CBSE Class 10 Mathematics 2022

What 2022 actually asked, chapter by chapter

Marks we counted in the 2022 papers themselves. CBSE allocates marks per unit, not per chapter — this is what was observed, not an official CBSE weightage.

All 102 questions from 2022

• Q1The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding…2 mkasked 2×
• Q1Solve the quadratic equation: x^2+2 √2 x-6=0 for x.2 mkasked 2×
• Q1Find the sum of first 30 terms of AP: - 30, - 24, - 18,...... OR In an AP if S n=n(4 n+1), then find the AP.2 mkasked 2×
• Q1Find the value of 'k' for which the quadratic equation 2 k x^2-40 x+25=0 has real and equal roots. OR Solve for x: 5/2…2 mk
• Q1Solve the quadratic equation for x: x^2-2 a x-(4 b^2-a^2)=0 OR If the quadratic equation (1+a^2) x^2+2 a b…2 mkasked 2×
• Q1In Figure 1, PQ and PR are tangents to the circle centred at O. If ∠ OPR=45^°, then prove that ORPQ is a square. Figure…2 mk
• Q2In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠…2 mk
• Q2A solid metallic sphere of radius 10 · 5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm…2 mkasked 2×
• Q2Which term of the A.P. -11/2,-3,-1/2, … is 49/2? OR Find a and b so that the numbers a, 7, b, 23 are in A.P.2 mkasked 2×
• Q2How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?2 mk
• Q2Find the sum of first 20 terms of an AP in which d=5 and a 20=135.2 mkasked 2×
• Q3Find the value of m for which the quadratic equation (m-1) x^2+2(m-1) x+1=0 has two real and equal roots. OR Solve the…2 mkasked 3×
• Q3Find the sum of the first twelve 2-digit numbers which are multiples of 6. OR In an AP, if a 2=26 and a 15=-26, then…2 mk
• Q3A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid…2 mkasked 3×
• Q3In an A.P. if the sum of third and seventh term is zero, find its 5^ th term. OR Determine the A.P. whose third term is…2 mk
• Q3If the sum of the roots of the quadratic equation ky^2-11 y+(k-23)=0 is 13/21 more than the product of the roots, then…2 mkasked 2×
• Q3Find the common difference 'd' of an AP whose first term is 10 and the sum of the first 14 terms is 1505.2 mk
• Q3Find the mode of the given frequency distribution:2 mkasked 3×
• Q4In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠…2 mkasked 2×
• Q4A cone of height 28 cm and radius of base 7 cm is made up of modelling clay. A child reshapes it in the form of a…2 mk
• Q4150 spherical marbles, each of diameter 1 · 4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some…2 mkasked 2×
• Q4Find the mode of the following frequency distribution:2 mkasked 3×
• Q4Find the sum of all 11 terms of an A.P. whose 6^ th term is 30.2 mk
• Q4Find the mean of the following frequency distribution:2 mk
• Q4For what value of m, the quadratic equation m x^2-2(m-1) x+(m+2)=0 has two real and equal roots? OR The diagonal of a…2 mk
• Q4If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.2 mk
• Q5Solve the quadratic equation: x^2-2 a x+(a^2-b^2)=0 for x.2 mk
• Q5In Fig. 1, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the…2 mkasked 3×
• Q5Find the median of the following distribution:2 mk
• Q5The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age.…2 mkasked 3×
• Q5If mode of the following frequency distribution is 55, then find the value of x.2 mkasked 3×
• Q5For what value of 'n', are the n ^ th terms of the APs: 9, 7, 5,..... and 15,12,9, …. the same?2 mkasked 3×
• Q5For the following frequency distribution, find the mode:2 mk
• Q6If the mean of the following frequency distribution is 18, then find the missing frequency ' f '.2 mk
• Q6Find the sum of first 20 terms of an A.P. whose n^ th term is given as a n=5-2 n.2 mkasked 3×
• Q6150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some…2 mk
• Q6The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of…2 mkasked 3×
• Q6Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the…2 mkasked 3×
• Q6In Figure 2, PQ and PR are tangents to the circle centred at O. If ∠ OPR=45^°, then prove that ORPQ is a square. Figure…2 mkasked 2×
• Q7Two boats are sailing in the sea 80 m apart from each other towards a cliff AB. The angles of depression of the boats…3 mk
• Q7An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a…3 mk
• Q7A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of…3 mk
• Q7Heights of 50 students of class X of a school are recorded and following data is obtained: Find the median height of…3 mkasked 2×
• Q7For what value of x, is the median of the following frequency distribution 34•5?3 mk
• Q7Construct a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 60°.3 mkasked 2×
• Q7Draw a line segment AB of length 8 cm and locate a point P on AB such that AP: PB=1: 5. OR Draw a circle of radius 3…3 mkasked 3×
• Q7Draw two concentric circles of radii 2 cm and 5 cm. From a point on the outer circle, construct a pair of tangents to…3 mk
• Q8In Fig. 3, AB is tower of height 50 m. A man standing on its top, observes two cars on the opposite sides of the tower…3 mk
• Q8Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from…3 mk
• Q8The percentage of marks obtained by 100 students in an examination are given below: Determine the median percentage of…3 mk
