CBSE Class 10 Mathematics 2026
310 questions · 698 marks · 306 with the board’s own marking-scheme answer, 4 with no official answer on the site.
Marks by chapter
Counted from the 310 questions listed below, as the 2026 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 |
|---|---|---|
| Introduction to Trigonometry44 questions | 82 | 11.7% |
| Statistics20 questions | 78 | 11.2% |
| Triangles31 questions | 74 | 10.6% |
| Surface Areas and Volumes24 questions | 57 | 8.2% |
| Coordinate Geometry21 questions | 52 | 7.4% |
| Circles26 questions | 51 | 7.3% |
| Pair of Linear Equations in Two Variables17 questions | 49 | 7.0% |
| Real Numbers24 questions | 46 | 6.6% |
| Arithmetic Progressions19 questions | 41 | 5.9% |
| Some Applications of Trigonometry13 questions | 41 | 5.9% |
| Polynomials20 questions | 33 | 4.7% |
| Probability19 questions | 33 | 4.7% |
| Areas Related to Circles13 questions | 27 | 3.9% |
| Quadratic Equations10 questions | 11 | 1.6% |
310 questions from 2026
- Q1If the quadratic equation 9 x^2+8 k x+16=0 has real and equal roots, then the value of k is1 mk
- Q1The LCM of 960 and 240 is:1 mk
- Q1The roots of the quadratic equation (x-1)^2=16 are:1 mk
- Q1The HCF of 960 and 432 is:1 mk
- Q1The value of k for which the equation k x^2-6 x-4=0 has real and equal roots, is1 mk
- Q1The number of multiples of 6 lying between 25 and 363 is:1 mk
- Q2The line segment joining the points P(-4,-2) and Q(10,4) is divided by y-axis in the ratio1 mk
- Q2The natural number 1 is:1 mk
- Q2There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the…1 mk
- Q2It is given that ABC ∼ EDF. Which of the following is not true?1 mk
- Q2The natural number 2 is:1 mk
- Q2In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If ∠ QPR=60^°, then the length…1 mk
- Q3In DEF, AB ∥ EF. The value of x is:1 mk
- Q3The pair of linear equations (3 x)/2+(5 y)/3=7 and 9 x+10 y=14, is:1 mk
- Q3For any natural number n, 6^n ends with the digit:1 mk
- Q3The value of k for which the system of linear equations k x-y-2=0 and 6 x-2 y-3=0 has infinitely many solutions, is…1 mk
- Q3If the zeroes of a polynomial p(x) are -3 and 8, then p(x) equals1 mk
- Q3The n^th term of an A.P. is √2 n+1. Its common difference is1 mk
- Q3For any natural number n, 5^n ends with the digit:1 mk
- Q3In an A.P., if a_14-a_8=24, then the common difference of the A.P. is1 mk
- Q3Given cot θ=3, the value of cos θ is:1 mk
- Q4In the given figure, PQ is tangent to the circle with centre O. S is a point on the circle such that ∠ SQT=55^°. The m…1 mk
- Q4(3 × 11 × 13+3) is:1 mk
- Q4The graph of y=f(x) is given. The number of distinct zeroes of y=f(x) is:1 mk
- Q4The graph of y=f(x) is given. The number of zeroes of f(x) is:1 mk
- Q4For an event E, P(E)+P(Ē)=x, then the value of x^2-3 is:1 mk
- Q4If PQ and PR are tangents to the circle with centre O and radius 4 cm such that ∠ QPR=90^°, then the length OP is1 mk
- Q5PQ is tangent to a circle with centre O. If OQ=a, OP=a+2 and PQ=2 b, then relation between a and b is1 mk
- Q5Observe the graph of polynomial p(x). Number of zeroes of p(x) is1 mk
- Q5The value of x for which 2 x,(x+10) and (3 x+2) are the three consecutive terms of an A.P. is:1 mk
- Q5If α and β are two zeroes of a polynomial f(x)=px^2-2 x+3 p and α+β=α β, then value of p is:1 mk
- Q5Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by 6, is:1 mk
- Q5If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has:1 mk
- Q5Devansh proved that ABC ∼ PQR using SAS similarity criteria. If he found ∠ C=∠ R, then which of the following was…1 mk
- Q6A polynomial p(x), which has sum of its zeroes equal to their product, is:1 mk
- Q6In the given figure, DE ∥ BC. If AD/DB=1/3 and AC=6 cm, then length AE is1 mk
