Sample paper class 10 maths with solution pdf standard
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Sample paper class 10 maths with solution pdf standard

Sample paper class 10 maths with solution pdf standard

CLASS – X (SESSION: 2024-25)

SUBJECT – MATHEMATICS (STANDARD)

Time Allowed:  3 Hrs                                                                         Maximum Marks: 80

General Instructions:

  1. This Question Paper has 5 Sections A-E
  2. Section A has 20 MCQs carrying 1 mark each.
  3. Section B has 5 questions carrying 02 marks each.
  4. Section C has 6 questions carrying 03 marks each.
  5. Section D has 4 questions carrying 05 marks each.
  6. Section E has 3 case based integrated units of assessment (04 marks each) with sub- parts of the values of 1, 1 and 2 marks each respectively.
  7. All Questions are compulsory. However, an internal choice in 2 Questions of 5 marks, 2 Questions of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E
  8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.

SECTION-A

Section A consists of 20 Multiple Choice questions of 1 mark each.

  1. Let the ages of Payal and Kavita be p and q such that p = a2 b4 and q = a4 b2, where a and b are prime numbers. If HCF of p and q is ambn and LCM of p and q is ar bs, then (m+n) (r+s) =
    (a) 15         (b) 32                c) 35               d) 72

2.  If m and n are the zeroes of the polynomial x² – 6x + k and 3m + 2n = 20 then the value of k is

a) -8               b) 16                c) -10               d) 8

3.  A quadratic polynomial, whose zeroes are -4 and -5, is
(a) x²-9x + 20              (b) x² + 9x + 20          (c) x²-9x- 20                                      (d) x² + 9x- 20

4. The pair of linear equations y = 0 and y = – 5 has
(a) one solution           (b) two solutions        (c) infinitely many solutions              (d) no solution

5. The equation (x +1)² – x² = 0 has
(a) four real roots                  (b) two real roots          (c) no real roots.                    (d) one real root

6. The next term of AP   √6 , √24 ,√54 ……… is
(a) √60                (b)  √96 (c)  √72            (d) √216

7. The distance of the point P(4, 3) from the origin is

(a) 4 units             b) 3 units          c) 1 unit                        d) 5 units   

8. The coordinates of point A, where AB is the diameter of the circle whose centre is (2,-3) and B(1,4) are                               (a) (3,-10)                       (b) (-3,-10)                  (c)  (-3,10)                    (d)  (10,-3)  

9. If tan A=3/4 , then cos²A – sin² A =
a) 7/25             b) 1                  c) 1/12          d)

3/4
10. If  p tan45⁰ cos60⁰ =  sin60⁰ cot60⁰ , then p is equal to
(a) 1           (b) √2 ( c) 1/√2            (d) ½

11. The maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is
a) 1            b) 3                      c) 2                  d) 4

12.  Rectangular sheet of paper 40 cm x 22 cm is rolled to form a hollow cylinder of height 40 cm. Then radius of the cylinder in cm is
(a) 3.5                            (b) 7                           (c)   80/7        (d) 5

13. If a circle touches all four sides of quadrilateral PQRS whose sides are PQ = 6.5 cm, QR = 7.3 cm and    PS= 4.2 cm then RS equal to                           
(a) 7cm                                (b) 2.6cm                          (c) 5cm                 (d) 11.5cm

14. Total surface area of solid hemisphere of radius r is :
     (a) πr2                              (b)2πr2                          (c) 3πr2                  (d) 4πr2 

15.  A box contains 90 discs numbered from 1 to 90. If one disc is drawn at random from the box the probability that it bears a prime number less than 23 is
     (a)7/90                         (b)  10/90             (c)   4/25              (d)  9/89

16. Two different coins are tossed simultaneously, the probability of getting at least one head is
(a)  1/4                (b)  1/8                       (c)  3/4                (d) 7/8

17. If from a point A which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents AB and AC to the circle are drawn, then the area of quadrilateral ABOC in cm² is

a) 60             b) 120              c) 50                d) 80

18. If 35 is removed from the data 30 ,34 ,35, 36, 37 ,38, 39 ,40 then the median increases by

a) 2               b) 1.5                c) 1                d) 0.5

Direction for questions 19 & 20: In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option

  1. Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true but Reason (R) is false.
  4. Assertion (A) is false but Reason (R) is true.

    19. Assertion (A):  A tangent to a circle is perpendicular to the radius through the point of contact.
    Reason (R):  The lengths of tangents drawn from an external point to a circle are equal.

