CBSE Class 10 Mathematics 2025
365 questions · 779 marks · 363 with the board’s own marking-scheme answer, 2 with no official answer on the site.
Marks by chapter
Counted from the 365 questions listed below, as the 2025 papers print them. CBSE allocates marks per unit, not per chapter — this is what was observed, not an official CBSE weightage. Every year compared →
| Chapter | Marks | Share |
|---|---|---|
| Statistics28 questions | 91 | 11.7% |
| Pair of Linear Equations in Two Variables32 questions | 90 | 11.6% |
| Triangles30 questions | 75 | 9.6% |
| Introduction to Trigonometry42 questions | 65 | 8.3% |
| Surface Areas and Volumes18 questions | 61 | 7.8% |
| Probability35 questions | 58 | 7.4% |
| Real Numbers34 questions | 53 | 6.8% |
| Circles31 questions | 53 | 6.8% |
| Coordinate Geometry32 questions | 50 | 6.4% |
| Polynomials27 questions | 50 | 6.4% |
| Arithmetic Progressions15 questions | 39 | 5.0% |
| Some Applications of Trigonometry13 questions | 37 | 4.7% |
| Areas Related to Circles14 questions | 31 | 4.0% |
| Quadratic Equations14 questions | 26 | 3.3% |
365 questions from 2025
- Q1The quadratic equation whose sum and product of roots are 'a' and ' 1/a, respectively is:1 mk
- Q1√0.4 is a/an1 mk
- Q1(√3+2)^2+(√3-2)^2 is a/an1 mk
- Q1What is the mode of a data if median and mean of the same data are 9 · 6 and 10 · 5, respectively?1 mk
- Q1If α and β are the zeroes of polynomial 3 x^2+6 x+k such that α+β+α β=-2/3, then the value of k is:1 mk
- Q1If x=a b^3 and y=a^3 b, where a and b are prime numbers, then [HCF(x, y)-LCM(x, y)] is equal to:1 mk
- Q1The system of equations x+5=0 and 2 x-1=0, has1 mk
- Q1The diameter of a wheel is 63 cm. The distance travelled by the wheel in 100 revolutions is:1 mk
- Q1If for any event E, P(E)+P(Ē)=q, then the value of q^2-3 is:1 mk
- Q1If tan 3 θ=√3, then (θ)/2 equals:1 mk
- Q1If 7 cos^2 θ+3 sin^2 θ=4, then the value of θ is:1 mk
- Q2(1+√3)^2-(1-√3)^2 is:1 mk
- Q2If x is the LCM of 4,6, 8 and y is the LCM of 3,5, 7 and p is the LCM of x and y, then which of the following is true?1 mk
- Q2In the adjoining figure, AP and AQ are tangents to the circle with centre O. If reflex ∠ POQ=210^°, the value of 2 x is1 mk
- Q2The 9^th term from the end (towards first term) of the AP 7,11,15,19, …., 147 is:1 mk
- Q2The probability of drawing an even prime number out of numbers from 1 to 30 is:1 mk
- Q2A pair of dice is thrown once. The probability that sum of numbers appearing on top faces is at least 4 is:1 mk
- Q2The value of ( tan A cosec A)^2-( sin A sec A)^2 is:1 mk
- Q2If x=1 and y=2 is a solution of the pair of linear equations 2 x-3 y+a=0 and 2 x+3 y-b=0, then:1 mk
- Q2Let x=a^2 b^3 c^n and y=a^3 b^m c^2, where a, b, c are prime numbers. If LCM of x and y is a^3 b^4 c^3, then the value…1 mk
- Q2Which of the following cannot be the unit digit of 8^n, where n is a natural number?1 mk
- Q2If sin θ= cos θ(0^°<θ<90^°), then the value of sec θ · sin θ is:1 mk
- Q2The mean of seven observations is 17. If the mean of the first four observations is 15 and that of the last four…1 mk
- Q3The distance of the point (4,0) from x -axis is:1 mk
- Q3The quadratic equation whose roots are 7 and 1/7 is:1 mk
- Q3The value of ' a ' for which a x^2+x+a=0 has equal and positive roots is:1 mk
- Q3The mid-point of the line segment joining the points P(-4,5) and Q(4,6) lies on:1 mk
- Q3The value of'k'for which the system of linear equations 6 x+y=3k and 36 x+6 y=3 have infinitely many solutions is:1 mk
- Q3For any prime number p, if p divides a ^2, where a is any real number then p also divides1 mk
- Q3Three numbers in AP have the sum 30. What is its middle term?1 mk
- Q3The perimeter of the triangle formed by the vertices (0, 0), (2,0) and (0,2) is:1 mk
- Q3The value of (1-2 sin^2 60^°) is same as that of1 mk
- Q3Which of the following quadratic equations has real and equal roots?1 mk
- Q3If x=2 sin 60^° cos 60^° and y= sin^2 30^°- cos^2 30^° and x^2=ky^2, the value of k is1 mk
- Q3If an arc of a circle of diameter 10 cm subtends an angle of 144° at the centre of the circle, then the length of the…1 mk
- Q4An arc of a circle is of length 5 π cm and the sector it bounds has an area of 20 π cm^2. Its radius is:1 mk
- Q4If α and β are the zeroes of the polynomial p(x)=x^2-a x-b, then the value of (α+β+α β) is equal to:1 mk
- Q4Let a=p^2 q^3 r^n and b=p^3 q^m r^2, where p, q, r are prime numbers. If LCM of a and b is p^3 q^4 r^3, then the value…1 mk
- Q4If the zeroes of the polynomial a x^2+b x+(2 a)/b are reciprocal of each other, then the value of b is1 mk
- Q4If α and β are zeroes of the polynomial p(x)=kx^2-30 x+45 k and α+β=α β, then the value of 'k' is:1 mk