- Q6While calculating mean of a grouped frequency distribution, step deviation method was used ((x-a)/h=u). It was found…1 mk
- Q6If the pair of linear equations: a_1 x+b_1 y+c_1=0 and a_2 x+b_2 y+c_2=0 is consistent and dependent, then1 mk
- Q6For an acute angle θ, if cos θ=1/8, then (8 sec θ+1)/(8 sec θ-1) equals1 mk
- Q6The number of multiples of 4 lying between 12 and 250 is:1 mk
- Q6The common difference of the AP: √2, 2 √2, 3 √2, 4 √2, ….. is:1 mk
- Q7In the given figure, a circle is centred at (1, 2). The diameter of the circle is1 mk
- Q7ABCD is a parallelogram such that AF=7 cm, FB=3 cm and EF=4 cm, length FD = equals1 mk
- Q7Which of the following sequence is not an A.P.?1 mk
- Q7The first term of an AP is p and the common difference is q, then its 10th term is:1 mk
- Q7If Δ ABC and Δ DEF are similar such that 2 AB=DE and BC=8 cm, then EF is equal to:1 mk
- Q7Observe the graph of polynomial p(x). The zeroes of the polynomial are1 mk
- Q7A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of…1 mk
- Q7The roots of the quadratic equation 4 x^2-(a-1)^2=0 are:1 mk
- Q7A cone of maximum size is carved out from a solid cube of edge length l. The volume of the cone is:1 mk
- Q8The value of k for which the system of linear equations x/2+y/3=5 and 2 x+ky=7 is inconsistent, is1 mk
- Q8In the given figure, OA × OB=OC × OD. Which of the following option is correct?1 mk
- Q8From an external point P, a tangent PT has been drawn to a circle with centre at O and radius 3 cm, intersecting its…1 mk
- Q8The mid-point of the line segment joining the points (5,-4) and (6,4) lies on:1 mk
- Q8Shown below are three triangles. The measures of two adjacent sides and included angle are given for each triangle:…1 mk
- Q8If a_n represents n^th term of the A.P. -15/4,-10/4,-5/4, ….. then value of a_16-a_12 is1 mk
- Q8Equation of another line parallel to the line represented by 2 x-6 y=7 is:1 mk
- Q8How many zeroes does p(x)=(x-2)(x+3) have?1 mk
- Q8In triangles ABC and PQR, ∠ A=∠ Q and ∠ B=∠ R, then AB: AC is equal to:1 mk
- Q9A circle centred at (-1, 2) passes through the point (0, 3). Radius of the circle is1 mk
- Q9Three coins are tossed together. The probability of getting exactly one head, is:1 mk
- Q9The string of a flying kite is tied to a point on the ground. The length of the string between the kite and the point…1 mk
- Q9In the given figure, AB ∥ EF. If AB=24 cm, EF=36 cm and DA=7 cm, then AE equals1 mk
- Q9A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is1 mk
- Q9Given that sin θ=a/b, then cos θ is equal to:1 mk
- Q9(sec^2 A-1)/(sin^2 A) is same as1 mk
- Q9The distance of the point A(4 a, 3 a) from x -axis is:1 mk
- Q9If the length of the shadow of a tower is √3 times that of its height, then altitude of the Sun is:1 mk
- Q9The value of p for which roots of the quadratic equation x^2-p x+6=0 are rational, is1 mk
- Q10If cos A=1/2, then the value of sin^2 A+2 cos^2 A is:1 mk
- Q10If the distance between the points (4, p) and (1,0) is 5, then p is equal to:1 mk
- Q10Which of the following can not be the probability of an event?1 mk
- Q10If cos y=0, then what is the value of 1/2 cos y/2?1 mk
- Q10Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is1 mk
- Q10If the roots of the quadratic equation √3 x^2-kx+2 √3=0 are real and equal, then the value(s) of k is/are:1 mk
- Q10If cos A=4/5, then the value of tan A is:1 mk
- Q11A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is either a ten or a…1 mk
- Q11When sin A=1/3, the value of cot A is1 mk
- Q11If 2 sin A=1, then the value of tan A+ cot A is:1 mk
- Q11A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at…1 mk
- Q11If roots of the quadratic equation x^2-k √3 x+2=0 are real and equal, then value of k is1 mk
