CBSE Class 10 Mathematics 2025

What 2025 actually asked, chapter by chapter

Marks we counted in the 2025 papers themselves. CBSE allocates marks per unit, not per chapter — this is what was observed, not an official CBSE weightage.

All 337 questions from 2025

• Q1The quadratic equation whose sum and product of roots are 'a' and ' 1/, respectively is:1 mk
• Q1√0.4 is a/an1 mkasked 3×
• Q1(√3+2)^2+(√3-2)^2 is a/an1 mkasked 3×
• Q1What is the mode of a data if median and mean of the same data are 9 · 6 and 10 · 5, respectively?1 mk
• Q1If α and β are the zeroes of polynomial 3 x^2+6 x+k such that α+β+α β=-2/3, then the value of k is:1 mkasked 2×
• Q1If x=a b^3 and y=a^3 b, where a and b are prime numbers, then [HCF(x, y)-LCM(x, y)] is equal to:1 mkasked 3×
• Q1The system of equations x+5=0 and 2 x-1=0, has1 mk
• Q1The diameter of a wheel is 63 cm. The distance travelled by the wheel in 100 revolutions is:1 mk
• Q1If for any event E, P(E)+P( E)=q, then the value of q^2-3 is:1 mk
• Q1If tan 3 θ=√3, then (θ)/2 equals:1 mkasked 2×
• Q1If 7 cos^2 θ+3 sin^2 θ=4, then the value of θ is:1 mk
• Q2(1+√3)^2-(1-√3)^2 is:1 mkasked 3×
• Q2If x is the LCM of 4,6, 8 and y is the LCM of 3,5, 7 and p is the LCM of x and y, then which of the following is true?1 mkasked 3×
• Q2In the adjoining figure, AP and AQ are tangents to the circle with centre O. If reflex ∠ POQ=210^°, the value of 2 x is1 mk
• Q2The 9^ th term from the end (towards first term) of the AP 7,11,15,19, …., 147 is:1 mk
• Q2The value of ( tan A cosec A)^2-( sin A sec A)^2 is:1 mk
• Q2If x=1 and y=2 is a solution of the pair of linear equations 2 x-3 y+a=0 and 2 x+3 y-b=0, then:1 mkasked 3×
• Q2Let x=a^2 b^3 c^n and y=a^3 b^m c^2, where a, b, c are prime numbers. If LCM of x and y is a^3 b^4 c^3, then the value…1 mk
• Q2Which of the following cannot be the unit digit of 8^n, where n is a natural number?1 mkasked 3×
• Q2If sin θ= cos θ(0^°<θ<90^°), then the value of sec θ · sin θ is:1 mk
• Q2The mean of seven observations is 17. If the mean of the first four observations is 15 and that of the last four…1 mk
• Q3The distance of the point (4,0) from x -axis is:1 mk
• Q3The quadratic equation whose roots are 7 and 1/7 is:1 mkasked 2×
• Q3The mid-point of the line segment joining the points P(-4,5) and Q(4,6) lies on:1 mkasked 2×
• Q3The value of'k'for which the system of linear equations 6 x+y=3k and 36 x+6 y=3 have infinitely many solutions is:1 mkasked 2×
• Q3For any prime number p, if p divides a ^2, where a is any real number then p also divides1 mkasked 3×
• Q3Three numbers in AP have the sum 30. What is its middle term?1 mk
• Q3The perimeter of the triangle formed by the vertices (0, 0), (2,0) and (0,2) is:1 mk
• Q3The value of (1-2 sin^2 60^°) is same as that of1 mk
• Q3Which of the following quadratic equations has real and equal roots?1 mk
• Q3If x=2 sin 60^° cos 60^° and y= sin^2 30^°- cos^2 30^° and x^2=ky^2, the value of k is1 mk
• Q3If an arc of a circle of diameter 10 cm subtends an angle of 144° at the centre of the circle, then the length of the…1 mk
• Q4An arc of a circle is of length 5 π cm and the sector it bounds has an area of 20 π cm^2. Its radius is:1 mk
• Q4If α and β are the zeroes of the polynomial p(x)=x^2-a x-b, then the value of (α+β+α β) is equal to:1 mkasked 2×
• Q4Let a=p^2 q^3 r^n and b=p^3 q^m r^2, where p, q, r are prime numbers. If LCM of a and b is p^3 q^4 r^3, then the value…1 mk
• Q4If the zeroes of the polynomial a x^2+b x+(2 a)/ are reciprocal of each other, then the value of b is1 mkasked 3×
• Q4If mode and median of given set of observations are 13 and 11 respectively, then the value of mean is:1 mk
• Q4If a^b=32, where 'a' and 'b' are positive integers, then the value of b^ab is:1 mk
• Q4If θ is an acute angle and 7+4 sin θ=9, then the value of θ is:1 mkasked 2×
• Q4The distance of a point A from x -axis is 3 units. Which of the following cannot be coordinates of the point A?1 mk
• Q5The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a red ball at…1 mkasked 3×
• Q5The distance of the point A(-3, -4) from x -axis is1 mk
• Q5If one zero of the polynomial q(x)=(p^2+4) x^2+65 x+4 p is reciprocal of the other, then the value of ' p ' is:1 mk
• Q5In the adjoining figure, AC is diameter of larger circle with centre O. AB is tangent to smaller circle with centre O.…1 mk
• Q5If sin 4 θ=(√3)/2, then (θ)/3 equals:1 mk