- Q4If mode and median of given set of observations are 13 and 11 respectively, then the value of mean is:1 mk
- Q4If a^b=32, where 'a' and 'b' are positive integers, then the value of b^ab is:1 mk
- Q4If θ is an acute angle and 7+4 sin θ=9, then the value of θ is:1 mk
- Q4The least number which is a perfect square and is divisible by each of 16, 20 and 50, is:1 mk
- Q4Which of the following equations is a quadratic equation?1 mk
- Q4The distance of a point A from x -axis is 3 units. Which of the following cannot be coordinates of the point A?1 mk
- Q5The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a red ball at…1 mk
- Q5The distance of the point A(-3, -4) from x -axis is1 mk
- Q5If one zero of the polynomial q(x)=(p^2+4) x^2+65 x+4 p is reciprocal of the other, then the value of ' p ' is:1 mk
- Q5In the adjoining figure, AC is diameter of larger circle with centre O. AB is tangent to smaller circle with centre O.…1 mk
- Q5If sin 4 θ=(√3)/2, then (θ)/3 equals:1 mk
- Q5The value of tan^2 θ-(1/(cos θ) × sec θ) is:1 mk
- Q5If x/12-3/x=0, then the values of x are:1 mk
- Q5The radii 'r' of a sphere and that of the base of a cone are same. If their volumes are also same, then the height of…1 mk
- Q5Which of the following quadratic equations has real and distinct roots?1 mk
- Q5If x^2+b x+b=0 has two real and distinct roots, then the value of b can be1 mk
- Q5The coordinates of the end points of a diameter of a circle are (5, -2) and (5, 2). The length of the radius of the…1 mk
- Q6The distance of which of the following points from origin is less than 5 units?1 mk
- Q6The equation of a line parallel to y -axis and at a distance of 5 units to the right of y -axis is:1 mk
- Q6Zeroes of the polynomial p(y)=7 y^2-11/3 y-2/3 are:1 mk
- Q6The points (- 5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an:1 mk
- Q6If in a lottery, there are 10 prizes and 30 blanks, then the probability of winning a prize is:1 mk
- Q6In the figure given below, points P, Q, R divides the line segment AB in four equal parts. The point Q divides PB in…1 mk
- Q6In the adjoining figure, PQ∥XY∥ BC, AP=2 cm, PX=1.5 cm and BX=4 cm. If QY=0.75 cm, then AQ+CY=1 mk
- Q6The point P divides the line segment AB in the ratio 3: 1 as shown below: The value of AB/PB is1 mk
- Q6If HCF(98,28)=m and LCM(98,28)=n, then the value of n-7 m is:1 mk
- Q6The value of ' p ' for which the equations p x+3 y=p-3,12 x+p y=p has infinitely many solutions is:1 mk
- Q6The line represented by x/4+y/6=1, intersects x -axis and y -axis respectively at P and Q. The coordinates of the…1 mk
- Q7If α+β=90^° and α=2 β, then cos^2 α+ sin^2 β is equal to:1 mk
- Q7The tangents drawn at the extremities of the diameter of a circle are always:1 mk
- Q7Two of the vertices of Δ PQR are P(-1,5) and Q(5,2). The coordinates of a point which divides PQ in the ratio 2: 1 are:1 mk
- Q7A bag contains red balls and black balls in the ratio 3: 7. A ball is drawn at random. The probability that ball so…1 mk
- Q7In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If ∠ NML=30^°, then ∠ RLM…1 mk
- Q7Given ABC ∼ PQR, ∠ A=30^° and ∠ Q=90^°. The value of (∠ R+∠ B) is1 mk
- Q7ABC and PQR are shown in the adjoining figures. The measure of ∠ C is:1 mk
- Q7A system of two linear equations in two variables is inconsistent, if the lines in the graph are:1 mk
- Q7The distance of point (a, -b) from x -axis is1 mk
- Q8In triangles ABC and DEF, ∠ B=∠ E, ∠ F=∠ C and AB=3 DE. Then, the two triangles are:1 mk
- Q8tan 2 A=3 tan A is true, when the measure of ∠ A is:1 mk
- Q8Two coins are tossed simultaneously. The probability of getting atleast one head is1 mk
- Q8Which of the following equations is a quadratic equation?1 mk
- Q8The system of equations y+a=0 and 2 x=b has1 mk
- Q8If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle…1 mk
- Q8Which of the following statements is false?1 mk
- Q8In the given figure, PQ ∥ BC. If AP/PB=4/13 and AC=20 · 4 cm, then the length of AQ is:1 mk
- Q9A piggy bank contains ₹ 1 coins and ₹ 2 coins in the ratio 9: 11 respectively. The piggy bank is accidently dropped and…1 mk
- Q9Which of the following statements is incorrect?1 mk
- Q9( cot θ+ tan θ) equals:1 mk
- Q9Which of the following statements is true?1 mk
- Q9If (-1)^n+(-1)^8=0, then n is:1 mk
- Q9Letters A to F are mentioned on six faces of a die such that each face has a different letter. Two such dice are thrown…1 mk
- Q9In the adjoining figure, PA and PB are tangents to a circle with centre O such that ∠ P=90^°. If AB=3 √2 cm, then the…1 mk
- Q9In the adjoining figure, ABCD is a trapezium in which XY∥AB∥ CD. If AX=2/3 AD, then CY: YB=1 mk
- Q10Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:1 mk
- Q10Which of the following statements is false?1 mk