- Q11The n^th term of the A.P. -1/3, 2/3, 5/3, 8/3, … is:1 mk
- Q11The value of (1/3 cot^2 30^°-1/2 sec^2 60^°) is:1 mk
- Q11If sum and product of zeroes of a polynomial are (-3) and (-2) respectively, then a polynomial is1 mk
- Q12A camping tent in hemispherical shape of radius 1.4 m, has a door opening of area 0.50 m^2. Outer surface area of the…1 mk
- Q12(1+ tan^2 A)/(1+ cot^2 A) equals to:1 mk
- Q12If TP and TQ are two tangents to a circle with centre O from an external point T so that ∠ POQ=120^°, then ∠ PTQ is…1 mk
- Q12From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of…1 mk
- Q12Shown in the given figure is a circle with centre O. The area of the minor sector is 7 cm^2. Area of circle is:1 mk
- Q12In the given figure, PT is a tangent to the circle with centre O and radius r. If ∠ POT=45^°, then the length of OP is:1 mk
- Q13In the given figure, O is the centre of circle. XYZ is an arc of the circle subtending an angle of 45° at the centre.…1 mk
- Q13An arc of length 2.2 cm subtends an angle θ at the centre of the circle with radius 2.8 cm. The value of θ is1 mk
- Q13In the given figure, PA and PB are tangents to a circle centred at O. If ∠ OAB=15^°, then ∠ APB equals:1 mk
- Q13In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=125^°, then ∠ APO is…1 mk
- Q13It is given that Δ ABC ∼ Δ QRP such that AB=9 cm, BC=5 cm and PR=2 cm. Length of side QR is:1 mk
- Q13Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is1 mk
- Q14Equation of a line coincident with 2 · 5 x-2 y=3 is:1 mk
- Q14PQ is tangent to a circle with centre O. If ∠ POR=65^°, then m ∠ PTR is1 mk
- Q14PA and PB are tangents to a circle centred at O. If ∠ PBA=65^°, then ∠ APB equals:1 mk
- Q14The radius of a sphere (in cm) whose volume is 36 π cm^3, is:1 mk
- Q14The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is:1 mk
- Q14In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=125^°, then ∠ APO is…1 mk
- Q14The sum and product of zeroes of a quadratic polynomial p(x) are -1/3 and 2 respectively. The polynomial p(x) is:1 mk
- Q14In the given figure, PA and PB are tangents to a circle centred at O. If ∠ AOB=130^°, then ∠ APB is equal to:1 mk
- Q14Area of sector of a circle with radius 18 cm is 198 cm^2. The measure of central angle is1 mk
- Q14For an acute angle θ, if sin θ=1/9, then value of (9 cosec θ+1)/(9 cosec θ-1) is1 mk
- Q14The value of m for which the quadratic equation 3 x^2-7 x+m=0 has real and equal roots, is1 mk
- Q15Given that sin 2 α=(√3)/2, the value of sin 3 α is:1 mk
- Q15Area of a segment of a circle of radius ' r ' and central angle 60^° is:1 mk
- Q15The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is:1 mk
- Q15The area of a semicircle of diameter 'd' is:1 mk
- Q15If 2 tan A=3, then value of sec A equals1 mk
- Q15The area of a sector of a circle of radius 10 cm is 55/3 cm^2. The value of central angle is1 mk
- Q15In the given figure, PQ ∥ YZ such that XP: PY=2: 3. If PQ=5 cm, then YZ equals1 mk
- Q15The distance between the points (a cos θ+b sin θ, 0) and (0, a sin θ-b cos θ) is1 mk
- Q16The total surface area of a solid hemisphere of diameter ' 2 d ' is:1 mk
- Q16A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used…1 mk
- Q16Meena calculates that the probability of her winning the first prize in a lottery is 0.08. If total 800 tickets were…1 mk
- Q16In the given figure Δ ABC is shown, in which DE ∥ BC. If AD=5 cm, DB=2 · 5 cm and DE=8 cm, then the length of BC is:1 mk
- Q16An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of…1 mk
- Q16If sum of first ten terms of an A.P. is zero with a as the first term and d, the common difference, which of the…1 mk
- Q16The median and mode of a distribution are 25 · 2 and 26 · 1 respectively. The mean of the distribution is:1 mk