• Q5The value of tan^2 θ-(1/( cos θ) × sec θ) is:1 mkasked 2×
• Q5If (x)/12-3/(x)=0, then the values of x are:1 mkasked 2×
• Q5The radii 'r' of a sphere and that of the base of a cone are same. If their volumes are also same, then the height of…1 mk
• Q5Which of the following quadratic equations has real and distinct roots?1 mk
• Q5If x^2+b x+b=0 has two real and distinct roots, then the value of b can be1 mkasked 3×
• Q5The coordinates of the end points of a diameter of a circle are (5, -2) and (5, 2). The length of the radius of the…1 mkasked 3×
• Q6The distance of which of the following points from origin is less than 5 units?1 mk
• Q6The equation of a line parallel to y -axis and at a distance of 5 units to the right of y -axis is:1 mk
• Q6The points (- 5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an:1 mkasked 2×
• Q6In the figure given below, points P, Q, R divides the line segment AB in four equal parts. The point Q divides PB in…1 mk
• Q6In the adjoining figure, PQ XY BC, AP=2 cm, PX=1.5 cm and BX=4 cm. If QY=0.75 cm, then AQ+CY=1 mkasked 3×
• Q6The point P divides the line segment AB in the ratio 3: 1 as shown below: The value of (AB)/(PB) is1 mk
• Q6If HCF(98,28)=m and LCM(98,28)=n, then the value of n-7 m is:1 mkasked 3×
• Q6The value of ' p ' for which the equations p x+3 y=p-3,12 x+p y=p has infinitely many solutions is:1 mkasked 3×
• Q6The line represented by x/4+y/6=1, intersects x -axis and y -axis respectively at P and Q. The coordinates of the…1 mkasked 2×
• Q7The tangents drawn at the extremities of the diameter of a circle are always:1 mkasked 2×
• Q7Two of the vertices of Δ PQR are P(-1,5) and Q(5,2). The coordinates of a point which divides PQ in the ratio 2: 1 are:1 mkasked 3×
• Q7A bag contains red balls and black balls in the ratio 3: 7. A ball is drawn at random. The probability that ball so…1 mk
• Q7In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If ∠ NML=30^°, then ∠ RLM…1 mkasked 3×
• Q7Given ABC PQR, ∠ A=30^° and ∠ Q=90^°. The value of (∠ R+∠ B) is1 mkasked 3×
• Q7ABC and PQR are shown in the adjoining figures. The measure of ∠ C is:1 mkasked 3×
• Q7A system of two linear equations in two variables is inconsistent, if the lines in the graph are:1 mk
• Q7The distance of point (a, -b) from x -axis is1 mk
• Q8In triangles ABC and DEF, ∠ B=∠ E, ∠ F=∠ C and AB=3 DE. Then, the two triangles are:1 mkasked 3×
• Q8tan 2 A=3 tan A is true, when the measure of ∠ A is:1 mk
• Q8Two coins are tossed simultaneously. The probability of getting atleast one head is1 mkasked 3×
• Q8Which of the following equations is a quadratic equation?1 mk
• Q8The system of equations y+a=0 and 2 x=b has1 mk
• Q8If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle…1 mkasked 3×
• Q8Which of the following statements is false?1 mkasked 3×
• Q8In the given figure, PQ BC. If (AP)/(PB)=4/13 and AC=20 · 4 cm, then the length of AQ is:1 mkasked 3×
• Q9A piggy bank contains ₹ 1 coins and ₹ 2 coins in the ratio 9: 11 respectively. The piggy bank is accidently dropped and…1 mk
• Q9Which of the following statements is incorrect?1 mkasked 3×
• Q9( cot θ+ tan θ) equals:1 mkasked 2×
• Q9Which of the following statements is true?1 mkasked 3×
• Q9If (-1)^n+(-1)^8=0, then n is:1 mkasked 2×
• Q9In the adjoining figure, PA and PB are tangents to a circle with centre O such that ∠ P=90^°. If AB=3 √2 cm, then the…1 mkasked 3×
• Q9In the adjoining figure, ABCD is a trapezium in which XY AB CD. If AX=2/3 AD, then CY: YB=1 mkasked 3×
• Q10Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:1 mkasked 3×
• Q10Which of the following statements is false?1 mkasked 3×
• Q10The sum of the exponents of prime factors in the prime factorisation of 4004 is:1 mkasked 2×
• Q10Which of the following is a trigonometric identity?1 mk
• Q10If in two triangles DEF and PQR, ∠ D=∠ Q and ∠ R=∠ E, then which of the following is not true?1 mkasked 3×
• Q10For a circle with centre O and radius 5 cm, which of the following statements is true? P: Distance between every pair…1 mkasked 3×
• Q10A 30 m long rope is tightly stretched and tied from the top of pole to the ground. If the rope makes an angle of 60°…1 mkasked 3×
• Q11In the adjoining figure, PA and PB are tangents to a circle with centre O. The measure of angle APB is1 mkasked 3×
• Q11In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2 x^° is1 mkasked 2×
