CBSE Class 10 Mathematics 2026
310 questions · 698 marks · 305 with the board’s own marking-scheme answer so far.
What 2026 actually asked, chapter by chapter
Marks we counted in the 2026 papers themselves. CBSE allocates marks per unit, not per chapter — this is what was observed, not an official CBSE weightage.
| 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% |
All 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 mkasked 2×
- Q1The LCM of 960 and 240 is:1 mkasked 2×
- Q1The roots of the quadratic equation (x-1)^2=16 are:1 mkasked 2×
- Q1The HCF of 960 and 432 is:1 mkasked 3×
- Q1The value of k for which the equation k x^2-6 x-4=0 has real and equal roots, is1 mkasked 2×
- 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 mkasked 3×
- Q2The natural number 1 is:1 mkasked 3×
- 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 mkasked 3×
- Q2The natural number 2 is:1 mkasked 3×
- 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 mkasked 2×
- Q3In DEF, AB EF. The value of x is:1 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- Q4(3 × 11 × 13+3) is:1 mkasked 3×
- Q4The graph of y=f(x) is given. The number of distinct zeroes of y=f(x) is:1 mkasked 2×
- Q4The graph of y=f(x) is given. The number of zeroes of f(x) is:1 mkasked 3×
- Q4For an event E, P(E)+P( E)=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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- Q5Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by 6, is:1 mkasked 2×
- Q5If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has:1 mkasked 3×
- Q5Devansh proved that ABC PQR using SAS similarity criteria. If he found ∠ C=∠ R, then which of the following was proved…1 mkasked 3×
- 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 mkasked 2×
- Q6While calculating mean of a grouped frequency distribution, step deviation method was used ((x-a)/(h)=u). It was found…1 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- Q6The common difference of the AP: √2, 2 √2, 3 √2, 4 √2, ….. is:1 mkasked 2×
- Q7In the given figure, a circle is centred at (1, 2). The diameter of the circle is1 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- Q8The value of k for which the system of linear equations x/2+y/3=5 and 2 x+ky=7 is inconsistent, is1 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- Q8Equation of another line parallel to the line represented by 2 x-6 y=7 is:1 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 2×
- Q9Given that sin θ=a/b, then cos θ is equal to:1 mkasked 2×
- 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 mkasked 2×
- Q9If the length of the shadow of a tower is √3 times that of its height, then altitude of the Sun is:1 mkasked 3×
- Q9The value of p for which roots of the quadratic equation x^2-p x+6=0 are rational, is1 mkasked 3×
- Q10If cos A=1/2, then the value of sin^2 A+2 cos^2 A is:1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- Q10If cos A=4/5, then the value of tan A is:1 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- Q12(1+ tan^2 A)/(1+ cot^2 A) equals to:1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- Q13In the given figure, PA and PB are tangents to a circle centred at O. If ∠ OAB=15^°, then ∠ APB equals:1 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- Q13Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- Q14In the given figure, PA and PB are tangents to a circle centred at O. If ∠ AOB=130^°, then ∠ APB is equal to:1 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- Q15Area of a segment of a circle of radius ' r ' and central angle 60^° is:1 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 2×
- Q15The distance between the points (a cos θ+b sin θ, 0) and (0, a sin θ-b cos θ) is1 mkasked 2×
- Q16The total surface area of a solid hemisphere of diameter ' 2 d ' is:1 mkasked 2×
- 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 mkasked 3×
- Q16Meena calculates that the probability of her winning the first prize in a lottery is 0.08. If total 800 tickets were…1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q17If the mean and mode of a data are 12 and 21 respectively, then its median is:1 mkasked 3×
- Q17In the given figure, Δ ABC is an equilateral triangle. AD is a median of the triangle joining the points A(0, (5…1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q18The probability for a randomly selected number out of 1,2,3,4, …, 25 to be a composite number is:1 mkasked 3×
- Q18A die is thrown once. Probability of getting a number other than 3 is:1 mkasked 2×
- Q18Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is1 mkasked 3×
- Q18The value of (1/2 tan^2 45^°- cos^2 60^°) is:1 mkasked 2×
- 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 mkasked 3×
- Q19Assertion: Radius is the smallest distance of a tangent from the centre of the circle. Reason (R): Radius is…1 mkasked 3×
- Q19Assertion: If probability of happening of an event is 0.2 p, p 0, then p can't be more than 5. Reason (R): P( E)=1-P(E)…1 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- Q19Assertion: The probability that a leap year has 53 Mondays is 2/7. Reason (R): The probability that a non-leap year has…1 mkasked 3×
- 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 mkasked 3×
- Q20Assertion: The mean of first 'n' natural numbers is (n-1)/2. Reason (R): The sum of first 'n' natural numbers is…1 mkasked 3×
- 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 mkasked 3×
- Q20Assertion: tan 2 θ is not defined at θ=45^°. Reason (R): sin 90^° ≠ cos 90^°.1 mkasked 3×
- Q20Assertion: (√3+√5) is an irrational number. Reason (R): Sum of the any two irrational numbers is always irrational.1 mkasked 3×
- 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 mkasked 2×
- 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 figure,…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 mkasked 3×
- 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 mkasked 3×
- 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 Δ…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^°)/(…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…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 mkasked 2×
- 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 Δ…2 mkasked 2×
- 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 figure,…2 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 length DE.2 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 2×
- Q25α and β are the zeroes of the polynomial 5 x^2-16 x-10. Find the value of (α)/(β)+(β)/(α).2 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- Q25In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.2 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- Q26A circle of diameter 20 cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.3 mkasked 2×
- Q26Prove that √5 is an irrational number.3 mkasked 3×
- Q27In the given figure, chord AB subtends an angle of 120° at the centre of the circle with radius 7 cm. Find (i)…3 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- Q27Find the coordinates of the points of trisection of the line segment joining the points A(-1, 4) and B(-3, -2).3 mkasked 2×
- Q28Prove that: ( tan θ)/(1- cot θ)+( cot θ)/(1- tan θ)=1+ tan θ+ cot θ.3 mkasked 2×
- 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…3 mkasked 3×
- 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- sec…3 mkasked 3×
- 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 mkasked 3×
- Q29Prove that the lengths of tangents drawn from an external point to a circle are equal. OR Two tangents TP and TQ are…3 mkasked 2×
- Q29Find two consecutive negative integers, sum of whose squares is 481.3 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- Q31Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the…3 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- Q36During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented…4 mkasked 3×
- 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 mkasked 3×
- Q36An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting…4 mkasked 3×
- 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 mkasked 3×
- Q37Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some…4 mkasked 2×
- Q37A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are…4 mkasked 3×
- 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 mkasked 3×
- 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 mkasked 2×
- 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 mkasked 2×
- 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 mkasked 3×
- 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 mkasked 2×
- Q38A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a…4 mkasked 3×
- Q38Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is…4 mkasked 2×
- 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 mkasked 2×
Other Mathematics years
Answers come from CBSE’s own marking schemes. How we source them.