- Q17A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as 60^°. If AB=5…1 mk
- Q17If the mean and mode of a data are 12 and 21 respectively, then its median is:1 mk
- Q17In the given figure, Δ ABC is an equilateral triangle. AD is a median of the triangle joining the points A(0, (5…1 mk
- Q17In an A.P., a=-3 and S_17=357. The value of a_17 is1 mk
- Q17Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If PQ=11 cm, then the value of θ is1 mk
- Q17Two dice are rolled together. The probability that sum of the numbers obtained is atmost 12, is1 mk
- Q17The mean and median of a frequency distribution are 43 and 43 · 4 respectively. The mode of the distribution is:1 mk
- Q18The probability for a randomly selected number out of 1,2,3,4, …, 25 to be a composite number is:1 mk
- Q18A die is thrown once. Probability of getting a number other than 3 is:1 mk
- Q18Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is1 mk
- Q18The value of (1/2 tan^2 45^°- cos^2 60^°) is:1 mk
- Q18Two dice are rolled together. The probability of getting an outcome ( x, y ) where x>y, is1 mk
- Q18Simplest form of (sec A)/(√(sec^2 A-1)) is1 mk
- Q19Assertion: Radius is the smallest distance of a tangent from the centre of the circle. Reason (R): Radius is…1 mk
- Q19Assertion: If probability of happening of an event is 0.2 p, p > 0, then p can't be more than 5. Reason (R):…1 mk
- Q19Assertion: The system of linear equations 3 x-5 y+7=0 and -6 x+10 y+14=0 is inconsistent. Reason (R): When two linear…1 mk
- Q19Assertion: The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm^2.…1 mk
- Q19Assertion: The probability that a leap year has 53 Mondays is 2/7. Reason (R): The probability that a non-leap year has…1 mk
- Q20Assertion: The polynomial p(y)=y^2+4 y+3 has two zeroes. Reason (R): A quadratic polynomial can have at most two zeroes.1 mk
- Q20Assertion: The mean of first 'n' natural numbers is (n-1)/2. Reason (R): The sum of first 'n' natural numbers is…1 mk
- Q20Assertion: H.C.F. (36 m^2, 18 m)=18 m, where m is a prime number. Reason (R): H.C.F. of two numbers is always less than…1 mk
- Q20Assertion: tan 2 θ is not defined at θ=45^°. Reason (R): sin 90^° ≠ cos 90^°.1 mk
- Q20Assertion: (√3+√5) is an irrational number. Reason (R): Sum of the any two irrational numbers is always irrational.1 mk
- Q21If α, β are the zeroes of the polynomial p(x)=x^2-3 x-1, then find the value of 1/(α)+1/(β).2 mk
- Q21Prove that 2-5 √3 is an irrational number given that √3 is irrational.2 mk
- Q21If the distance between the points (4, p) and (1, 0) is 5, what is the value of p?2 mk
- Q21If α, β are the zeroes of the quadratic polynomial px^2+qx+r, then find the value of α^3 β+β^3 α.2 mk
- Q21In the given figure, Δ AHK ∼ Δ ABC. If AK=10 cm, BC=3 · 5 cm and HK=7 cm, find the length of AC. OR In the given…2 mk
- Q21In the given figure, point D divides the side BC of ABC in the ratio 1: 2. Find length AD.2 mk
- Q21Verify that roots of the quadratic equation (p-q) x^2+(q-r) x+(r-p)=0 are equal when q+r=2 p.2 mk
- Q21Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.2 mk
- Q21Do the points P(1,0), Q(-5,0) and R(-2,5) form a triangle? If so, name the type of triangle formed.2 mk
- Q21In Δ ABC, DE ∥ BC. If AD=x, DB=x-2, AE=x+2 and EC=x-1, then find the value of x. OR In the figure given above, Δ ABC ∼…2 mk
- Q21Prove that: (tan θ)/(1+ tan^2 θ)+(cot θ)/(1+ cot^2 θ)=2 sin θ cos θ. OR Evaluate: (1-2 tan^2 30^°- sec^2 45^°)/(sin^2…2 mk
- Q22Evaluate: (5 cos^2 60^°+4 sec^2 30^°- tan^2 45^°)/(sin^2 30^°+ cos^2 30^°) OR Prove that: 1+(cot^2 α)/(1+cosec α)=cosec…2 mk
- Q22In an A.P., the first term is 32 and the last term is - 10. If the common difference is -2, then find the number of…2 mk