• Q11Let p=x^2 y^3 z^n and q=x^3 y^m z^2, where x, y, z are prime numbers. If LCM (p, q)=x^3 y^4 z^3, then the value of (2…1 mk
• Q11On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking…1 mkasked 3×
• Q11If the sum of first m terms of an AP is 2 m^2+3 m, then its second term is:1 mk
• Q11The measurements of Δ LMN and Δ ABC are shown in the figure given below. The length of side AC is:1 mkasked 3×
• Q12Which of the following equations does not have a real root?1 mk
• Q12Mode and Mean of a data are 15x and 18x, respectively. Then the median of the data is:1 mkasked 2×
• Q12(1- tan^2 30^°)/(1+ tan^2 30^°) is equal to1 mk
• Q12If x((2 tan 30^°)/(1+ tan^2 30^°))=y((2 tan 30^°)/(1- tan^2 30^°)), then x: y=1 mk
• Q12If x= cos 30^°- sin 30^° and y= tan 60^°- cot 60^°, then1 mk
• Q12If a large circular pizza is divided into 5 equal sectors, then the central angle of each sector will be:1 mkasked 2×
• Q12The value of (2 tan 60^°)/(1- tan^2 60^°) is same as the value of1 mk
• Q12If the volumes of two cubes are in the ratio 8: 125, then the ratio of their surface areas is:1 mkasked 2×
• Q12If 1080=2^p × 3^q × 5, then (p-q) is equal to:1 mk
• Q12The cumulative frequency for calculating median is obtained by adding the frequencies of all the:1 mkasked 3×
• Q13The distance of point P(1,-1) from x -axis is:1 mk
• Q13A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is:1 mkasked 2×
• Q13If sin 30^° tan 45^°=( sec 60^°)/(k), then the value of k is:1 mkasked 3×
• Q13If mean and median of given set of observations are 10 and 11 respectively, then the value of mode is:1 mk
• Q13If the length of a chord of a circle is equal to its radius, then the angle subtended by chord at the centre is:1 mk
• Q13If the area of a sector of circle of radius 36 cm is 54 π cm^2, then the length of the corresponding arc of the sector…1 mkasked 2×
• Q13cos θ√1- cos^2 θ is equal to:1 mk
• Q13A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is 10 √3 m…1 mkasked 3×
• Q13If mean and mode of given set of observations are 10 and 13 respectively, then the value of median is:1 mk
• Q13An observer 1.8 m tall stands away from a chimney at a distance of 38.2 m along the ground. The angle of elevation of…1 mkasked 3×
• Q14The greatest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is:1 mk
• Q14A die is thrown once. The probability of getting a number which is not a factor of 36, is:1 mkasked 2×
• Q14In the adjoining figure, AB is the chord of the larger circle touching the smaller circle. The centre of both the…1 mk
• Q14The discriminant of the quadratic equation bx^2+ax+c=0; b ≠ 0 is given by:1 mk
• Q14The line represented by the equation x-y=0 is:1 mkasked 3×
• Q14The distance of point P(3 a, 4 a) from y -axis is1 mk
• Q14In the adjoining figure, AB is the chord of larger circle which touches the smaller circle at P. If length of AB=…1 mk
• Q14In the adjoining figure, the sum of radii of two concentric circles is 16 cm. The length of chord A B which touches the…1 mkasked 3×
• Q14If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of…1 mkasked 3×
• Q14Which of the following is a rational number between √3 and √5?1 mkasked 3×
• Q15A ladder 14 m long leans against a wall. If the foot of the ladder is 7 m from the wall, then the angle of elevation of…1 mk
• Q15If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are1 mkasked 3×
• Q15If the mean of 2,9, x+6,2 x+3,5,10,5 is 7, then the value of x is:1 mkasked 2×
• Q15If the mid-point of the line segment joining the points (a, 4) and (2, 2b) is ( 2,6 ), then the value of ( a+b ) is…1 mk
• Q15If a sector of a circle has an area of 40 π sq. units and a central angle of 72°, the radius of the circle is:1 mkasked 2×
• Q15A parallelogram having one of its sides 5 cm circumscribes a circle. The perimeter of parallelogram is:1 mkasked 3×
• Q15A cone of height 12 cm and slant height 13 cm is surmounted on a hemisphere having radius equal to that of cone. The…1 mkasked 3×
• Q15In the following figure, P and Q are points of trisection of line segment AB: the value of (AB)/(PB)=1 mk
• Q16AOBC is a rectangle whose three vertices are A (0,2), O (0,0) and B (4,0). The square of the length of its diagonal is…1 mkasked 2×
• Q16E and F are points on the sides AB and AC respectively of a ABC such that (AE)/(EB)=(AF)/(FC)=1/2. Which of the…1 mkasked 3×
• Q16If x median + y mean = z mode; is the empirical relationship between mean, median and mode, then the value of x+y+z is1 mkasked 3×
