CBSE Class 10 Mathematics 2024
304 questions · 661 marks · 303 with the board’s own marking-scheme answer so far.
What 2024 actually asked, chapter by chapter
Marks we counted in the 2024 papers themselves. CBSE allocates marks per unit, not per chapter — this is what was observed, not an official CBSE weightage.
| 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% |
All 304 questions from 2024
- Q1The next (4^ th ) term of the A.P. √18, √50, √98, … is:1 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- Q1The LCM of the smallest prime number and the smallest odd composite number is:1 mk
- Q2In an A.P., if the first term =-16 and the common difference =-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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- Q3If 4 sec θ-5=0, then the value of cot θ is:1 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- Q3Two dice are thrown together. The probability that they show different numbers is:1 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- Q5The ratio of the sum and product of the roots of the quadratic equation 5 x^2-6 x+21=0 is:1 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- Q6AD is a median of ABC with vertices A(5, -6), B(6,4) and C(0, 0). Length AD is equal to:1 mkasked 3×
- 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 mkasked 2×
- Q6The zeroes of the quadratic polynomial 2 x^2-3 x-9 are:1 mkasked 2×
- 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 mkasked 3×
- Q7If sin θ= cos θ,(0^°<θ<90^°), then value of ( sec θ · sin θ) is:1 mkasked 3×
- Q7One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket…1 mkasked 2×
- Q7If sec θ- tan θ=m, then the value of sec θ+ tan θ is:1 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- Q8Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is:1 mkasked 2×
- Q8If cos θ=(√3)/2 and sin φ=1/2, then tan (θ+φ) is:1 mkasked 2×
- Q8Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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- x) is equal…1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q10If sin θ=1, then the value of 1/2 sin ((θ)/2) is:1 mkasked 2×
- Q10The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is:1 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q11If the distance between the points (3, -5) and (x,-5) is 15 units, then the values of x are:1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- Q12If value of each observation in a data is increased by 2, then median of the new data1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q12Three numbers in A.P. have the sum 30. What is its middle term?1 mkasked 2×
- 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 mkasked 3×
- Q13A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken…1 mkasked 3×
- 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 mkasked 3×
- Q13The LCM of three numbers 28, 44, 132 is:1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q14If the product of two co-prime numbers is 553, then their HCF is:1 mkasked 2×
- 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 mkasked 2×
- Q14In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If…1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- Q15The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is:1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- Q16The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is:1 mkasked 3×
- 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 mkasked 2×
- Q16Which term of the A.P. -29, -26, -23,....., 61 is 16?1 mkasked 3×
- Q16In the given figure, RJ and RL are two tangents to the circle. If ∠ RJL=42^°, then the measure of ∠ JOL is:1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- Q17For an event E, if P(E)+P( E)=q, then the value of q^2-4 is:1 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- Q18In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets…1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q19Assertion: Mid-point of a line segment divides the line segment in the ratio 1: 1. Reason(R): The ratio in which the…1 mkasked 3×
- 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 mkasked 3×
- Q19Assertion: ABCD is a trapezium with DC AB. E and F are points on AD and BC respectively, such that EF AB. Then…1 mkasked 3×
- Q20Assertion: In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a…1 mkasked 3×
- Q20Assertion: If the graph of a polynomial touches x -axis at only one point, then the polynomial cannot be a quadratic…1 mkasked 3×
- Q20Assertion: Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is…1 mkasked 3×
- Q20Assertion: If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference =2 π ×…1 mkasked 3×
- Q20Assertion: Degree of a zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q21Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time…2 mkasked 2×
- Q22In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the…2 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q22Evaluate: (2 tan 30^° · sec 60^° · tan 45^°)/(1- sin^2 60^°)2 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q25A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam, a trader,…2 mkasked 2×
- 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 mkasked 3×
- Q26Prove that √3 is an irrational number. OR Prove that (√2+√3)^2 is an irrational number, given that √6 is an irrational…3 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q27In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively.…3 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q28Solve the following system of linear equations graphically:3 mkasked 3×
- Q28Prove that the parallelogram circumscribing a circle is a rhombus.3 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- Q30Prove that (2-√3)/5 is an irrational number, given that √3 is an irrational number.3 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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. (O)/CD1BA/223 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. 4…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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 Sides…5 mkasked 3×
- 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 mkasked 3×
- Q33From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are…5 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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. /DA2AB/215 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 mkasked 3×
- Q35The following table shows the ages of the patients admitted in a hospital during a year: Find the mode and mean of the…5 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- Q36Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of…4 mkasked 3×
- Q36Essel World is one of India's largest amusement parks that offers a diverse range of thrilling rides, water attractions…4 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q37BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers…4 mkasked 3×
- Q37The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human…4 mkasked 3×
- Q37Vocational training complements traditional education by providing practical skills and hands-on experience. While…4 mkasked 3×
- Q37Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover…4 mkasked 3×
- 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 mkasked 3×
- Q38Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality,…4 mkasked 3×
- Q38Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement.…4 mkasked 3×
- Q38Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build…4 mkasked 3×
- Q38In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The…4 mkasked 3×
Other Mathematics years
Answers come from CBSE’s own marking schemes. How we source them.