- Q22In Δ ABC, DE ∥ BC. If AD=x, DB=x-2, AE=x+2 and EC=x-1, then find the value of x. OR In the figure given above, Δ ABC ∼…2 mk
- Q22In the given figure, Δ AHK ∼ Δ ABC. If AK=10 cm, BC=3 · 5 cm and HK=7 cm, find the length of AC. OR In the given…2 mk
- Q22In the given figure, DE ∥ AC and DF ∥ AE. Prove that: BF/FE=BE/EC.2 mk
- Q22Two right triangles PRQ and PSQ are drawn on the same hypotenuse PQ. If PR and QS intersect at T, prove that ST × TQ=PT…2 mk
- Q22In the given figure, Δ ABE ≅ Δ ACD. Prove that Δ ADE ∼ Δ ABC.2 mk
- Q22For acute angles A and B, if sec (2 A-B)=√2 and cosec(A+B)=2, then find the values of A and B. OR Evaluate: (2 cos…2 mk
- Q22Vertices of a right triangle ABC with ∠ B=90^° are A(3,4), B(1,1) and C(-8, 7). Find the value of tan A. OR Using…2 mk
- Q22D is a point on the side BC of ABC such that ∠ CAB=∠ CDA. Show that CA^2=CB × CD.2 mk
- Q22If tan θ=24/7, then find the value of sin θ+ cos θ. If cot θ=7/8, then find the value of ((1+ sin θ)(1- sin θ))/((1+…2 mk
- Q23Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, -2) and (1,6) respectively.…2 mk
- Q23The coordinates of the centre of a circle are ( x-7,2 x ). Find the value(s) of ' x ', if the circle passes through the…2 mk
- Q23In an A.P., the first term is 4 and the last term is 31. If sum of all the terms is 175, find the number of terms and…2 mk
- Q23In the given figure, DEFG is a square. ABC is right angle triangle with ∠ A=90^°. Prove that AG × DG=AF × DB.2 mk
- Q23If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then…2 mk
- Q23In the given figure, AB ∥ DE and AC ∥ DF. Show that ABC ∼ DEF. If BC=10 cm, EB=CF=5 cm and AB=7 cm, then find the…2 mk
- Q23Prove that 4-2 √5 is an irrational number given that √5 is irrational.2 mk
- Q23Prove that: √((1+ sin A)/(1- sin A))= sec A+ tan A OR Evaluate: (3 cos^2 30^°-6 cosec^2 30^°)/(tan^2 60^°)2 mk
- Q24α, β are zeroes of the polynomial p(x)=3 x^2-6 x-5. Find the value of 1/(α^2)+1/(β^2).2 mk
- Q24In the given figure, a circle with centre O is inscribed inside Δ LMN. A and B are the points of tangency. Find ∠ ANB.2 mk
- Q24If tan θ+1/(tan θ)=2, find the value of tan^2 θ+1/(tan^2 θ). OR Prove that: √((1- sin θ)/(1+ sin θ))= sec θ- tan θ2 mk
- Q24The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/OC=BO/OD. Show that…2 mk
- Q24Prove that 2+3 √5 is an irrational number given that √5 is irrational number. OR If the HCF of 210 and 55 is expressed…2 mk
- Q24Find the value of p, for which one zero of the quadratic polynomial px^2-14 x+8 is 6 times the other.2 mk
- Q24Evaluate: (sin^3 60^°- tan 30^°)/(cos^2 45^°) OR For acute angles A and B and A + 2B and 2A + B are acute if tan (A+2…2 mk
- Q24If tan θ=24/7, then find the value of sin θ+ cos θ. OR If cot θ=7/8, then find the value of ((1+ sin θ)(1- sin θ))/((1+…2 mk
- Q24Find a quadratic polynomial whose zeroes are (5-2 √3) and (5+2 √3).2 mk
- Q251000 small thermocol balls of radius 0•5 cm are kept in a spherical balloon of radius 20 cm. Find the volume of air in…2 mk
- Q25A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the…2 mk
- Q25α and β are the zeroes of the polynomial 5 x^2-16 x-10. Find the value of (α)/(β)+(β)/(α).2 mk
- Q25Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the…2 mk
- Q25Prove that 14-2 √3 is an irrational number, given that √3 is irrational.2 mk
- Q25A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of…2 mk
- Q25In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.2 mk
- Q25If tan A=4/3, find sin A and cos A. OR Express cos A and tan A in terms of sin A.2 mk
- Q25Find the zeroes of the quadratic polynomial x^2+7 x+10, and verify the relationship between the zeroes and its…2 mk
- Q26In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks,…3 mk
