CBSE Class 10 Mathematics 2024
304 questions · 661 marks · every one with the board’s own marking-scheme answer.
Marks by chapter
Counted from the 304 questions listed below, as the 2024 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 |
|---|---|---|
| Some Applications of Trigonometry19 questions | 75 | 11.3% |
| Introduction to Trigonometry36 questions | 70 | 10.6% |
| Surface Areas and Volumes15 questions | 47 | 7.1% |
| Circles24 questions | 45 | 6.8% |
| Pair of Linear Equations in Two Variables18 questions | 45 | 6.8% |
| Probability29 questions | 45 | 6.8% |
| Triangles17 questions | 43 | 6.5% |
| Statistics19 questions | 42 | 6.4% |
| Areas Related to Circles17 questions | 42 | 6.4% |
| Coordinate Geometry20 questions | 41 | 6.2% |
| Real Numbers24 questions | 38 | 5.7% |
| Arithmetic Progressions21 questions | 37 | 5.6% |
| Quadratic Equations11 questions | 33 | 5.0% |
| Polynomials20 questions | 29 | 4.4% |
304 questions from 2024
- Q1The next (4^th ) term of the A.P. √18, √50, √98, … is:1 mk
- Q1The value of k for which the system of equations 3 x-y+8=0 and 6 x-ky+16=0 has infinitely many solutions, is1 mk
- Q1If the sum of zeroes of the polynomial p(x)=2 x^2-k √2 x+1 is √2, then value of k is:1 mk
- Q1The distance between the points (a cos θ,-a sin θ) and (a sin θ, a cos θ) is1 mk
- Q1The pair of linear equations x+2 y+5=0 and -3 x=6 y-1 has1 mk
- Q1A bag contains 3 red balls, 5 white balls and 7 black balls. The probability that a ball drawn from the bag at random…1 mk
- Q1If ax+by=a^2-b^2 and bx+ay=0, then the value of x+y is:1 mk
- Q1The LCM of the smallest prime number and the smallest odd composite number is:1 mk
- Q2In an A.P., if the first term (a)=-16 and the common difference (d)=-2, then the sum of first 10 terms is:1 mk
- Q2The common difference of the A.P. 1/(2 x), (1-4 x)/(2 x), (1-8 x)/(2 x) is:1 mk
- Q2The probability of getting a bad egg in a lot of 400 eggs is 0.045. The number of good eggs in the lot is:1 mk
- Q2The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is:1 mk
- Q2In the given figure, PT is tangent to a circle with centre O. Chord PQ subtends an angle of 65° at the centre. The…1 mk
- Q2If the probability of a player winning a game is 0.79, then the probability of his losing the same game is:1 mk
- Q2If the mean of the first n natural numbers is (5 n)/9, then the value of n is:1 mk
- Q2If x/3=2 sin A, y/3=2 cos A, then the value of x^2+y^2 is:1 mk
- Q2Point P divides the line segment joining the points A(4, -5) and B(1, 2) in the ratio 5:2. Co-ordinates of point P are1 mk
- Q3If 4 sec θ-5=0, then the value of cot θ is:1 mk
- Q3The common difference of an A.P. in which a_15-a_11=48, is1 mk
- Q3The next (4^th ) term of the A.P. √7, √28, √63, … is:1 mk
- Q3If 5 tan θ-12=0, then the value of sin θ is:1 mk
- Q3If the roots of equation a x^2+b x+c=0, a ≠ 0 are real and equal, then which of the following relation is true?1 mk
- Q3If a polynomial p(x) is given by p(x)=x^2-5 x+6, then the value of p(1)+p(4) is:1 mk
- Q3Two dice are thrown together. The probability that they show different numbers is:1 mk
- Q4The quadratic equation x^2+x+1=0 has roots.1 mk
- Q4If the discriminant of the quadratic equation 3 x^2-2 x+c=0 is 16, then the value of c is:1 mk
- Q4The pair of linear equations y=0 and y=-7 have1 mk
- Q4If sin A=2/3, then value of cot A is:1 mk
- Q4If in the given figure, ∠ C=∠ D=90^°, ∠ B=60^° and AP=3 cm, then the area of the shaded region is:1 mk
- Q4The probability of guessing the correct answer to a certain test question is x/6. If the probability of not guessing…1 mk
- Q4Which out of the following type of straight lines will be represented by the system of equations 3 x+4 y=5 and 6 x+8…1 mk