- Q10The sum of the exponents of prime factors in the prime factorisation of 4004 is:1 mk
- Q10Which of the following is a trigonometric identity?1 mk
- Q10If in two triangles DEF and PQR, ∠ D=∠ Q and ∠ R=∠ E, then which of the following is not true?1 mk
- Q10For a circle with centre O and radius 5 cm, which of the following statements is true? P: Distance between every pair…1 mk
- Q10A 30 m long rope is tightly stretched and tied from the top of pole to the ground. If the rope makes an angle of 60°…1 mk
- Q11In the adjoining figure, PA and PB are tangents to a circle with centre O. The measure of angle APB is1 mk
- Q11In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2 x^° is1 mk
- Q11Let p=x^2 y^3 z^n and q=x^3 y^m z^2, where x, y, z are prime numbers. If LCM (p, q)=x^3 y^4 z^3, then the value of (2…1 mk
- Q11In a cricket match, a batsman hits the boundary 7 times out of the 42 balls he plays. The probability of his not…1 mk
- Q11On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking…1 mk
- Q11If the sum of first m terms of an AP is 2 m^2+3 m, then its second term is:1 mk
- Q11If sin (α+β)=1, then the value of sin ((α+β)/2) is:1 mk
- Q11The measurements of Δ LMN and Δ ABC are shown in the figure given below. The length of side AC is:1 mk
- Q11The sum of the zeroes of the polynomial p(x)=5 x-7 x^2+3 is:1 mk
- Q12Which of the following equations does not have a real root?1 mk
- Q12Mode and Mean of a data are 15x and 18x, respectively. Then the median of the data is:1 mk
- Q12(1- tan^2 30^°)/(1+ tan^2 30^°) is equal to1 mk
- Q12If x((2 tan 30^°)/(1+ tan^2 30^°))=y((2 tan 30^°)/(1- tan^2 30^°)), then x: y=1 mk
- Q12If x= cos 30^°- sin 30^° and y= tan 60^°- cot 60^°, then1 mk
- Q12If a large circular pizza is divided into 5 equal sectors, then the central angle of each sector will be:1 mk
- Q12The value of (2 tan 60^°)/(1- tan^2 60^°) is same as the value of1 mk
- Q12If the volumes of two cubes are in the ratio 8: 125, then the ratio of their surface areas is:1 mk
- Q12If 1080=2^p × 3^q × 5, then (p-q) is equal to:1 mk
- Q12The cumulative frequency for calculating median is obtained by adding the frequencies of all the:1 mk
- Q13The distance of point P(1,-1) from x -axis is:1 mk
- Q13A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is:1 mk
- Q13If sin 30^° tan 45^°=(sec 60^°)/k, then the value of k is:1 mk
- Q13If mean and median of given set of observations are 10 and 11 respectively, then the value of mode is:1 mk
- Q13If the length of a chord of a circle is equal to its radius, then the angle subtended by chord at the centre is:1 mk
- Q13If the area of a sector of circle of radius 36 cm is 54 π cm^2, then the length of the corresponding arc of the sector…1 mk
- Q13(cos θ)/(√(1- cos^2 θ)) is equal to:1 mk
- Q13Which of the following equation is a quadratic equation?1 mk
- Q13A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is 10 √3 m…1 mk
- Q13If all the red face cards are removed from the deck of 52 playing cards, then the probability of getting a black jack…1 mk
- Q13If mean and mode of given set of observations are 10 and 13 respectively, then the value of median is:1 mk
- Q13An observer 1.8 m tall stands away from a chimney at a distance of 38.2 m along the ground. The angle of elevation of…1 mk
- Q14The greatest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is:1 mk
- Q14A die is thrown once. The probability of getting a number which is not a factor of 36, is:1 mk
- Q14In the adjoining figure, AB is the chord of the larger circle touching the smaller circle. The centre of both the…1 mk
- Q14The discriminant of the quadratic equation bx^2+ax+c=0; b ≠ 0 is given by:1 mk
- Q14The line represented by the equation x-y=0 is:1 mk
- Q14The distance of point P(3 a, 4 a) from y -axis is1 mk
- Q14In the adjoining figure, AB is the chord of larger circle which touches the smaller circle at P. If length of AB=…1 mk
- Q14In the adjoining figure, the sum of radii of two concentric circles is 16 cm. The length of chord A B which touches the…1 mk
- Q14If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of…1 mk
- Q14Which of the following is a rational number between √3 and √5?1 mk
- Q15The 10^th term of the AP 5, 19/4, 9/2, 17/4, … is:1 mk
- Q15A ladder 14 m long leans against a wall. If the foot of the ladder is 7 m from the wall, then the angle of elevation of…1 mk
- Q15If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are1 mk
- Q15If the mean of 2,9, x+6,2 x+3,5,10,5 is 7, then the value of x is:1 mk
- Q15If the mid-point of the line segment joining the points (a, 4) and (2, 2b) is ( 2,6 ), then the value of ( a+b ) is…1 mk