• Q16In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=115^°, then ∠ APO is…1 mkasked 3×
• Q16If - 4 is a zero of the polynomial p(x)=x^2-x-(2+2 k), then the value of k is:1 mkasked 2×
• Q16If the maximum number of students has obtained 52 marks out of 80, then1 mkasked 3×
• Q17sec A=2 cos A is true for A=1 mk
• Q17The 11^ th and 13^ th term of an AP are 39 and 45, respectively. What is the common difference of the AP?1 mk
• Q17The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is:1 mkasked 2×
• Q17A kite is flying at a height of 150 m from the ground. It is attached to a string inclined at an angle of 30° to the…1 mkasked 2×
• Q17Following data shows the marks obtained by 100 students in a class test: The median will be the average of which two…1 mkasked 3×
• Q17Zeroes of the polynomial p(x)=x^2-3 √2 x+4 are:1 mkasked 2×
• Q17Which of the following statements is true for a polynomial p(x) of degree 3?1 mkasked 3×
• Q17The system of equations 2 x+1=0 and 3 y-5=0 has1 mk
• Q18The HCF of 40, 110 and 360 is:1 mkasked 2×
• Q18A piece of wire 20 cm long is bent into the form of an arc of a circle of radius 60/(π) cm. The angle subtended by the…1 mkasked 3×
• Q18In the given figure, in Δ ABC, AD ⊥ BC and ∠ BAC=90^°. If BC=16 cm and DC=4 cm, then the value of x is:1 mkasked 3×
• Q18In a right triangle ABC, right-angled at A, if sin B = 1/4, then the value of sec B is1 mkasked 3×
• Q19Assertion: For an acute angle θ, value of cosec θ cannot be 1/(√2). Reason (R): cosec θ ≥ 1 for 0^° ≤ θ ≤ 90^°1 mk
• Q19Assertion: A line drawn perpendicular to the tangent at point of contact passes through the centre of the circle.…1 mk
• Q19Assertion: Common difference of the AP: 5,1,-3,-7, … is 4. Reason (R): Common difference of the AP: a 1, a 2, a 3, …, a…1 mkasked 3×
• Q19Assertion: A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the…1 mkasked 3×
• Q19Assertion: For an acute angle θ, sin θ=3/5 ⇒ cos θ=-4/5. Reason (R): For any value of θ, (0^° ≤ θ ≤ 90^°) sin^2 θ+…1 mk
• Q19Assertion: For any two prime numbers p and q, their HCF is 1 and LCM is p + q. Reason (R): For any two natural numbers,…1 mk
• Q19Assertion: The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R): For any event E,…1 mkasked 3×
• Q19Assertion: 4^n ends with digit 0 for some natural number n. Reason (R): For a number ' x ' having 2 and 5 as its prime…1 mkasked 2×
• Q19Assertion: For two prime numbers x and y(x<y), HCF(x, y)=x and LCM(x, y)=y. Reason (R): HCF(x, y) ≤ LCM(x, y), where x,…1 mk
• Q20Assertion: The pair of linear equations px + 3y + 59=0 and 2 x+6 y+118=0 will have infinitely many solutions if p=1.…1 mkasked 3×
• Q20Assertion: If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre…1 mkasked 3×
• Q20In an experiment of throwing a die, Assertion: Event E 1: getting a number less than 3 and Event E 2: getting a number…1 mkasked 3×
• Q21Solve the following pair of equations algebraically: OR In a pair of supplementary angles, the greater angle exceeds…2 mkasked 3×
• Q21Find a quadratic polynomial whose zeroes are 2 and -7/5.2 mk
• Q21In the adjoining figure, (AD)/(BD)=(AE)/(EC) and ∠ BDE=∠ CED, prove that ABC is an isosceles triangle.2 mk
• Q21If 4 k= tan^2 60^°-2 cosec^2 30^°-2 tan^2 30^°, then find the value of k.2 mkasked 2×
• Q21If the sum of the zeroes of the polynomial p(x)=(p+1) x^2+(2 p+3) x+(3 p+4) is -1, then find the value of 'p'. OR If α…2 mk
• Q21If x cos 60^°+y cos 0^°+ sin 30^°- cot 45^°=5, then find the value of x+2 y. OR Evaluate: ( tan^2 60^°)/( sin^2 60^°+…2 mkasked 3×
• Q21If the zeroes of the polynomial x^2+ax+b are in the ratio 3: 4, then prove that 12 a^2=49 b.2 mk
• Q21If p and q are zeroes of the polynomial p(y)=21 y^2-y-2, then find the value of (1-p).(1-q).2 mkasked 2×
• Q21If tan A+ cot A=6, then find the value of tan^2 A+ cot^2 A-4.2 mk
• Q21Solve the following system of equations algebraically: 30 x+44 y=10; 40 x+55 y=132 mk
• Q21AD and PS are angle bisectors of ∠ A and ∠ P of triangles ABC and PQR. If ABC PQR, prove that ACD PRS.2 mk
• Q21The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg grapes was…2 mkasked 3×
• Q22The coordinates of the end points of the line segment AB are A(-2, -2) and B(2,-4). P is the point on AB such that…2 mkasked 3×
• Q22The probability of guessing the correct answer of a certain test question is x/12. If the probability of not guessing…2 mkasked 3×
