 3x – 10 = 0 are<br/>
Question 33 :
If {tex} \frac { 1 }{ 2 } {/tex} is a root of the quadratic equation 4x<sup>2</sup> – 4kx + k + 5 = 0, then the value of k is<br/>
Question 34 :
The slope of the line passing through the points (3, -2) and (-7, -2) is<br/>
Question 35 :
When 2x<sup>3</sup> – x<sup>2</sup> – 3x + 5 is divided by 2x + 1, then the remainder is<br/>
Question 36 :
If in two triangles ABC and PQR,<br/> {tex}\frac { AB }{ QR } =\frac { BC }{ PR } =\frac { CA }{ PQ } {/tex}<br/> then<br/>
Question 37 : In the given figure, O is the centre of the circle. If ∠ABC = 20°, then ∠AOC is equal to<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e69819305523f23291f"/>
Question 38 : In the given figure, ∆ABC ~ ∆QPR. Then ∠R is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e5a1766ce1c2c83a5c7"/>
Question 39 : In the given figure, if ∠DAB = 60° and ∠ABD = 50° then ∠ACB is equal to<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e6b819305523f232922"/>
Question 40 :
If in triangles ABC and DEF,{tex}\frac { AB }{ DE } =\frac { BC }{ FD } {/tex} , then they will be similar when<br/>
Question 41 :
If ∆ABC ~ ∆PQR, BC = 8 cm and QR = 6 cm, then the ratio of the areas of ∆ABC and ∆PQR is<br/>
Question 42 :
The areas of two similar triangles are 81 cm² and 49 cm² respectively. If an altitude of the smaller triangle is 3.5 cm, then the corresponding altitude of the bigger triangle is<br/>
Question 43 : In the given figure, O is the centre of a circle and PQ is a chord. If the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e75819305523f232937"/>
Question 44 :
If ∆ABC ~ ∆PQR, area of ∆ABC = 81 cm², area of ∆PQR = 144 cm² and QR = 6 cm, then length of BC is<br/>
Question 45 :
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140°, then ∠BAC is equal to<br/>
Question 46 :
D and E are respectively the points on the sides AB and AC of a ∆ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then the length of DE is<br/>
Question 47 : In the given figure, MN || QR. If PN = 3.6 cm, NR = 2.4 cm and PQ = 5 cm, then PM is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e611766ce1c2c83a5d6"/>
Question 48 :
Given ∆ABC ~ ∆PQR, area of ∆ABC = 54 cm² and area of ∆PQR = 24 cm². If AD and PM are medians of ∆’s ABC and PQR respectively, and length of PM is 10 cm, then length of AD is<br/>
Question 49 :
If ∆ABC ~ ∆QRP, {tex}\frac { area\quad of\quad \Delta ABC }{ area\quad of\quad \Delta PQR } = \frac {9}{4} {/tex}, AB = 18 cm and BC = 15 cm, then the length of PR is equal to<br/>
Question 50 :
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE, then the two triangles are<br/>
Question 51 : In the given figure, $FI$ is the common tangent to the two circles. $FG\ \&\ FH$ are also tangents. Given $FG$ = {tex} 15 \mathrm{~cm} {/tex}, find $FH$<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e622282923f071fae47"><br>
Question 52 :
If two circles touch internally, the number of their common tangents is
Question 53 : In the given figure, $CA$ and $C$. $B$ are tangent segments to the circle with centre $O$. Given {tex} \angle \mathrm{BCD}=22^{\circ} {/tex}, find {tex} \angle \mathrm{ABO} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e5bdba5935f6cc6ee57"><br>(i) Prove that {tex} \Delta \mathrm{ADF} \sim \Delta \mathrm{CEF} {/tex}.
Question 54 : In the given figure, {tex} \mathrm{O} {/tex} is the centre of the circle and {tex} \mathrm{DF} {/tex} is the tangent at {tex} \mathrm{E} {/tex}. If {tex} \angle \mathrm{CBE}=25^{\circ}, {/tex} find {tex} \angle \mathrm{CDE}+\angle \mathrm{CED} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e3bdba5935f6cc6ee26"><br>
Question 55 :
Two circles are of radii {tex} 3 \mathrm{~cm} {/tex} and {tex} 3 \mathrm{~cm} {/tex}. If the distance between their centres is {tex} 10 \mathrm{~cm} {/tex}, what is the length of their transverse common tangent?