- Q15If a sector of a circle has an area of 40 π sq. units and a central angle of 72°, the radius of the circle is:1 mk
- Q15A parallelogram having one of its sides 5 cm circumscribes a circle. The perimeter of parallelogram is:1 mk
- Q15A cone of height 12 cm and slant height 13 cm is surmounted on a hemisphere having radius equal to that of cone. The…1 mk
- Q15In the following figure, P and Q are points of trisection of line segment AB: the value of AB/PB=1 mk
- Q16The end points of a diameter of circle are (2, 4) and (- 3, - 1). The length of its radius is:1 mk
- Q16AOBC is a rectangle whose three vertices are A (0,2), O (0,0) and B (4,0). The square of the length of its diagonal is…1 mk
- Q16E and F are points on the sides AB and AC respectively of a ABC such that AE/EB=AF/FC=1/2. Which of the following…1 mk
- Q16If x median + y mean = z mode; is the empirical relationship between mean, median and mode, then the value of x+y+z is1 mk
- Q16In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=115^°, then ∠ APO is…1 mk
- Q16A bag contains red coloured, blue coloured and green coloured balls in the ratio 2: 3: 4. A ball is drawn at random…1 mk
- Q16If - 4 is a zero of the polynomial p(x)=x^2-x-(2+2 k), then the value of k is:1 mk
- Q16If the maximum number of students has obtained 52 marks out of 80, then1 mk
- Q17sec A=2 cos A is true for A=1 mk
- Q17The 11^th and 13^th term of an AP are 39 and 45, respectively. What is the common difference of the AP?1 mk
- Q17The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is:1 mk
- Q17A kite is flying at a height of 150 m from the ground. It is attached to a string inclined at an angle of 30° to the…1 mk
- Q17Following data shows the marks obtained by 100 students in a class test: The median will be the average of which two…1 mk
- Q17Zeroes of the polynomial p(x)=x^2-3 √2 x+4 are:1 mk
- Q17Which of the following statements is true for a polynomial p(x) of degree 3?1 mk
- Q17The system of equations 2 x+1=0 and 3 y-5=0 has1 mk
- Q18The HCF of 40, 110 and 360 is:1 mk
- Q18A piece of wire 20 cm long is bent into the form of an arc of a circle of radius 60/(π) cm. The angle subtended by the…1 mk
- Q18In the given figure, in Δ ABC, AD ⊥ BC and ∠ BAC=90^°. If BC=16 cm and DC=4 cm, then the value of x is:1 mk
- Q18A pair of dice is thrown. The probability that sum of numbers appearing on top faces is at most 10 is:1 mk
- Q18In a right triangle ABC, right-angled at A, if sin B = 1/4, then the value of sec B is1 mk
- Q18The probability of getting a composite number greater than 3 on throwing a die is1 mk
- Q18A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a spade or a king?1 mk
- Q19Assertion: For an acute angle θ, value of cosec θ cannot be 1/(√2). Reason (R): cosec θ ≥ 1 for 0^° ≤ θ ≤ 90^°1 mk
- Q19Assertion: A line drawn perpendicular to the tangent at point of contact passes through the centre of the circle.…1 mk
- Q19Assertion (A): Common difference of the AP: 5,1,-3,-7, … is 4. Reason (R): Common difference of the AP: a_1, a_2, a_3,…1 mk
- Q19Assertion: A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the…1 mk
- Q19Assertion: For an acute angle θ, sin θ=3/5 ⇒ cos θ=-4/5. Reason (R): For any value of θ, (0^° ≤ θ ≤ 90^°) sin^2 θ+…1 mk
- Q19Assertion: For any two prime numbers p and q, their HCF is 1 and LCM is p + q. Reason (R): For any two natural numbers,…1 mk
- Q19Assertion: The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R): For any event E,…1 mk
- Q19Assertion: 4^n ends with digit 0 for some natural number n. Reason (R): For a number ' x ' having 2 and 5 as its prime…1 mk
- Q19Assertion: For two prime numbers x and y(x<y), HCF(x, y)=x and LCM(x, y)=y. Reason (R): HCF(x, y) ≤ LCM(x, y), where x,…1 mk
- Q20Assertion: Tangents drawn at the end points of a diameter of a circle are always parallel to each other. Reason (R):…1 mk
- Q20Assertion: Unit digit of 3^n cannot be an even number for any natural number n. Reason (R): 2 is not a prime factor of…1 mk
- Q20Assertion: The pair of linear equations px + 3y + 59=0 and 2 x+6 y+118=0 will have infinitely many solutions if p=1.…1 mk
- Q20Assertion: If we join two hemispheres of same radius along their bases, then we get a sphere. Reason (R): Total Surface…1 mk
- Q20Assertion: If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre…1 mk
- Q20In an experiment of throwing a die, Assertion: Event E_1: getting a number less than 3 and Event E_2: getting a number…1 mk
- Q20Assertion: For an A.P., 3,6,9, …, 198,10^th term from the end is 168. Reason (R): If 'a' and ' l ' are the first term…1 mk
- Q20Assertion: For an acute angle θ, sec θ=3 ⇒ tan θ=2 √2. Reason (R): sec^2 θ=1- tan^2 θ for all values of θ.1 mk