• Q22A bag contains cards which are numbered from 5 to 100 such that each card bears a different number. A card is drawn at…2 mk
• Q22All the face cards are removed from the pack of 52 cards and a card is drawn at random from the remaining cards. Find…2 mk
• Q22Find the zeroes of the polynomial p(x)=x^2+4/3 x-4/3.2 mkasked 2×
• Q22A 1.5 m tall boy is walking away from the base of a lamp post which is 12 m high, at the speed of 2.5 m/sec. Find the…2 mkasked 3×
• Q22Saima and Aryaa were born in the month of June in the year 2012. Find the probability that: (i) they have different…2 mk
• Q22If a sec θ+b tan θ=m and b sec θ+a tan θ=n, prove that a^2+n^2=b^2+m^2 OR Use the identity: sin^2 A+ cos^2 A=1 to prove…2 mkasked 3×
• Q22In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠ AOB=90^°. If…2 mkasked 3×
• Q23The coordinates of the centre of a circle are (2a, a - 7). Find the value(s) of 'a' if the circle passes through the…2 mkasked 2×
• Q23Find the coordinates of the point C which lies on the line AB produced such that AC=2 BC, where coordinates of points A…2 mkasked 3×
• Q23In ABC and PQR, AD and PS are altitudes such that ABD PQS and ACD PRS. Prove that ABC PQR.2 mk
• Q23Find the smallest number which is divisible by both 644 and 462. OR Two numbers are in the ratio 4: 5 and their HCF is…2 mkasked 3×
• Q23In the adjoining figure, AP=1 cm, BP=2 cm, AQ=1.5 cm and AC=4.5 cm. Prove that APQ ABC. Hence find the length of PQ, if…2 mk
• Q23Solve the following system of equations algebraically: 37 x+63 y=137 63 x+37 y=1632 mk
• Q23Prove that abscissa of a point P which is equidistant from points with coordinates A(7, 1) and B(3, 5) is 2 more than…2 mkasked 3×
• Q23If tan A=√3; where A is an acute angle, then find the value of ( sin^2 A)/(1+ cos^2 A).2 mkasked 3×
• Q23It is given that sin (A-B)= sin A cos B- cos A sin B. Use it to find the value of sin 15^°. OR If sin A=y, then express…2 mkasked 3×
• Q24Find the value(s) of 'k' so that the quadratic equation 4 x^2+kx+1=0 has real and equal roots. OR If ' α ' and ' β '…2 mkasked 2×
• Q24In the given figure, D is a point on the side BC of Δ ABC such that ∠ ADC=∠ BAC. Show that CA^2=CD. CB. OR In the given…2 mkasked 2×
• Q24A bag contains balls numbered 2 to 91 such that each ball bears a different number. A ball is drawn at random from the…2 mk
• Q24If ABC PQR in which AB=6 cm, BC=4 cm, AC=8 cm and PR=6 cm, then find the length of ( PQ+QR ). OR In the given figure,…2 mkasked 3×
• Q24From a pack of 52 cards, all aces and all kings are removed. A card is drawn at random from the remaining cards. Find…2 mk
• Q24P is a point on the side BC of ABC such that ∠ APC=∠ BAC. Prove that AC^2=BC · CP.2 mk
• Q24Find the value of x for which ( sin A+cosec A)^2+( cos A+ sec A)^2=x+ tan^2 A+ cot^2 A OR Evaluate the following: (3…2 mkasked 3×
• Q24Renu and Simran were born in the year 2000 which is a leap year. Find the probability that: (i) both have same…2 mk
• Q24AD and PS are medians of triangles ABC and PQR respectively such that ABD PQS. Prove that ABC PQR.2 mk
• Q25While shuffling a pack of 52 cards, one card was accidently dropped. Find the probability that the dropped card (i) is…2 mk
• Q25At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the…2 mkasked 3×
• Q25A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that…2 mkasked 3×
• Q25Solve the following system of equations algebraically: 73 x-37 y=109 37 x-73 y=12 mk
• Q25Two friends Anil and Ashraf were born in the December month in the year 2010. Find the probability that: (i) they share…2 mk
• Q25The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball…2 mk
• Q25Find the length of the median through the vertex B of ABC with vertices A(9, -2), B(-3, 7) and C(-1, 10).2 mk
• Q25In the given figure, (PS)/(SQ)=(PT)/(TR) and ∠ PST=∠ PRQ. Prove that Δ PQR is an isosceles triangle. OR In the given…2 mk
• Q25Prove that the tangents drawn at the ends of a diameter of a circle are parallel.2 mkasked 3×
• Q26α and β are zeroes of a quadratic polynomial x^2-a x-b. Obtain a quadratic polynomial whose zeroes are 3 α+1 and 3 β+1.3 mk
• Q26Check whether the given system of equations is consistent or not. If consistent, solve graphically.3 mk
• Q26Prove that √3 is an irrational number. OR State true or false for each of the following statements and justify in each…3 mkasked 3×
• Q26Find the zeroes of the polynomial p(x)=6 x^2-5 x-1. Hence, obtain a polynomial each of whose zeroes is three times the…3 mk