    20. Assertion(A): If a right circular cylinder of radius r and height h ( h>2r) just encloses a Sphere ,then the diameter of sphere is 2r.Reason (R) : The surface area of the sphere is 2r(h+r).

SECTION-B

Section B consists of 5 questions of 2 marks each

21.The HCF of 85 and 238 is expressible in the form 85m -238. Find the value of m.

                                                     OR
On a morning walk, 3 persons step out together and their steps measure 30 cm, 36 cm and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps ?

22. Find the ratio in which the line segment joining the points A(6,3) , B(-2,-5) is divided by x-axis.

23. If point P(x, y) is equidistant from points A(5,1) and B(1,5). Prove that x=y.

24. The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting                                                  (a)  a card of club               (b)  a face card

25. If fig. AB || DC . Find the value of x.  

Sample paper class 10 maths with solution pdf standard

                                          OR

In fig , P is the mid-point of  BC and Q is the mid-point of AP.  If BQ when produced meets AC at R, and PS is drawn parallel to BR , prove that RA =   CA.

SECTION-C

Section C consists of 6 questions of 3 marks each.

26. It is given that √5 is irrational number. Prove that 3- 2√5 is irrational.

27. If α and β are the two zeroes of the polynomial 2p2 – 5p + 7, find a quadratic polynomial whose zeroes are 2α+3β and  3α+2β.

                                   OR

Find the zeroes of the polynomial 8x²+14x + 3 and verify the relationship between the zeroes and their coefficients.

28. The area of a rectangular plot is 528 m². The length of the plot is  1m more than twice its breadth. Find the length and breadth of the plot.

29. Prove that if a line is drawn parallel to one side of a triangle, then it divides the other two sides in the same ratio.

                                                           OR

Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of triangle PQR. Show that  ∆ABC ~ ∆PQR.

30. If sinA +cosA =p and secA + cosecA = q. Show that q(p² -1) = 2p

31. The minute hand of a clock is 10 cm long. Find the area of the face of the clock described by the minute hand between 9:00 a.m. and 9:35 a.m.

SECTION-D

                                  Section D consists of 4 questions of 5 marks each

32. Two years ago, a father was five times as old as his son. 2 years later his age will be 8 more than three times the age of the son. Find the present ages of a father and son.

                                                         OR

The sum of digits of a two digit number is 15. The number obtained by reversing the order of the digits of the given number exceeds the given number by 9. Find the given number.

33. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.

                                                           OR

A triangle PQR is drawn to circumscribe a circle of radius 8 cm such that the segments QT and TR into which QR is divided by the point of contact T are of lengths 14 cm and 16 cm respectively. If area of triangle PQR is 336 cm². Find the sides PQ and PR.

34. A man standing on the deck of a ship which is 10 m above water level. He observes the angle of elevation of the top of a hill as 60⁰ and the angle of depression of the base of the hill as 30⁰. Calculate the distance of the hill from the ship and the height of the hill.

35. If the median of the distribution given below is 28.5 , find the values of x and y.

Class intervals0-1010-2020-3030-4040-5050-60Total
Frequency  5x2015y560

SECTION-E

This section comprises 3 case study based questions of 4 marks each

Case Study – 1

36. The school Auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

(i). If the first circular row has 30 seats, how many seats will be there in the 10th row?

(ii). If there are 17 rows in the auditorium, how many seats will be there in the middle row?

(iii). (a) For 1500 seats in the auditorium, how many rows need to be there ?

                   OR

(b) If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10th row?

Case Study – 2

37. The word “Circus” has the same root as a “circle”. In a closed circular area various entertainment acts including human skills and animal training are presented before the crowd. A circus tent is cylindrical up to a height of 8m and conical above it. The diameter of the base is 28m and total height of tent is 18.5m. Based on the above, answer the following questions.

        (i) Find slant height of the conical part.

 (ii) Determine the floor area of the tent.

 (iii) (a) Find area of the cloth used for making  tent.
                                    OR

        (b) Find total volume of air inside the empty tent.


Case study – 3

38. A group of students to volunteer are working in making a safety board for school. They prepared on triangular safety board for their school with title “School Ahead” and “Drive Slow” in two parts of the triangular board as shown in the below figure. Where DE || BC. Based on the above information, answer the following questions.

(i) Show that △ADE ~ △ABC.

(ii) If ∠A= 60⁰ and ∠ADE = 50⁰, then find ∠C.

 (iii) (a) if  AD = 2 cm,  BD = 5 cm and AE = 3 cm, then find EC.

                                OR

 (b) if AD= 3 cm , AB = 9cm,  BC = 6cm, then evaluate DE.

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