- Q4In an A.P., if the first term a=7, n th term a_n=84 and the sum of first n terms s_n=2093/2, then n is equal to:1 mk
- Q5If x=a cos θ and y=b sin θ, then the value of b^2 x^2+a^2 y^2 is:1 mk
- Q5If a=2^2 × 3^x, b=2^2 × 3 × 5, c=2^2 × 3 × 7 and LCM(a, b, c)=3780, then x is equal to1 mk
- Q5The ratio of the sum and product of the roots of the quadratic equation 5 x^2-6 x+21=0 is:1 mk
- Q5If the HCF (2520, 6600) = 40 and LCM (2520, 6600) = 252 ´ k, then the value of k is1 mk
- Q5The area of the square inscribed in a circle of radius 5 √2 cm is:1 mk
- Q5If two positive integers p and q can be expressed as p=18 a^2 b^4 and q=20 a^3 b^2, where a and b are prime numbers,…1 mk
- Q5If a pair of linear equations in two variables is consistent, then the lines represented by the two equations are:1 mk
- Q5If the mean of 6, 7, p, 8, q, 14 is 9, then1 mk
- Q5If an arc subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the…1 mk
- Q6In the given figure ABC is shown. DE is parallel to BC. If AD=5 cm, DB=2.5 cm and BC=12 cm, then DE is equal to1 mk
- Q6AD is a median of ABC with vertices A(5, -6), B(6,4) and C(0, 0). Length AD is equal to:1 mk
- Q6If the area of a sector of a circle is 7/20 of the area of the circle, then the angle at the centre is equal to1 mk
- Q6If the quadratic equation ax^2+bx+c=0 has real and equal roots, then the value of c is:1 mk
- Q6If α and β are zeroes of the polynomial 2 x^2-9 x+5, then value of α^2+β^2 is1 mk
- Q6For the data 2,9, x+6,2 x+3,5,10,5; if the mean is 7, then the value of x is:1 mk
- Q6The area of the sector of a circle of radius 12 cm is 60 π cm^2. The central angle of this sector is:1 mk
- Q6The zeroes of the quadratic polynomial 2 x^2-3 x-9 are:1 mk
- Q7From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of…1 mk
- Q7If sin θ= cos θ,(0^°<θ<90^°), then value of ( sec θ · sin θ) is:1 mk
- Q7One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket…1 mk
- Q7If sec θ- tan θ=m, then the value of sec θ+ tan θ is:1 mk
- Q7One card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is a red ace card,…1 mk
- Q7If the difference of mode and median of a data is 24, then the difference of its median and mean is:1 mk
- Q7Which of the following is not probability of an event?1 mk
- Q8The roots of the quadratic equation 4 x^2-5 x+4=0 are1 mk
- Q8The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle, is:1 mk
- Q8Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is:1 mk
- Q8If cos θ=(√3)/2 and sin φ=1/2, then tan (θ+φ) is:1 mk
- Q8Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is1 mk
- Q8Two identical solid cubes of side 'a' are joined end-to-end. The total surface area of the resulting cuboid is:1 mk
- Q8The mean of five numbers is 15. If we include one more number, the mean of six numbers becomes 17. The included number…1 mk
- Q8From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a…1 mk
- Q9For θ=30^°, the value of (2 sin θ cos θ) is:1 mk
- Q9Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:1 mk
- Q9The common difference of an A.P. in which a_20-a_15=20, is1 mk
- Q9If α and β are zeroes of the polynomial 5 x^2+3 x-7, the value of 1/(α)+1/(β) is1 mk
- Q9The ratio of total surface area of a solid hemisphere to the square of its radius is:1 mk
- Q9For some data x_1, x_2, … … x_n with respective frequencies f_1, f_2, ….. f_n, the value of Σ_1^n f_i(x_i-x̄) is equal…1 mk
- Q9The length of an arc of a circle with radius 12 cm is 10 π cm. The angle subtended by the arc at the centre of the…1 mk
- Q9The 14^th term from the end of the A.P. -11,-8,-5, …, 49 is:1 mk
- Q10In the given figure, if PT is a tangent to a circle with centre O and ∠ TPO=35^°, then the measure of ∠ x is:1 mk