• Q26If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x+y-10=0, find the value of…3 mkasked 3×
• Q26Prove that (4 √2+5/3) is an irrational number given that √2 is an irrational number.3 mk
• Q26Prove that √5 is an irrational number. OR Let p, q and r be three distinct prime numbers. Check whether p · q · r+q is…3 mkasked 3×
• Q26Prove that √2 is an irrational number. OR Let x and y be two distinct prime numbers and p=x^2 y^3, q=x y^4, r=x^5 y^2.…3 mkasked 3×
• Q26Prove that √5 is an irrational number.3 mk
• Q26In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠ BAC+∠ ACD=90^°. OR Prove…3 mkasked 3×
• Q26Prove that: √ sec^2 θ+cosec^2 θ= tan θ+ cot θ OR If cosec θ=x+1/(4 x), prove that cosec θ+ cot θ=2 x or 1/(2 x).3 mk
• Q26All face cards of spades are removed from a pack of 52 playing cards and the remaining pack is shuffled well. A card is…3 mk
• Q26If tan θ+ sin θ=m and tan θ- sin θ=n, then prove that m^2-n^2=4 √mn. OR Prove that: ( cot A-1)/(2- sec^2 A)=( cot…3 mk
• Q26If the radii of the bases of a cylinder and a cone are in the ratio 3: 4 and their heights are in the ratio 2: 3, find…3 mk
• Q26Prove that the parallelogram circumscribing a circle is a rhombus. OR Prove that the angle between the two tangents…3 mkasked 3×
• Q27Three sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored…3 mk
• Q27Find the sum of all 3-digit natural numbers which are divisible by 11.3 mk
• Q27Prove that: (1+1/( tan^2 θ))(1+1/( cot^2 θ))=1/( sin^2 θ- sin^4 θ) OR Prove that: √(cosec θ-1)/(cosec θ+1)+√(cosec…3 mk
• Q27Prove that (5 √3+2/3) is an irrational number given that √3 is an irrational number.3 mkasked 2×
• Q27If (a, b) is the mid-point of the line segment joining the points A(10, - 6) and B(k, 4) and a-2 b=18, then find the…3 mk
• Q27If 65\% of the population has black eyes, 25\% have brown eyes and the remaining have blue eyes, what is the…3 mk
• Q27Two dice are rolled together. Find the probability of getting: (i) a multiple of 2 on one and a multiple of 3 on the…3 mk
• Q27Obtain the zeroes of the polynomial 7 x^2+18 x-9. Hence, write a polynomial each of whose zeroes is twice the zeroes of…3 mk
• Q27Find the zeroes of the polynomial p(x)=3 x^2-4 x-4. Hence, write a polynomial whose each of the zeroes is 2 more than…3 mk
• Q27Prove that: ( tan θ)/(1- cot θ)+( cot θ)/(1- tan θ)=1+ sec θ cosec θ OR Prove that: ( sin A+ cos A)/( sin A- cos A)+(…3 mkasked 3×
• Q27In the given figure, PB is a tangent to the circle with centre O at B. AB is a chord of the circle of length 24 cm and…3 mk
• Q27The monthly incomes of two persons are in the ratio 9: 7 and their monthly expenditures are in the ratio 4: 3. If each…3 mk
• Q28If α and β are the zeroes of the polynomial a x^2-x+c. Obtain a polynomial whose zeroes are α-3 and β-3.3 mk
• Q28Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the…3 mkasked 3×
• Q28Check whether the following pair of equations is consistent or not. If consistent, solve graphically3 mk
• Q28Prove that: √( sec A-1)/( sec A+1)+√( sec A+1)/( sec A-1)=2 cosec A OR Prove that: (1/( cos A)- cos A)(1/( sin A)- sin…3 mkasked 3×
• Q28P(x, y), Q(-2,-3) and R(2,3) are the vertices of a right triangle PQR right angled at P. Find the relationship between…3 mkasked 3×
• Q28Solve the following system of equations graphically: Also, find the absolute difference between the ordinates of the…3 mk
• Q28If the mid-point of the line segment joining the points A(3,4) and B(k, 6) is P(x, y) and x+y-10=0, then find the value…3 mkasked 2×
• Q29The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock…3 mkasked 3×
• Q29Prove that 1/(√5) is an irrational number.3 mk
• Q29Obtain the zeroes of the polynomial p(x)=2 x^2-5 x-3. Hence, obtain a polynomial each of whose zeroes is one less than…3 mk
• Q29Find a relation between x and y such that P(x, y) is equidistant from the points A(3, 5) and B(7, 1). Hence, write the…3 mkasked 3×
• Q29A chord of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the…3 mkasked 3×
• Q29Prove that ( cos A+ sin A-1)/( cos A- sin A+1)=cosec A- cot A OR If cot θ+ cos θ=p and cot θ- cos θ=q, prove that…3 mkasked 3×
• Q29The two angles of a right angled triangle other than 90° are in the ratio 2: 3. Express the given situation…3 mk
• Q29Find the zeroes of the polynomial q(x)=8 x^2-2 x-3. Hence, find a polynomial whose zeroes are 2 less than the zeroes of…3 mk