- Q26If sin θ+ cos θ=√3, then prove that tan θ+ cot θ=1 OR Prove that: ( sin A+ sec A)^2+( cos A+cosec A)^2=(1+ sec A cosec…3 mk
- Q26Prove that √2 is an irrational number.3 mk
- Q26A trader has three different types of oils of volume 870 l, 812 l and 638 l. Find the least number of containers of…3 mk
- Q26Prove that √2 is an irrational number.3 mk
- Q26Prove that √3 is an irrational number.3 mk
- Q26A circle of diameter 20 cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.3 mk
- Q26Prove that √5 is an irrational number.3 mk
- Q27In the given figure, chord AB subtends an angle of 120° at the centre of the circle with radius 7 cm. Find (i)…3 mk
- Q27A point P divides the line segment joining the points A(-3,5) and B(7, -4) in a certain ratio. If the point P lies on…3 mk
- Q27Chord AB of a circle with centre O and radius 21 mm subtends an angle of 120^o at the centre. Find the perimeters of…3 mk
- Q27Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and ∠ AOB=120^°. [Use π=22/7…3 mk
- Q27Use graphical method to solve the system of linear equations: x=-3 and 5 x-2 y=-5.3 mk
- Q27Find the ratio in which the x -axis divides the line segment joining the points (-6, 5) and (-4, -1). Also, find the…3 mk
- Q27In an A.P., 15^th term exceeds the 8^th term by 21. If sum of first 10 terms is 55, then form the A.P. OR The sum of…3 mk
- Q27Find the coordinates of the points of trisection of the line segment joining the points A(-1, 4) and B(-3, -2).3 mk
- Q28Prove that: (tan θ)/(1- cot θ)+(cot θ)/(1- tan θ)=1+ tan θ+ cot θ.3 mk
- Q28Determine the ratio in which the line 3 x+y-9=0 divides the line segment joining the points (1,3) and (2,5). Find the…3 mk
- Q28Prove that: (sec^3 θ)/(sec^2 θ-1)+(cosec^3 θ)/(cosec^2 θ-1)= sec θ · cosec θ( sec θ+cosec θ) OR If (sec α)/(cosec β)=p…3 mk
- Q28Prove that √5 is an irrational number.3 mk
- Q28A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas…3 mk
- Q28If x=h+a cos θ, y=k+b sin θ, then prove that: ((x-h)/a)^2+((y-k)/b)^2=1 OR Prove that: (tan A)/(1+ sec A)-(tan A)/(1-…3 mk
- Q28Prove that: (sin θ- cos θ+1)/(sin θ+ cos θ-1)=1/(sec θ- tan θ)3 mk
- Q28Use graphical method to solve the system of linear equations: y=-3 and x+2 y=4.3 mk
- Q28In the given figure, Δ ABC is a right triangle in which ∠ B=90^°, AB=4 cm and BC=3 cm. Find the radius of the circle…3 mk
- Q28Find the greatest number which divides 764 and 1198, leaving remainders 8 and 10 respectively.3 mk
- Q29To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a…3 mk
- Q29Prove that the lengths of tangents drawn from an external point to a circle are equal. OR Two tangents TP and TQ are…3 mk
- Q29Find two consecutive negative integers, sum of whose squares is 481.3 mk
- Q29Two different coins are tossed simultaneously. What is the probability of getting: (i) at least one head? (ii) at most…3 mk
- Q29In the given figure, ABC is a right triangle in which ∠ B=90^°, AB=4 cm and BC=3 cm. Find the radius of the circle…3 mk
- Q29A circle centered at (2,1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of…3 mk
- Q29The three vertices of a rhombus PQRS are P(2,-3), Q(6,5) and R(-2,1). Find the coordinates of the fourth vertex S and…3 mk
- Q30Two different dice are thrown together. Find the probability that the numbers obtained have: (i) even sum, (ii) even…3 mk
- Q30Chord AB subtends an angle of 120° at the centre O of the circle with radius 21/2 cm. Find the perimeter of shaded…3 mk
- Q30A point P(x, 7) divides a line segment joining the points A(-5,4) and B(7, 9) in a certain ratio. Find the ratio and…3 mk
- Q30Prove that: 1/(sec x- tan x)-1/(cos x)=1/(cos x)-1/(sec x+ tan x)3 mk
- Q30A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter…3 mk