- Q10The zeroes of a polynomial x^2+p x+q are twice the zeroes of the polynomial 4 x^2-5 x-6. The value of p is:1 mk
- Q10If sin θ=1, then the value of 1/2 sin ((θ)/2) is:1 mk
- Q10The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is:1 mk
- Q10The length of the shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of…1 mk
- Q10The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ / AB is equal to1 mk
- Q10Two coins are tossed simultaneously. The probability of getting at most one tail is:1 mk
- Q11If the diagonals of a quadrilateral divide each other proportionally, then it is a:1 mk
- Q11Two lines are given to be parallel. The equation of one of these lines is 5 x-3 y=2. The equation of the second line…1 mk
- Q11If the distance between the points (3, -5) and (x,-5) is 15 units, then the values of x are:1 mk
- Q11What is the probability that a number selected randomly from the numbers 1, 2, 3,..., 15 is a multiple of 4?1 mk
- Q11AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the following:1 mk
- Q11If the mean of five observations x, x+2, x+4, x+6 and x+8 is 11, then the value of x is:1 mk
- Q11The number of terms in the A.P. 3,6,9,12, …, 111 is:1 mk
- Q12If value of each observation in a data is increased by 2, then median of the new data1 mk
- Q12If cos (α+β)=0, then value of cos ((α+β)/2) is equal to:1 mk
- Q12If α and β(α>β) are the zeroes of the polynomial -x^2+8 x+9, then (α-β) is equal to1 mk
- Q12A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is:1 mk
- Q12In Δ ABC, DE ∥ BC (as shown in the figure). If AD=2 cm, BD=3 cm, BC=7.5 cm, then the length of DE (in cm) is:1 mk
- Q12Three numbers in A.P. have the sum 30. What is its middle term?1 mk
- Q12If the prime factorisation of 2520 is 2^3 × 3^a × b × 7, then the value of a+2 b is:1 mk
- Q13If sin α=(√3)/2, cos β=(√3)/2, then tan α · tan β is:1 mk
- Q13A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn card has…1 mk
- Q13A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken…1 mk
- Q13In Δ ABC, DE ∥ BC (as shown in the figure). If AD=4 cm, AB=9 cm and AC=13 · 5 cm, then the length of EC is:1 mk
- Q13The LCM of three numbers 28, 44, 132 is:1 mk
- Q13If the sum and the product of zeroes of a quadratic polynomial are 2 √3 and 3 respectively, then a quadratic polynomial…1 mk
- Q13Given HCF(2520,6600)=40, LCM(2520,6600)=252 × k, then the value of k is:1 mk
- Q13Value of k for which x=2 is a solution of the equation 5 x^2-4 x+(2+k)=0, is1 mk
- Q14The middle most observation of every data arranged in order is called:1 mk
- Q14If the product of two co-prime numbers is 553, then their HCF is:1 mk
- Q14What should be added from the polynomial x^2-5 x+4, so that 3 is the zero of the resulting polynomial?1 mk
- Q14A pair of irrational numbers whose product is a rational number is:1 mk
- Q14In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If…1 mk
- Q14At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun's altitude at that…1 mk
- Q15XOYZ is a rectangle with vertices X(-3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each diagonal is1 mk
- Q15If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9; then the probability that this digit is an…1 mk
- Q15The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is:1 mk
- Q15The smallest irrational number by which √20 should be multiplied so as to get a rational number, is:1 mk
- Q15From the letters of the word "MOBILE", a letter is selected at random. The probability that the selected letter is a…1 mk
- Q15In the given figure, AB and AC are tangents to the circle. If ∠ ABC=42^°, then the measure of ∠ BAC is:1 mk
- Q15If α and β are the 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