- Q20Assertion: For two odd prime numbers x and y,(x ≠ y), LCM(2 x, 4 y)=4 x y Reason (R): LCM(x, y) is a multiple of HCF(x,…1 mk
- Q21Solve the following pair of equations algebraically: 101 x+102 y=304; 102 x+101 y=305 OR In a pair of supplementary…2 mk
- Q21Find a quadratic polynomial whose zeroes are 2 and -7/5.2 mk
- Q21In the adjoining figure, AD/BD=AE/EC and ∠ BDE=∠ CED, prove that ABC is an isosceles triangle.2 mk
- Q21If 4 k= tan^2 60^°-2 cosec^2 30^°-2 tan^2 30^°, then find the value of k.2 mk
- Q21If the sum of the zeroes of the polynomial p(x)=(p+1) x^2+(2 p+3) x+(3 p+4) is -1, then find the value of 'p'. OR If α…2 mk
- Q21If x cos 60^°+y cos 0^°+ sin 30^°- cot 45^°=5, then find the value of x+2 y. OR Evaluate: (tan^2 60^°)/(sin^2 60^°+…2 mk
- Q21If the zeroes of the polynomial x^2+ax+b are in the ratio 3: 4, then prove that 12 a^2=49 b.2 mk
- Q21If p and q are zeroes of the polynomial p(y)=21 y^2-y-2, then find the value of (1-p).(1-q).2 mk
- Q21If tan A+ cot A=6, then find the value of tan^2 A+ cot^2 A-4.2 mk
- Q21Solve the following system of equations algebraically: 30 x+44 y=10; 40 x+55 y=132 mk
- Q21AD and PS are angle bisectors of ∠ A and ∠ P of triangles ABC and PQR. If ABC ∼ PQR, prove that ACD ∼ PRS.2 mk
- Q21The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg grapes was…2 mk
- Q22The coordinates of the end points of the line segment AB are A(-2, -2) and B(2,-4). P is the point on AB such that…2 mk
- Q22The probability of guessing the correct answer of a certain test question is x/12. If the probability of not guessing…2 mk
- Q22A bag contains cards which are numbered from 5 to 100 such that each card bears a different number. A card is drawn at…2 mk
- Q22All the face cards are removed from the pack of 52 cards and a card is drawn at random from the remaining cards. Find…2 mk
- Q22Find the zeroes of the polynomial p(x)=x^2+4/3 x-4/3.2 mk
- Q22A 1.5 m tall boy is walking away from the base of a lamp post which is 12 m high, at the speed of 2.5 m/sec. Find the…2 mk
- Q22Saima and Aryaa were born in the month of June in the year 2012. Find the probability that: (i) they have different…2 mk
- Q22If a sec θ+b tan θ=m and b sec θ+a tan θ=n, prove that a^2+n^2=b^2+m^2 OR Use the identity: sin^2 A+ cos^2 A=1 to prove…2 mk
- Q22In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠ AOB=90^°. If…2 mk
- Q23The coordinates of the centre of a circle are (2a, a - 7). Find the value(s) of 'a' if the circle passes through the…2 mk
- Q23Find the coordinates of the point C which lies on the line AB produced such that AC=2 BC, where coordinates of points A…2 mk
- Q23In ABC and PQR, AD and PS are altitudes such that ABD ∼ PQS and ACD ∼ PRS. Prove that ABC ∼ PQR.2 mk
- Q23Find the smallest number which is divisible by both 644 and 462. OR Two numbers are in the ratio 4: 5 and their HCF is…2 mk
- Q23In the adjoining figure, AP=1 cm, BP=2 cm, AQ=1.5 cm and AC=4.5 cm. Prove that APQ ∼ ABC. Hence find the length of PQ,…2 mk
- Q23Solve the following system of equations algebraically: 37 x+63 y=137 63 x+37 y=1632 mk
- Q23Prove that abscissa of a point P which is equidistant from points with coordinates A(7, 1) and B(3, 5) is 2 more than…2 mk
- Q23If tan A=√3; where A is an acute angle, then find the value of (sin^2 A)/(1+ cos^2 A).2 mk
- Q23It is given that sin (A-B)= sin A cos B- cos A sin B. Use it to find the value of sin 15^°. OR If sin A=y, then express…2 mk
- Q24Find the value(s) of 'k' so that the quadratic equation 4 x^2+kx+1=0 has real and equal roots. OR If ' α ' and ' β '…2 mk
- Q24In the given figure, D is a point on the side BC of Δ ABC such that ∠ ADC=∠ BAC. Show that CA^2=CD. CB. OR In the given…2 mk
- Q24A bag contains balls numbered 2 to 91 such that each ball bears a different number. A ball is drawn at random from the…2 mk
- Q24If ABC ∼ PQR in which AB=6 cm, BC=4 cm, AC=8 cm and PR=6 cm, then find the length of ( PQ+QR ). OR In the given figure,…2 mk
- Q24From a pack of 52 cards, all aces and all kings are removed. A card is drawn at random from the remaining cards. Find…2 mk
- Q24P is a point on the side BC of ABC such that ∠ APC=∠ BAC. Prove that AC^2=BC · CP.2 mk
- Q24Find the value of x for which ( sin A+cosec A)^2+( cos A+ sec A)^2=x+ tan^2 A+ cot^2 A OR Evaluate the following: (3…2 mk
- Q24Renu and Simran were born in the year 2000 which is a leap year. Find the probability that: (i) both have same…2 mk
- Q24AD and PS are medians of triangles ABC and PQR respectively such that ABD ∼ PQS. Prove that ABC ∼ PQR.2 mk
- Q25While shuffling a pack of 52 cards, one card was accidently dropped. Find the probability that the dropped card (i) is…2 mk
- Q25At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the…2 mk