• Q29If the points A(6,1), B(p, 2), C(9,4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p…3 mkasked 3×
• Q30Solve the following system of equations graphically: 2 x+y=5 and 4 x-y=7. Hence, write the coordinates of the points…3 mk
• Q30Check whether the following system of equations is consistent or not. If consistent, solve graphically x-2 y+4=0,2…3 mk
• Q30Three unbiased coins are tossed simultaneously. Find the probability of getting: exactly two tails at least one head at…3 mk
• Q30Prove that √3 is an irrational number.3 mkasked 3×
• Q30Prove that: ( cos θ-2 cos^3 θ)/( sin θ-2 sin^3 θ)+ cot θ=0. OR Given that sin θ+ cos θ=x, prove that sin^4 θ+ cos^4…3 mkasked 3×
• Q30Prove the following trigonometric identity: (1+cosec A)/(cosec A)=( cos^2 A)/(1- sin A) OR Let 2 A+B and A+2 B be acute…3 mkasked 3×
• Q30α and β are zeroes of a quadratic polynomial p x^2+q x+1. Form a quadratic polynomial whose zeroes are 2/(α) and 2/(β).3 mk
• Q30A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of…3 mkasked 2×
• Q31In the adjoining figure, XY and X'Y' are parallel tangents to a circle with centre O. Another tangent AB touches the…3 mkasked 3×
• Q31In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the tangent at…3 mkasked 2×
• Q31The perimeter of a rectangle is 70 cm. The length of the rectangle is 5 cm more than twice is breadth. Express the…3 mk
• Q31Find the zeroes of the polynomial r(x)=4 x^2+3 x-1. Hence, write a polynomial whose zeroes are reciprocal of the zeroes…3 mk
• Q31Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.3 mkasked 2×
• Q31Rectangle ABCD circumscribes the circle of radius 10 cm. Prove that ABCD is a square. Hence, find the perimeter of ABCD.3 mkasked 3×
• Q31A sum of ₹ 2,000 is invested at 7 % per annum simple interest. Calculate the interests at the end of 1^ st, 2^ nd and…3 mkasked 2×
• Q31Solve the following system of equations graphically: Also, find the sum of ordinates of the points where given lines…3 mk
• Q31In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠ OPQ=15^° and ∠ PTQ=θ, then find…3 mkasked 3×
• Q32Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed…5 mkasked 2×
• Q32A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the…5 mk
• Q32State the basic proportionality theorem. Use the theorem to do the following: In ABC, AD is the angle bisector of angle…5 mk
• Q32An AP consists of 'n' terms whose n^ th term is 4 and the common difference is 2. If the sum of ' n ' terms of AP is…5 mk
• Q32The perimeter of an isosceles triangle is 32 cm. If each equal side is 5/6 th of the base, find the area of the…5 mk
• Q32Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8\% per annum and…5 mkasked 2×
• Q32Following data shows the number of family members living in different bungalows of a locality: If the median number of…5 mk
• Q32The sides of a right triangle are such that the longest side is 4 m more than the shortest side and the third side is 2…5 mkasked 3×
• Q32There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to…5 mkasked 3×
• Q32The following table shows the number of traffic challans issued in the month of April by the traffic police: Find the…5 mk
• Q32A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the…5 mkasked 3×
• Q32During a medical checkup, height of 35 students of a class were recorded as follows: Find the difference between the…5 mk
• Q33The sum of the areas of two squares is 52 cm^2 and difference of their perimeters is 8 cm. Find the lengths of the…5 mkasked 2×
• Q33The students of a class are made to stand equally in rows. If 3 students are extra in each row, there would be 1 row…5 mk
• Q33A bag contains some red and blue balls. Ten percent of the red balls, when added to twenty percent of the blue balls,…5 mk
• Q33The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find…5 mk
• Q33A bat manufacturing company made a huge bat for charity and got it signed by world cup winning team. The dimensions of…5 mk
• Q33The sum of the third term and the seventh term of an AP is 6 and their product is 8. Find the sum of the first sixteen…5 mkasked 2×
• Q33If a line drawn parallel to one side of triangle intersecting the other two sides in distinct points divides the two…5 mkasked 2×
• Q33Fermentation tanks are designed in the form of cylinder mounted on a cone as shown below: The total height of the tank…5 mk
• Q33The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side…5 mkasked 3×