- Q30A bag contains 30 balls out of which 'm' number of balls are blue in colour. (i) Find the probability that a ball drawn…3 mk
- Q30Solve the system of linear equations: x=4 and 3 x-2 y=6 graphically.3 mk
- Q30Find the area of the sector of a circle of radius 42 cm and of central angle 30^°. Also, find the area of the…3 mk
- Q31Prove that: (1+ cot θ-cosec θ)(1+ tan θ+ sec θ)=23 mk
- Q31The dimensions of a window are 156 cm × 216 cm. Arjun wants to put grill on the window creating complete squares of…3 mk
- Q31The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also…3 mk
- Q31Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. OR If a…3 mk
- Q31Parthi and Alisha found a treasure that is exactly on the straight line joining their locations. Parthi's location is…3 mk
- Q31Prove that √3 is an irrational number.3 mk
- Q31Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.3 mk
- Q31Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5,…3 mk
- Q31Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the…3 mk
- Q31Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠ APB=2 ∠ OAB. OR In…3 mk
- Q31A chord of a circle, of radius 14 cm, subtends an angle of 60° at the centre. Find the area of the smaller sector and…3 mk
- Q31If sec θ+ tan θ=m, show that (m^2-1)/(m^2+1)= sin θ.3 mk
- Q32D is the mid-point of side BC of ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD=DG.…5 mk
- Q32By selling an article for ₹ 48, a trader loses as much percent as half of the cost price of the article. Calculate the…5 mk
- Q32A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses…5 mk
- Q32Venkat can row a boat in still water at the speed of 12 km/h. He ferries tourists 15 km upstream and 18 km downstream…5 mk
- Q32A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff. From a point on the ground 30…5 mk
- Q32Determine graphically, the coordinates of vertices of a triangle whose equations are 2 x-3 y+6=0; 2 x+3 y-18=0 and x=0.…5 mk
- Q32Aarush bought 2 pencils and 3 chocolates for ₹ 11 and Tanish bought 1 pencil and 2 chocolates for ₹ 7 from the same…5 mk
- Q32State and prove Basic Proportionality Theorem. OR In the given figure, CM and RN are respectively the medians of ABC…5 mk
- Q32The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68. OR Find…5 mk
- Q32If the median of the following distribution is 32•5, then find the values of x and y.5 mk
- Q33The marks obtained by 80 students of class X in a mock test of Mathematics are given below in the table. Find median…5 mk
- Q33A person on a tour has ₹ 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses…5 mk
- Q33A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10…5 mk
- Q33The mean of the following distribution is 53. Find the missing frequency p. Class Interval: 0-20 20-40 40-60 60-80…5 mk
- Q33D is the mid-point of side BC of ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD=DG.…5 mk
- Q33In Δ ABC, AD is a median. X is a point on AD such that AX: XD=2: 3. BX is extended so that it intersects AC at Y. Prove…5 mk
- Q33Find the mean and the mode of the following frequency distribution:5 mk
- Q33State and prove Basic Proportionality Theorem. OR In the given figure, CM and RN are respectively the medians of Δ ABC…5 mk
- Q33Find mean and mode of the following frequency distribution: OR The median of the following data is 32.5, find the…5 mk
- Q33In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B…5 mk
- Q34Draw the graph of the pair of linear equations x-y+2=0 and 4 x-y-4=0. Calculate the area of the triangle formed by the…5 mk
- Q34Find mean and mode of the following frequency distribution: OR If the median of the distribution given below is 28.5,…5 mk