- Q15The sum of first 200 natural numbers is1 mk
- Q16If 3825=3^x × 5^y × 17^z, then the value of x+y-2 z is:1 mk
- Q16The probability of throwing a number greater than 2 with a fair die is:1 mk
- Q16If α, β are the zeroes of the polynomial 6 x^2-5 x-4, then 1/(α)+1/(β) is equal to:1 mk
- Q16Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3 or 5, is:1 mk
- Q16The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is:1 mk
- Q16The mean of five observations is 15. If the mean of first three observations is 14 and that of the last three…1 mk
- Q16If the HCF(2520,6600)=40 and LCM(2520,6600)=252 × k, then the value of k is1 mk
- Q16Which term of the A.P. -29, -26, -23,....., 61 is 16?1 mk
- Q16In the given figure, RJ and RL are two tangents to the circle. If ∠ RJL=42^°, then the measure of ∠ JOL is:1 mk
- Q17If the sum of first n terms of an A.P. is 3 n^2+4 n and its common difference is 6, then its first term is:1 mk
- Q17The centre of a circle is at (2,0). If one end of a diameter is at (6,0), then the other end is at:1 mk
- Q17A quadratic polynomial, one of whose zeroes is 2+√5 and the sum of whose zeroes is 4, is:1 mk
- Q17n th term of an A.P. is 7 n+4. The common difference is:1 mk
- Q17In the given figure, AT is tangent to a circle centred at O. If ∠ CAT=40^°, then ∠ CBA is equal to1 mk
- Q17If y=1 is one of the solutions of the quadratic equation py^2+py+3=0, then the value of p is:1 mk
- Q17Perimeter of a sector of a circle whose central angle is 90° and radius 7 cm is:1 mk
- Q17The ratio of the length of a pole and its shadow on the ground is 1: √3. The angle of elevation of the Sun is:1 mk
- Q17In the given figure, in Δ ABC, DE ∥ BC. If AD=2 · 4 cm, DB=4 cm and AE=2 cm, then the length of AC is:1 mk
- Q17For an event E, if P(E)+P(Ē)=q, then the value of q^2-4 is:1 mk
- Q18In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of…1 mk
- Q18The value of θ for which 2 sin^2 θ=1/2; 0^° ≤ θ ≤ 90^° is:1 mk
- Q18After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She…1 mk
- Q18In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets…1 mk
- Q18If the first three terms of an A.P. are 3 p-1,3 p+5,5 p+1 respectively; then the value of p is:1 mk
- Q18What should be subtracted from the polynomial x^2-16 x+30, so that 15 is the zero of the resulting polynomial?1 mk
- Q18If the mean and mode of a data are 24 and 12 respectively, then its median is:1 mk
- Q18In the given figure, graphs of two linear equations are shown. The pair of these linear equations is:1 mk
- Q18If a vertical pole of length 7 · 5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow…1 mk
- Q19Assertion: The tangents drawn at the end points of a diameter of a circle, are parallel. Reason (R): Diameter of a…1 mk
- Q19Assertion: If sin A=1/3(0^°<A<90^°), then the value of cos A is (2 √2)/3 Reason (R): For every angle θ, sin^2 θ+ cos^2…1 mk
- Q19Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1: 1. Reason(R): The ratio in which…1 mk
- Q19Assertion: The point which divides the line segment joining the points A(1,2) and B(-1,1) internally in the ratio 1: 2…1 mk
- Q19Assertion (A): ABCD is a trapezium with DC ∥ AB. E and F are points on AD and BC respectively, such that EF ∥ AB. Then…1 mk
- Q20Assertion: In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a…1 mk
- Q20Assertion: If the graph of a polynomial touches x -axis at only one point, then the polynomial cannot be a quadratic…1 mk
- Q20Assertion: Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is…1 mk
- Q20Assertion: If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference =2 π ×…1 mk
- Q20Assertion: Degree of a zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.1 mk