Question 56 : In the given figure, two circles intersect at points {tex} \mathrm{F} \& \mathrm{G} {/tex}. A tangent is drawn at point {tex} \mathrm{H} {/tex}. From the same point, two lines are drawn passing through points {tex} \mathrm{F} \& \mathrm{G} . {/tex} They meet the other end of the second circle at {tex} \mathrm{E} \& \mathrm{D} . {/tex} Given {tex} \angle \mathrm{H}= {/tex} {tex} 77^{\circ}, {/tex} find {tex} \angle \mathrm{EDG} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e65dba5935f6cc6ee65"><br>
Question 57 :
Which of the following statements are true?<br>a) A secant has two end points b) A radius is a limiting case of a diameter<br>c) A secant and a chord are same d) A diameter is a limiting case of a chord e) A tangent is the limiting case of a secant
Question 58 : Two chords AB and CD of a circle intersect externally at a point P. If PC = 15 cm, CD = 7 cm and AP = 12 cm, then AB is<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e7e819305523f232946"/>
Question 59 : A line which touches a circle at only one point is called a<br>(ii) If {tex} \mathrm{B D}=18 \mathrm{cm}, \mathrm{CD}=8 \mathrm{cm} {/tex} find {tex} \mathrm{AD} {/tex}.<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e4cdba5935f6cc6ee45">
Question 60 : In the given figure, FGHI is a cyclic quadrilateral such that HF bisects {tex} \angle \mathrm{IFG} {/tex} and {tex} \mathrm{JK} {/tex} is the tangent at {tex} \mathrm{H} . {/tex} If {tex} \angle \mathrm{HFG} {/tex} {tex} =58^{\circ}, {/tex} find {tex} \angle \mathrm{JHG} {/tex}<br /><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e59dba5935f6cc6ee53">
Question 61 : 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 62 : If the two radii $OP$ and {tex} \mathrm{OQ} {/tex} of a circle are at right angles to each other, then the sector {tex} \mathrm{OPQ} {/tex} is called a<br>(iii) Find the ratio of the area of {tex} \Delta \mathrm{ADB} {/tex} is to area of {tex} \Delta {/tex}{tex}\mathrm{CDA}{/tex}.<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e4c2282923f071fae2e">
Question 63 :
Which of the following statements are true?<br>a) One and only one tangent can be drawn to a circle from a point outside it b) Diameter of a circle is a part of the semi-circle of the circle c) Every circle has a unique diameter d) One and only one tangent can be drawn to pass through a point on a circle e) A secant of a circle is a segment having its end points on the circle<br>
Question 64 :
If two circles of radii {tex} 8 \mathrm{~cm} {/tex} and {tex} 2 \mathrm{~cm} {/tex} touch internally, the distance between their centres is
Question 65 : In the given figure, $BR \& CR$ are tangents to the circle with centre O. Given {tex} \mathrm{OB}=10 \mathrm{~cm} {/tex} and {tex} \mathrm{BC}=18 \mathrm{~cm}, {/tex} find {tex} \mathrm{BR} {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5fb79e6adba5935f6cc6ee6d"><br>
Question 66 :
The value of cos 65° sin 25° + sin 65° cos 25° is<br/>
Question 67 :
In ∆ABC, ∠A = 30° and ∠B = 90°. If AC = 8 cm, then its area is<br/>
Question 68 :
If a pole 6 m high casts shadow 2 √3 m long on the ground, then the angle of elevation is
Question 69 :
If the angle of depression of an object from a 75 m high tower is 30°, then the distance of the object from the tower is<br/>
Question 70 :
{tex}\frac { { 1+tan }^{ 2 }A }{ { 1+cot }^{ 2 }A } {/tex} is equal to<br/>
Question 73 : The top of a broken tree has its top touching the ground (shown in the given figure) at a distance of 10 m from the bottom. If the angle made by the broken part with the ground is 30°, then the length of the broken part is<br/>
<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef41b59ce7dae068a37f4a3' class="uploaded-image" />
Question 74 :
In the given figure, if the angle of elevation is 60° and the distance AB = 10 √3 m, then the height of the tower is<br/>
Question 75 :
If sec θ – tan θ = k, then the value of sec θ + tan θ is<br/>
Question 76 :
The measure of central tendency of statistical data which takes into account all the data is<br/>
Question 77 :
In a grouped frequency distribution, the mid-values of the classes are used to measure which of the following central tendency?<br/>
Question 78 :
Construction of a cumulative frequency distribution table is useful in determining the<br/>
Question 79 :
If the classes of a frequency distribution are 1-10, 11-20, 21-30,…, 61-70, then the upper limit of the class 11-20 is<br/>
Question 80 :
If the classes of a frequency distribution are 1-10, 11-20, 21-30, …, 51-60, then the size of each class is<br/>
Question 81 : Consider the following frequency distribution:<br/> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef1ad45819305523f232a5d"/><br/>The upper limit of the median class is:-
Question 82 :
In the formula: {tex}\overline { x } =a+c\left( \frac { \sum { { f }_{ i }{ u }_{ i } } }{ \sum { { f }_{ i } } } \right) {/tex}, for finding the mean of grouped frequency distribution, u<sub>i</sub> =<br/>
Question 83 :
While computing mean of grouped data, we assumed that the frequencies are<br/>
Question 84 :
If the class marks of a continuous frequency distribution are 22, 30, 38, 46, 54, 62, then the class corresponding to the classmark 46 is<br/>
Question 86 : Daily wages of factory workers are recorded as:<br/> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef1ad466150ce6eb5a147a8"/><br/>The lower limit of the modal class is
Question 87 : For the following distribution:<br/> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef1ad47819305523f232a60"/><br/>The sum of lower limits of the median class and modal class is
Question 88 :
In the formula: {tex}\overline { x } =a+\frac { \sum { { f }_{ i }{ d }_{ i } } }{ \sum { { f }_{ i } } } {/tex} for finding the mean of the grouped data, d’<sub>i</sub>s are deviations from a (assumed mean) of<br/>
Question 90 :
If one card is drawn from a well-shuffled pack of 52 cards, the probability of getting an ace is<br/>
Question 91 :
A bag contains 3 red balk, 5 white balls and 7 black balls. The probability that a ball drawn from the bag at random will be neither red nor black is<br/>
Question 92 :
A bag contains 5 red, 4 white and 3 black balls. If a ball is drawn from the bag at random, then the probability of the ball being not black is
Question 93 :
One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is<br/>
Question 94 : Rashmi has a die whose six faces show the letters as given below:<br/> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef1ad4e819305523f232a6c"/><br/>If she throws the die once, then the probability of getting C is
Question 95 :
Probability of getting a non-red ball from a bag containing 4 red, 5 blue and 3 black balls is
Question 96 :
Which of the following cannot be the probability of an event?<br/>
Question 97 :
If a fair dice is rolled once, then the probability of getting an even number or a number greater than 4 is<br/>
Question 98 :
If a (fair) coin is tossed twice, then the probability of getting two heads is<br/>
Question 99 :
A fair die is thrown once. The probability of getting an even prime number is<br/>
Question 100 :
A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is<br/>