- Q25A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that…2 mk
- Q25Solve the following system of equations algebraically: 73 x-37 y=109 37 x-73 y=12 mk
- Q25Two friends Anil and Ashraf were born in the December month in the year 2010. Find the probability that: (i) they share…2 mk
- Q25The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball…2 mk
- Q25Find the length of the median through the vertex B of ABC with vertices A(9, -2), B(-3, 7) and C(-1, 10).2 mk
- Q25In the given figure, PS/SQ=PT/TR and ∠ PST=∠ PRQ. Prove that Δ PQR is an isosceles triangle. OR In the given figure, Δ…2 mk
- Q25Prove that the tangents drawn at the ends of a diameter of a circle are parallel.2 mk
- Q26α and β are zeroes of a quadratic polynomial x^2-a x-b. Obtain a quadratic polynomial whose zeroes are 3 α+1 and 3 β+1.3 mk
- Q26Check whether the given system of equations is consistent or not. If consistent, solve graphically. x-2 y=0; 2 x+y=03 mk
- Q26Prove that √3 is an irrational number. OR State true or false for each of the following statements and justify in each…3 mk
- Q26Find the zeroes of the polynomial p(x)=6 x^2-5 x-1. Hence, obtain a polynomial each of whose zeroes is three times the…3 mk
- Q26If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x+y-10=0, find the value of…3 mk
- Q26Prove that (4 √2+5/3) is an irrational number given that √2 is an irrational number.3 mk
- Q26Prove that √5 is an irrational number. OR Let p, q and r be three distinct prime numbers. Check whether p · q · r+q is…3 mk
- Q26Prove that √2 is an irrational number. OR Let x and y be two distinct prime numbers and p=x^2 y^3, q=x y^4, r=x^5 y^2.…3 mk
- Q26Prove that √5 is an irrational number.3 mk
- Q26In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠ BAC+∠ ACD=90^°. OR Prove…3 mk
- Q26Prove that: √(sec^2 θ+cosec^2 θ)= tan θ+ cot θ OR If cosec θ=x+1/(4 x), prove that cosec θ+ cot θ=2 x or 1/(2 x).3 mk
- Q26All face cards of spades are removed from a pack of 52 playing cards and the remaining pack is shuffled well. A card is…3 mk
- Q26If tan θ+ sin θ=m and tan θ- sin θ=n, then prove that m^2-n^2=4 √mn. OR Prove that: (cot A-1)/(2- sec^2 A)=(cot A)/(1+…3 mk
- Q26If the radii of the bases of a cylinder and a cone are in the ratio 3: 4 and their heights are in the ratio 2: 3, find…3 mk
- Q26Prove that the parallelogram circumscribing a circle is a rhombus. OR Prove that the angle between the two tangents…3 mk
- Q27Three sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored…3 mk
- Q27Find the sum of all 3-digit natural numbers which are divisible by 11.3 mk
- Q27Prove that: (1+1/(tan^2 θ))(1+1/(cot^2 θ))=1/(sin^2 θ- sin^4 θ) OR Prove that: √((cosec θ-1)/(cosec θ+1))+√((cosec…3 mk
- Q27Prove that (5 √3+2/3) is an irrational number given that √3 is an irrational number.3 mk
- Q27If (a, b) is the mid-point of the line segment joining the points A(10, - 6) and B(k, 4) and a-2 b=18, then find the…3 mk
- Q27If 65\% of the population has black eyes, 25\% have brown eyes and the remaining have blue eyes, what is the…3 mk
- Q27Two dice are rolled together. Find the probability of getting: (i) a multiple of 2 on one and a multiple of 3 on the…3 mk
- Q27Obtain the zeroes of the polynomial 7 x^2+18 x-9. Hence, write a polynomial each of whose zeroes is twice the zeroes of…3 mk
- Q27Find the zeroes of the polynomial p(x)=3 x^2-4 x-4. Hence, write a polynomial whose each of the zeroes is 2 more than…3 mk
- Q27Prove that: (tan θ)/(1- cot θ)+(cot θ)/(1- tan θ)=1+ sec θ cosec θ OR Prove that: (sin A+ cos A)/(sin A- cos A)+(sin A-…3 mk
- Q27In the given figure, PB is a tangent to the circle with centre O at B. AB is a chord of the circle of length 24 cm and…3 mk
- Q27The monthly incomes of two persons are in the ratio 9: 7 and their monthly expenditures are in the ratio 4: 3. If each…3 mk
- Q28If α and β are the zeroes of the polynomial a x^2-x+c. Obtain a polynomial whose zeroes are α-3 and β-3.3 mk
- Q28Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the…3 mk
- Q28Check whether the following pair of equations is consistent or not. If consistent, solve graphically x+3 y=6; 3 y-2…3 mk
- Q28Prove that: √((sec A-1)/(sec A+1))+√((sec A+1)/(sec A-1))=2 cosec A OR Prove that: (1/(cos A)- cos A)(1/(sin A)- sin…3 mk
- Q28P(x, y), Q(-2,-3) and R(2,3) are the vertices of a right triangle PQR right angled at P. Find the relationship between…3 mk
- Q28Solve the following system of equations graphically: 2 x-y-2=0; -4 x+y+4=0 Also, find the absolute difference between…3 mk
- Q28If the mid-point of the line segment joining the points A(3,4) and B(k, 6) is P(x, y) and x+y-10=0, then find the value…3 mk
- Q29The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock…3 mk