- Q21Solve the following system of linear equations 7 x-2 y=5 and 8 x+7 y=15 and verify your answer.2 mk
- Q21In the given figure, Δ ABC is circumscribing a circle. Find the length of BC, if AR=4 cm, BR=3 cm and AC=11 cm.2 mk
- Q21Evaluate: (sec^2 45^°- tan^2 45^°)/(sin^2 45^°)2 mk
- Q21If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then find the length of each tangent.…2 mk
- Q21If α and β are zeroes of the quadratic polynomial p(x)=x^2-5 x+4, then find the value of 1/(α)+1/(β)-2 α β.2 mk
- Q21Can the number (15) ^n, n being a natural number, end with the digit 0? Give reasons.2 mk
- Q21The king, queen and ace of clubs and diamonds are removed from a deck of 52 playing cards and the remaining cards are…2 mk
- Q21Diagonals AC and BD of a trapezium ABCD intersect at O, where AB ∥ DC. If DO/OB=1/2, then show that AB=2 CD2 mk
- Q21One card is drawn at random from a well shuffled deck of 52 cards. Find the probability that the card drawn (i) is…2 mk
- Q21Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time…2 mk
- Q22In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the…2 mk
- Q22Evaluate: (5 tan 60^°)/(( sin^2 60^°+ cos^2 60^°) tan 30^°)2 mk
- Q22If 2 x+y=13 and 4 x-y=17, find the value of (x-y). OR Sum of two numbers is 105 and their difference is 45. Find the…2 mk
- Q22Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5).2 mk
- Q22The minute hand of a clock is 14 cm long. Find the area on the face of the clock described by the minute hand in 5…2 mk
- Q22Evaluate: (2 tan 30^° · sec 60^° · tan 45^°)/(1- sin^2 60^°)2 mk
- Q23In the given figure, EAEC = EB ED, prove that DEAB ~ DECD2 mk
- Q23Evaluate: 2 √2 cos 45^° sin 30^°+2 √3 cos 30^° OR If A=60^° and B=30^°, verify that: sin (A+B)= sin A cos B+ cos A sin B2 mk
- Q23In a school, there are two sections of class X. There are 40 students in the first section and 48 students in the…2 mk
- Q23Evaluate: (5 cos^2 60^°+4 sec^2 30^°- tan^2 45^°)/(sin^2 30^°+ sin^2 60^°) OR If sin (A-B)=1/2, cos ( A+B)=1/2; 0<A+B ≤…2 mk
- Q23Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.2 mk
- Q23Solve the following system of linear equations: 2 p+3 q=13 and 5 p-4 q=-22 mk
- Q23Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5). OR…2 mk
- Q23Evaluate: 2 sin^2 30^° sec 60^°+ tan^2 60^°. OR If 2 sin ( A+B)=√3 and cos (A-B)=1, then find the measures of angles A…2 mk
- Q23In the given figure, a circle centred at origin O has radius 7 cm, OC is median of Δ OAB. Find the length of median OC.2 mk
- Q23If α, β are zeroes of the polynomial p(x)=5 x^2-6 x+1, then find the value of α+β+α β.2 mk
- Q24In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that:2 mk
- Q24In the given figure, AB and CD are tangents to a circle centred at O. Is ∠ BAC=∠ DCA? Justify your answer.2 mk
- Q24Find the ratio in which the point P(-4,6) divides the line segment joining the points A(-6,10) and B(3, -8). OR Prove…2 mk
- Q24The vertices of a ABC are A(-2,4), B(4,3) and C(1,-6). Find length of the median BD.2 mk
- Q24In the given figure, O is the centre of the circle. If ∠ AOB=145^°, then find the value of x.2 mk
- Q24Solve the following system of linear equations algebraically: 2 x+5 y=-4; 4 x-3 y=52 mk
- Q24In the given figure, EA/EC=EB/ED, prove that Δ EAB ∼ Δ ECD2 mk
- Q25Evaluate: (cos 45^°+ sin 60^°)/(sec 30^°+cosec 30^°).2 mk
- Q25Can the number 8^n, n being a natural number, end with the digit 0? Give reasons.2 mk
- Q25Prove that 5-2 √3 is an irrational number. It is given that √3 is an irrational number. OR Show that the number 5 × 11…2 mk
- Q25In the given figure, EA/EC=EB/ED, prove that Δ EAB ∼ Δ ECD This section consists of 6 questions of 3 marks each.2 mk