• Q8The sum of the first three terms of an A.P. is 33. If the product of first and third term exceeds the second term by…3 mk
• Q8Draw a line segment AB=7 cm. Divide it in the ratio 3: 2.3 mk
• Q8The tops of two poles of heights 20 m and 28 m are connected with a wire. The wire is inclined to the horizontal at an…3 mk
• Q8Find the value of 'p' for which the quadratic equation p(x-4)(x-2)+ (x-1)^2=0 has real and equal roots. OR Had Aarush…3 mkasked 3×
• Q8From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30°…3 mk
• Q9The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top…3 mkasked 3×
• Q9For what value of x, is the median of the following frequency distribution 34•5?3 mk
• Q9If the median of the following data is 33 then, find the value of m:3 mk
• Q9Two men on either side of a cliff 75 m high observe the angles of elevation of the top of the cliff to be 30° and 60°.…3 mk
• Q9The weights (in kg) of 50 wild animals of a National Park were recorded and the following data was obtained: Find the…3 mkasked 2×
• Q9There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are points…3 mk
• Q9The mean of the following frequency distribution is 25. Find the value of f. OR Find the mean of the following data…3 mkasked 3×
• Q9An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when…3 mk
• Q10Heights of 50 students of class X of a school are recorded and following data is obtained: Find the median height of…3 mk
• Q10The following table gives the production yield of wheat of farms of a village: Find the mean production yield, using…3 mk
• Q10Construct a pair of tangents to a circle of radius 4 cm from a point P lying outside the circle at a distance of 6 cm…3 mk
• Q10In an A.P., the sum of first n terms is (n)/2(3 n+5). Find the 25^ th term of the A.P.3 mk
• Q10Construct a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.3 mk
• Q10If the last term of an A.P. of 30 terms is 119 and the 8^ th term from the end (towards the first term) is 91, then…3 mk
• Q10For the following frequency distribution, find the median:3 mkasked 2×
• Q10Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.3 mk
• Q10Construct a pair of tangents to a circle of radius 5 cm, which are inclined to each other at an angle of 60°.3 mk
• Q10Following is the daily expenditure on lunch by 30 employees of a company: Find the mean daily expenditure of the…3 mkasked 2×
• Q10Find the mean of the following frequency distribution:3 mk
• Q11In Figure 1, a right triangle ABC in which ∠ B=90^°, AB=12 cm and BC=5 cm is shown. Find the radius of the circle…4 mk
• Q11In Fig.-2, if a circle touches the side QR of PQR at S and extended sides PQ and PR at M and N, respectively, then Fig.…4 mkasked 3×
• Q11In Figure 3, two circles with centres at O and O' of radii 2r and r respectively, touch each other internally at A. A…4 mk
• Q11The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds, the angle of…4 mk
• Q11From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of…4 mkasked 2×
• Q11The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^°. From a point Y, 40 m…4 mk
• Q11The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two…4 mk
• Q11In Fig. 4, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the…4 mkasked 2×
• Q11From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed…4 mk
• Q12From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of…4 mk
• Q12From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed…4 mk
• Q12In Figure 2, from a solid cube of side 7 cm, a cylinder of radius 2 · 1 cm and height 7 cm is scooped out. Find the…4 mk
• Q12In Figure 3, two circles with centres at O and O^′ of radii 2 r and r respectively, touch each other internally at A. A…4 mk
• Q12In Figure 4, two circles with centres at O and O' of radii 2 r and r respectively, touch each other internally at A. A…4 mk
• Q12In Figure 1, a triangle ABC with ∠ B=90^° is shown. Taking AB as diameter, a circle has been drawn intersecting AC at…4 mkasked 2×
• Q12A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of…4 mk
• Q12Prove that a parallelogram circumscribing a circle is a rhombus.4 mk
• Q12A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits…4 mkasked 2×
• Q13In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard.…4 mkasked 3×
• Q13Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body…4 mkasked 2×
• Q13Case Study-1: Kite festival is celebrated in many countries at different times of the year. In India, every year 14^ th…4 mkasked 3×
• Q13In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations.…4 mkasked 3×
• Q13Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian…4 mk
• Q14Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian…4 mkasked 2×
• Q14Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by…4 mkasked 3×
• Q14John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by…4 mkasked 3×
• Q14Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body…4 mk
• Q14Case Study - 2 A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people…4 mkasked 3×