- Q29Prove that 1/(√5) is an irrational number.3 mk
- Q29Obtain the zeroes of the polynomial p(x)=2 x^2-5 x-3. Hence, obtain a polynomial each of whose zeroes is one less than…3 mk
- Q29Find a relation between x and y such that P(x, y) is equidistant from the points A(3, 5) and B(7, 1). Hence, write the…3 mk
- Q29A chord of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the…3 mk
- Q29Prove that (cos A+ sin A-1)/(cos A- sin A+1)=cosec A- cot A OR If cot θ+ cos θ=p and cot θ- cos θ=q, prove that…3 mk
- Q29The two angles of a right angled triangle other than 90° are in the ratio 2: 3. Express the given situation…3 mk
- Q29Find the zeroes of the polynomial q(x)=8 x^2-2 x-3. Hence, find a polynomial whose zeroes are 2 less than the zeroes of…3 mk
- Q29If the points A(6,1), B(p, 2), C(9,4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p…3 mk
- Q30Solve the following system of equations graphically: 2 x+y=5 and 4 x-y=7. Hence, write the coordinates of the points…3 mk
- Q30Check whether the following system of equations is consistent or not. If consistent, solve graphically x-2 y+4=0,2…3 mk
- Q30Three unbiased coins are tossed simultaneously. Find the probability of getting: exactly two tails at least one head at…3 mk
- Q30Prove that √3 is an irrational number.3 mk
- Q30Prove that: (cos θ-2 cos^3 θ)/(sin θ-2 sin^3 θ)+ cot θ=0. OR Given that sin θ+ cos θ=x, prove that sin^4 θ+ cos^4…3 mk
- Q30Prove the following trigonometric identity: (1+cosec A)/(cosec A)=(cos^2 A)/(1- sin A) OR Let 2 A+B and A+2 B be acute…3 mk
- Q30α and β are zeroes of a quadratic polynomial p x^2+q x+1. Form a quadratic polynomial whose zeroes are 2/(α) and 2/(β).3 mk
- Q30A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of…3 mk
- Q31In the adjoining figure, XY and X'Y' are parallel tangents to a circle with centre O. Another tangent AB touches the…3 mk
- Q31In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the tangent at…3 mk
- Q31The perimeter of a rectangle is 70 cm. The length of the rectangle is 5 cm more than twice is breadth. Express the…3 mk
- Q31Find the zeroes of the polynomial r(x)=4 x^2+3 x-1. Hence, write a polynomial whose zeroes are reciprocal of the zeroes…3 mk
- Q31Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.3 mk
- Q31Rectangle ABCD circumscribes the circle of radius 10 cm. Prove that ABCD is a square. Hence, find the perimeter of ABCD.3 mk
- Q31A sum of ₹ 2,000 is invested at 7 % per annum simple interest. Calculate the interests at the end of 1^st, 2^nd and…3 mk
- Q31Solve the following system of equations graphically: 2 x+3 y=6; x+y-1=0 Also, find the sum of ordinates of the points…3 mk
- Q31In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠ OPQ=15^° and ∠ PTQ=θ, then find…3 mk
- Q32Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed…5 mk
- Q32A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the…5 mk
- Q32State the basic proportionality theorem. Use the theorem to do the following: In ABC, AD is the angle bisector of angle…5 mk
- Q32An AP consists of 'n' terms whose n^th term is 4 and the common difference is 2. If the sum of ' n ' terms of AP is…5 mk
- Q32The perimeter of an isosceles triangle is 32 cm. If each equal side is 5/6 th of the base, find the area of the…5 mk
- Q32Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8\% per annum and…5 mk
- Q32Following data shows the number of family members living in different bungalows of a locality: If the median number of…5 mk
- Q32The sides of a right triangle are such that the longest side is 4 m more than the shortest side and the third side is 2…5 mk
- Q32There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to…5 mk
- Q32The following table shows the number of traffic challans issued in the month of April by the traffic police: Find the…5 mk
- Q32A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the…5 mk
- Q32During a medical checkup, height of 35 students of a class were recorded as follows: Find the difference between the…5 mk
- Q33The sum of the areas of two squares is 52 cm^2 and difference of their perimeters is 8 cm. Find the lengths of the…5 mk
- Q33The students of a class are made to stand equally in rows. If 3 students are extra in each row, there would be 1 row…5 mk
- Q33A bag contains some red and blue balls. Ten percent of the red balls, when added to twenty percent of the blue balls,…5 mk
- Q33The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find…5 mk
- Q33A bat manufacturing company made a huge bat for charity and got it signed by world cup winning team. The dimensions of…5 mk
- Q33The sum of the third term and the seventh term of an AP is 6 and their product is 8. Find the sum of the first sixteen…5 mk