- Q25In ABC, altitudes AD and BE are drawn. If AD=7 cm, BE=9 cm and EC=12 cm then, find the length of CD.2 mk
- Q25Evaluate: (2 tan 30^° · sec 60^° · tan 45^°)/(1- sin^2 60^°) This section comprises Short Answer (SA) type questions of…2 mk
- Q25In the given figure, Δ AHK ∼ Δ ABC. If AK=8 cm, BC=3 · 2 cm and HK=6 · 4 cm, then find the length of AC.2 mk
- Q25In what ratio is the line segment joining the points (3, -5) and (-1, 6) divided by the line y=x? OR A(3,0), B(6,4) and…2 mk
- Q25A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam, a trader,…2 mk
- Q26Prove that (sin θ- cos θ+1)/(sin θ+ cos θ-1)=1/(sec θ- tan θ)3 mk
- Q26Prove that (cosec^2 θ- sec^2 θ)/(cosec^2 θ+ sec^2 θ)=3/4, if tan θ=1/(√7)3 mk
- Q26If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first 20 terms. OR…3 mk
- Q26Prove that √3 is an irrational number. OR Prove that (√2+√3)^2 is an irrational number, given that √6 is an irrational…3 mk
- Q26Prove that: (tan θ- cot θ)/(sin θ cos θ)= sec^2 θ-cosec^2 θ3 mk
- Q26If the sum of first m terms of an A.P. is same as sum of its first n terms (m ≠ n), then show that the sum of its first…3 mk
- Q26Find the ratio in which the point (8/5, y) divides the line segment joining the points (1,2) and (2,3). Also, find the…3 mk
- Q26The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given…3 mk
- Q27In a test, the marks obtained by 100 students (out of 50 ) are given below: Marks obtained: 0-10 10-20 20-30 30-40…3 mk
- Q27Find the zeroes of the quadratic polynomial x^2-15 and verify the relationship between the zeroes and the coefficients…3 mk
- Q27The inner and outer radii of a hollow cylinder surmounted on a hollow hemisphere of same radii are 3 cm and 4 cm…3 mk
- Q27If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20^th term and the n^th…3 mk
- Q27A sector is cut from a circle of radius 21 cm. The central angle of the sector is 150°. Find the length of the arc of…3 mk
- Q27Prove that √5 is an irrational number.3 mk
- Q27In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively.…3 mk
- Q27In a chemistry lab, there is some quantity of 50\% acid solution and some quantity of 25\% acid solution. How much of…3 mk
- Q27Prove that (sin A+ cos A)/(sin A- cos A)+(sin A- cos A)/(sin A+ cos A)=2/(2 sin^2 A-1)3 mk
- Q27Three coins are tossed simultaneously. What is the probability of getting (i) at least one head? (ii) exactly two…3 mk
- Q28Rehana went to a bank to withdraw ₹ 2,000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25…3 mk
- Q28In the given figure, PQ is tangent to a circle centred at O and ∠ BAQ=30^°; show that BP=BQ. OR In the given figure,…3 mk
- Q28Solve the following system of linear equations graphically: x-y+1=0; x+y=53 mk
- Q28Prove that the parallelogram circumscribing a circle is a rhombus.3 mk
- Q28Three consecutive integers are such that sum of the square of second and product of other two is 161. Find the three…3 mk
- Q28In what ratio does the X-axis divides the line segment joining the points(2, -3) and (5,6)? Also, find the coordinates…3 mk
- Q28Prove that: (tan θ)/(1- cot θ)+(cot θ)/(1- tan θ)=1+ sec θ cosec θ3 mk
- Q29Find the ratio in which the line segment joining the points (5,3) and (-1, 6) is divided by Y-axis. OR P(-2,5) and…3 mk
- Q29If sin θ+ cos θ=p and sec θ+cosec θ=q, then prove that q(p^2-1)=2 p.3 mk
- Q29Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord.3 mk
- Q29Find the zeroes of the polynomial 4 x^2+4 x-3 and verify the relationship between zeroes and coefficients of the…3 mk
- Q29Prove that (1+ sec θ- tan θ)/(1+ sec θ+ tan θ)=(1- sin θ)/(cos θ).3 mk
- Q29A wooden toy is made by scooping out a hemisphere of same radius as of cylinder, from each end of a wooden solid…3 mk