- Q34The angle of elevation of the top of a building from a point A, on the ground, is 30°. On moving a distance of 24 m…5 mk
- Q34Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points,…5 mk
- Q34In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by…5 mk
- Q34The monthly expenditure on fruits in 200 families of a Housing Society is given below. Find the value of x and also…5 mk
- Q34Solve the following system of equations graphically: x-2 y=3,3 x-8 y=7 OR Five years ago, Adil was thrice as old as…5 mk
- Q34The mean of the following frequency distribution is 28. If sum of all frequencies is 100, then find the values of p and…5 mk
- Q34A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the…5 mk
- Q34D is the mid-point of side BC of ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD=DG.…5 mk
- Q34State and prove Basic Proportionality Theorem. OR In the given figure, CM and RN are respectively the medians of Δ ABC…5 mk
- Q34Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this…5 mk
- Q35PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which…5 mk
- Q35A boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of 30°.…5 mk
- Q35An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health…5 mk
- Q35In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and…5 mk
- Q35The median of the following data is 50 and sum of all frequencies is 90: Find the values of p and q. OR Find mean and…5 mk
- Q35The mean of the following frequency distribution is 35. Find the values of x and y, if the sum of frequencies is 25:5 mk
- Q35Two sections, A and B, of class X contributed a total of ₹ 1500 for the Uttarakhand flood victims. The contribution…5 mk
- Q35Find the mean and mode of the following frequency distribution: Class Interval: 400-450 450-500 500-550 550-600 600-650…5 mk
- Q35Solve the following system of equations graphically: 2 x+3 y=5,-3 x+y=-2 OR The sum of the digits of a 2-digit number…5 mk
- Q35Two water taps together can fill a tank in 8 8/9 hours. The tap of larger diameter takes 4 hours less than the smaller…5 mk
- Q36'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots.…4 mk
- Q36Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner.…4 mk
- Q36During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented…4 mk
- Q36In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are…4 mk
- Q36An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting…4 mk
- Q36Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is…4 mk
- Q36Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of ₹…4 mk
- Q37Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some…4 mk
- Q37A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are…4 mk
- Q37Tejas is standing at the top of a building and observes a car at an angle of depression of 30° as it approaches the…4 mk
- Q37'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots.…4 mk
- Q37On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's…4 mk
- Q37A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create…4 mk
- Q37A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical…4 mk
- Q37Radio towers are used for transmitting a range of communication services including radio and television. The tower will…4 mk
- Q38Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner.…4 mk
- Q38A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical…4 mk
- Q38A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a…4 mk
- Q38Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is…4 mk
- Q38A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create…4 mk
- Q38Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some…4 mk
- Q38On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's…4 mk
Other Mathematics years
Answers come from CBSE’s own marking schemes. How we source them.