• Q33The corresponding sides of ABC and PQR are in the ratio 3: 5. AD ⊥ BC and PS ⊥ QR as shown in the following figures:…5 mkasked 3×
• Q34Find the mean and median for the following data:5 mk
• Q34On the day of her examination, Riya sharpened her pencil from both ends as shown below: The diameter of the cylindrical…5 mk
• Q34The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the…5 mkasked 2×
• Q34A wooden cubical die is formed by forming hemispherical depressions on each face of the cube such that face 1 has one…5 mk
• Q34State the converse of basic proportionality theorem. Also find (BF)/(FC) in the following figure, given that AB DC EF…5 mk
• Q34From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area…5 mkasked 2×
• Q34From one of the faces of a solid wooden cube of side 14 cm, maximum number of hemispheres of diameter 1.4 cm are…5 mkasked 3×
• Q34The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is…5 mk
• Q34A man lent a part of his money at 10\% p.a. and the rest at 15\% p.a. His income at the end of the year is ₹ 1,900. If…5 mk
• Q34Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides…5 mkasked 3×
• Q34Following table shows the absentees record of 40 students in an academic year: Find the 'mean' and the 'mode' of the…5 mk
• Q34The following table gives the daily income of 50 cab drivers of a particular city: Find the mean income and the modal…5 mk
• Q34In the given figure, PA, QB and RC are perpendicular to AC. If PA=x units, QB=y units and RC=z units, prove that…5 mkasked 3×
• Q34Find the Mean and Mode of the following data:5 mk
• Q34The population of lions was noted in different regions across the world in the following table: If the median of the…5 mk
• Q35Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode.5 mk
• Q35A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It…5 mkasked 2×
• Q35Medical check-up was carried out for 35 students of a class and their weights were recorded as follows: Find the…5 mk
• Q35Following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find…5 mk
• Q35A two-digit number is such that the product of its digits is 12. When 36 is added to this number, the digits…5 mk
• Q35In order to provide shelter to flood victims, a shed was constructed using tin sheets which is in the form of cuboid…5 mk
• Q35The following table shows the number of patients of different age group who were discharged from the hospital in a…5 mk
• Q35The angle of elevation of an airborne helicopter from a point A on the ground is 45°. After a flight of 15 seconds, the…5 mk
• Q35The numerator of a fraction is 3 less than its denominator. If 2 is added to both numerator and denominator, then the…5 mk
• Q35Find the Mean and Mode of the following frequency distribution:5 mk
• Q36A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the…4 mkasked 3×
• Q36Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three parts by…4 mkasked 3×
• Q36A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds…4 mkasked 3×
• Q36The Olympic symbol comprising five interlocking rings represents the union of the five continents of the world and the…4 mkasked 3×
• Q36A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school…4 mkasked 3×
• Q36A farmer has a circular piece of land. He wishes to construct his house in the form of largest possible square within…4 mkasked 3×
• Q37Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride…4 mkasked 3×
• Q37In order to organise, Annual Sports Day, a school prepared an eight lane running track with an integrated football…4 mkasked 3×
• Q37Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he…4 mkasked 3×
• Q37A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from…4 mkasked 3×
• Q37In an equilateral triangle of side 10 cm, equilateral triangles of side 1 cm are formed as shown in the figure below,…4 mkasked 3×
• Q37A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching…4 mkasked 3×
• Q38Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile…4 mkasked 3×
• Q38A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical…4 mkasked 3×
• Q38Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to…4 mkasked 3×
• Q38A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there…4 mkasked 3×
• Q38The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our…4 mkasked 3×
• Q38The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of…4 mkasked 3×