- Q29Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are…3 mk
- Q29Prove that: (tan A)/(1- cot A)+(cot A)/(1- tan A)=1+ sec A cosec A3 mk
- Q30In a test, the marks obtained by 100 students (out of 50) are given below: Marks obtained: 40-50 Find the mean marks of…3 mk
- Q30A dealer sells an article for ₹ 75 and gains as much percent as the cost price of the article. Find the cost price of…3 mk
- Q30Prove that (sin θ-2 sin^3 θ)/(2 cos^3 θ- cos θ)= tan θ.3 mk
- Q30From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the…3 mk
- Q30Three unbiased coins are tossed simultaneously. Find the probability of getting: (i) at least one head. (ii) exactly…3 mk
- Q30Prove that (2-√3)/5 is an irrational number, given that √3 is an irrational number.3 mk
- Q30Prove that: (sin θ)/(1+ cos θ)+(1+ cos θ)/(sin θ)=2 cosec θ3 mk
- Q30In the given figure, AB is a diameter of the circle with centre O. AQ, BP and PQ are tangents to the circle. Prove that…3 mk
- Q30A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the…3 mk
- Q31Prove that the parallelogram circumscribing a circle is a rhombus.3 mk
- Q31Prove that sin^6 θ+ cos^6 θ=1-3 sin^2 θ cos^2 θ.3 mk
- Q31In a test, the marks obtained by 100 students (out of 50 ) are given below: Find the mean marks of the students.3 mk
- Q31In a 2-digit number, the digit at the unit's place is 5 less than the digit at the ten's place. The product of the…3 mk
- Q31Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord.3 mk
- Q31Prove that: (cosec θ- sin θ)( sec θ- cos θ)( tan θ+ cot θ)=1 This section consists of 4 questions of 5 marks each.3 mk
- Q31A jar contains 54 marbles, each of which is blue, green or white. The probability of selecting a blue marble at random…3 mk
- Q31Prove that √(sec^2 θ+cosec^2 θ)= tan θ+ cot θ. This section comprises Long Answer (LA) type questions of 5 marks each.…3 mk
- Q31A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was ₹ 15,000…3 mk
- Q31The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the…3 mk
- Q31An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the…3 mk
- Q32Find the value of 'k' for which the quadratic equation (k+1) x^2-2(3 k+1) x+(8 k+1)=0 has real and equal roots. OR A…5 mk
- Q32From the top of a 15 m high building, the angle of elevation of the top of a tower is found to be 30^°. From the bottom…5 mk
- Q32Find the value of 'k' for which the quadratic equation (k+1) x^2-6(k+1) x+3(k+9)=0, k ≠-1 has real and equal roots. OR…5 mk
- Q32Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a…5 mk
- Q32Using graphical method, solve the following system of equations: 3 x+y+4=0 and 3 x-y+2=0 OR Tara scored 40 marks in a…5 mk
- Q32A man on a cliff observes a boat at an angle of depression of 30° which is approaching the shore to the point…5 mk
- Q32The following distribution shows the daily pocket allowance of children of a locality. The mean daily pocket allowance…5 mk
- Q32The angle of elevation of an aircraft from a point A on the ground is 60°. After a flight of 30 seconds, the angle of…5 mk
- Q32An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find: (i) the length of the arc. (ii) the…5 mk
- Q32In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and by…5 mk
- Q32A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite…5 mk
- Q33E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE ∼ Δ CFB. OR…5 mk
- Q33State and prove Basic Proportionality theorem.5 mk
- Q33The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference…5 mk
- Q33From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are…5 mk
- Q33The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.5 mk
- Q33From the top of a building 60 m high, the angles of depression of the top and bottom of the vertical lamp post are…5 mk