- Q33If a line drawn parallel to one side of triangle intersecting the other two sides in distinct points divides the two…5 mk
- Q33Fermentation tanks are designed in the form of cylinder mounted on a cone as shown below: The total height of the tank…5 mk
- Q33If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points then it…5 mk
- Q33The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side…5 mk
- Q33The corresponding sides of ABC and PQR are in the ratio 3: 5. AD ⊥ BC and PS ⊥ QR as shown in the following figures:…5 mk
- Q34Find the mean and median for the following data:5 mk
- Q34On the day of her examination, Riya sharpened her pencil from both ends as shown below: The diameter of the cylindrical…5 mk
- Q34The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the…5 mk
- Q34A wooden cubical die is formed by forming hemispherical depressions on each face of the cube such that face 1 has one…5 mk
- Q34State the converse of basic proportionality theorem. Also find BF/FC in the following figure, given that AB∥DC∥ EF and…5 mk
- Q34From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area…5 mk
- Q34From one of the faces of a solid wooden cube of side 14 cm, maximum number of hemispheres of diameter 1.4 cm are…5 mk
- Q34The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is…5 mk
- Q34A man lent a part of his money at 10\% p.a. and the rest at 15\% p.a. His income at the end of the year is ₹ 1,900. If…5 mk
- Q34Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides…5 mk
- Q34Following table shows the absentees record of 40 students in an academic year: Find the 'mean' and the 'mode' of the…5 mk
- Q34The following table gives the daily income of 50 cab drivers of a particular city: Find the mean income and the modal…5 mk
- Q34In the given figure, PA, QB and RC are perpendicular to AC. If PA=x units, QB=y units and RC=z units, prove that…5 mk
- Q34Find the Mean and Mode of the following data:5 mk
- Q34The population of lions was noted in different regions across the world in the following table: If the median of the…5 mk
- Q35Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode.5 mk
- Q35A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It…5 mk
- Q35Medical check-up was carried out for 35 students of a class and their weights were recorded as follows: Find the…5 mk
- Q35Following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find…5 mk
- Q35A two-digit number is such that the product of its digits is 12. When 36 is added to this number, the digits…5 mk
- Q35In order to provide shelter to flood victims, a shed was constructed using tin sheets which is in the form of cuboid…5 mk
- Q35The following table shows the number of patients of different age group who were discharged from the hospital in a…5 mk
- Q35The angle of elevation of an airborne helicopter from a point A on the ground is 45°. After a flight of 15 seconds, the…5 mk
- Q35The numerator of a fraction is 3 less than its denominator. If 2 is added to both numerator and denominator, then the…5 mk
- Q35Find the Mean and Mode of the following frequency distribution:5 mk
- Q36A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the…4 mk
- Q36Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three parts by…4 mk
- Q36A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds…4 mk
- Q36The Olympic symbol comprising five interlocking rings represents the union of the five continents of the world and the…4 mk
- Q36A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school…4 mk
- Q36A farmer has a circular piece of land. He wishes to construct his house in the form of largest possible square within…4 mk
- Q37Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride…4 mk
- Q37In order to organise, Annual Sports Day, a school prepared an eight lane running track with an integrated football…4 mk
- Q37Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he…4 mk
- Q37A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from…4 mk
- Q37In an equilateral triangle of side 10 cm, equilateral triangles of side 1 cm are formed as shown in the figure below,…4 mk
- Q37A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching…4 mk
- Q38Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile…4 mk
- Q38A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical…4 mk
- Q38Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to…4 mk
- Q38A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there…4 mk
- Q38The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our…4 mk
- Q38The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of…4 mk
Other Mathematics years
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