- Q33If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, then the area of the rectangle is…5 mk
- Q33If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove…5 mk
- Q34From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are…5 mk
- Q34Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD…5 mk
- Q34A train travels a distance of 90 km at a constant speed. Had the speed been 15 km/h more, it would have taken 30…5 mk
- Q34From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top…5 mk
- Q34In the given figure, Δ FEC ≅ GDB and ∠ 1=∠ 2. Prove that Δ ADE ∼ Δ ABC. OR Sides AB and AC and median AD of a ABC are…5 mk
- Q34A tent is in the shape of a cylinder, surmounted by a conical top. If the height and diameter of the cylindrical part…5 mk
- Q34If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove…5 mk
- Q34From a window 15 metres high above the ground in a street, the angles of elevation and depression of the top and the…5 mk
- Q35The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.5 mk
- Q35The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are…5 mk
- Q35A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If…5 mk
- Q35The angles of depression of the top and the bottom of a 50 m high building from the top of a tower are 45° and 60°,…5 mk
- Q35A 2-digit number is such that the product of the digits is 14. When 45 is added to the number, the digits are reversed.…5 mk
- Q35A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm…5 mk
- Q35Using graphical method, solve the following system of equations: 3 x-2 y=10 and 5 x+3 y=4 OR If three times the greater…5 mk
- Q35The angle of elevation of a jet plane from a point A on the ground is 60^°. After a flight of 30 seconds, the angle of…5 mk
- Q35In the given figure, diameters AC and BD of the circle intersect at O. If ∠ AOB=60^° and OA=10 cm, then: (i) find the…5 mk
- Q35In ABC, if AD ⊥ BC and AD^2=BD × DC, then prove that ∠ BAC=90^°. /CD1BA/22 This section consists of 3 case study based…5 mk
- Q35A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another…5 mk
- Q35The following table shows the ages of the patients admitted in a hospital during a year: Find the mode and mean of the…5 mk
- Q35A juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical…5 mk
- Q35A pole 6m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P on…5 mk
- Q36A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by…4 mk
- Q36A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given…4 mk
- Q36Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of…4 mk
- Q36Essel World is one of India's largest amusement parks that offers a diverse range of thrilling rides, water attractions…4 mk
- Q36A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square…4 mk
- Q37A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the…4 mk
- Q37BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers…4 mk
- Q37The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human…4 mk
- Q37Vocational training complements traditional education by providing practical skills and hands-on experience. While…4 mk
- Q37Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover…4 mk
- Q38A backyard is in the shape of a triangle ABC with right angle at B. AB=7 m and BC=15 m. A circular pit was dug inside…4 mk
- Q38Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality,…4 mk
- Q38Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement.…4 mk
- Q38Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build…4 mk
- Q38In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The…4 mk
Other Mathematics years
Answers come from CBSE’s own marking schemes. How we source them.