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WarriorMegaPreBoard QUESTIONPAPER
CLASSโX(2025-26)
WARRIOR
MEGA PRE BOARD
PHYSICS
WALLAH
MAX.MARKS:80 CLASS- X TIME ALLOWED :3 HOURS
Mathematics Standard
- Code no. 041
MATHEMATICS โ Code no. 041 SAMPLE QUESTION PAPER CLASS โ X (2025-26) Max. Marks: 80 Time allowed: 3 hours General Instructions: Read the following instructions carefully and follow them: i. This question paper contains 38 questions. All Questions are compulsory. ii. This Question Paper is divided into 5 Sections A, B, C, D and E. iii. In Section A, Question numbers 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion- Reason based questions of 1 mark each. iv. In Section B, Question numbers 21-25 are very short answer (VSA) type questions, carrying 02 marks each. v. In Section C, Question numbers 26-31 are short answer (SA) type questions, carrying 03 marks each. vi. In Section D, Question numbers 32-35 are long answer (LA) type questions, carrying 05 marks each. vii. In Section E, Question numbers 36-38 are case study-based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. viii. There is no overall choice. However, an internal choice in 2 questions of Section B, 2 questions of Section C and 2 questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E. ix. Draw neat and clean figures wherever required.^ ๏ฆ๏ง๏จ^ Use ๏ฐ ๏ฝ^227 ๏ถ๏ท๏ธ wherever required if not stated. x. Use of calculators is not allowed SECTION - A Marks
- If p is prime, then HCF and LCM of p and p + 1 would be A. HCF = p, LCM = p + 1 B. HCF = p(p + 1), LCM = 1 C. HCF = 1, LCM = p(p + 1) D. None of the above
- Pens are sold in packs of 8 and notepads are sold in packs of 12. Find the least number of packs of each type that one should buy so that there are equal number of pens and notepads. A. 3 and 2 B. 2 and 5 C. 3 and 4 D. 4 and 5
- Zeroes of a quadratic polynomial are in the ratio 2 : 3 and their sum is 15. The product of zeroes of this polynomial is A. 36 B. 48 C. 54 D. 60
- If the mid-point of the line joining (3, 4) and (k, 7) is (x, y), which satisfies 2x + 2y + 1 = 0. Find the value of k. A. 10 B. โ 15 C. 15 D. โ 10
- (^) Find the acute angle ๏ฑ, satisfying the equation sec 2 ๏ฑ + tan 2 ๏ฑ =3.
A. 30ยฐ B. 45ยฐ C. 60ยฐ D. None of these
- The length of a string between a kite and a point on the ground is 85 m. If the string makes an
angle ๏ฑ with level ground such that tan ๏ฑ ๏ฝ 158 , then how high is the kite? A. 75 m B. 78.05 m C. 226 m D. None of these
- There are two concentric circles with centre O and of diameters 10 cm and 6 cm respectively. AB, a chord of outer circle touches the inner circle at T, then length of AB is:
A. 8 cm B. 16 cm C. 9 cm D. 12 cm
- From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is: A. 7 cm B. 12 cm C. 15 cm D. 24.5 cm
- The area (in cm 2 ) of the largest circle that can be inscribed in a square of side 12 cm is A. 6ฯ B. 44ฯ C. 12ฯ D. 36ฯ
- In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and
๏AOB = 90ยฐ. If AO = OB = 42 cm, then find the perimeter of the top of the table. ๏ฆ๏ง๏จ^ Use ๏ฐ ๏ฝ^227 ๏ถ๏ท๏ธ
A. 150 cm B. 250 cm C. 282 cm D. 182 cm
If ๏ก๏ฌ ๏ข are roots of x 2 โ 5x + 6 = 0, then ๏จ^ ๏จ ๏ฉ๏ฉ
2 2 ๏ก๏ก ๏ซ ๏ข ๏ซ ๏ข (^) ๏ฝ?
A. 2
B. 3
C. 1
D. 135
- The volume of the largest right circular cone that can be carved out of a solid hemisphere of radius r can be calculated as: Radius of largest cone = Radius of hemisphere = r (Step 1) Height of largest cone = Radius of hemisphere = r (Step 2) ๏ Volume of cone ๏ฝ^13 ๏ฐr h^2 ๏ฝ^13 ๏ฐr r^2 ๏ฝ^13 ๏ฐr^3 (Step 3) In which step is there an error involving? A. Step- B. Step- C. Step- D. There is no error.
SECTION โ C
- Solve graphically the pair of linear equations: 3x โ 4y + 3 = 0 and 3x + 4y โ 21 = 0 Find the co-ordinates of the vertices of the triangular region formed by these lines and x-axis.
- Let a and b be two distinct prime numbers. If m = a 3 b 2 , n = a^2 b 5 , k = a^4 b. Find the HCF and LCM of m, n and k. Also verify whether HCF ร LCM ๏น m ร n ร k.
- ABC is a right-angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 24 cm and 10 cm. Find the radius of the incircle.
- If ฮฑ and ฮฒ are the zeros of the quadratic polynomial f(x) = ax^2 + bx + c, then evaluate:
a b a b
OR
If ฮฑ and ฮฒ are the zeros of the polynomial f(x) = x 2 โ 5x + k such that ฮฑ โ ฮฒ = 1, find the value of k.
- Show that 1 tan A 1 cot A (^) cosec A sec A 2sin A 2cos A
31.(A) (^) Find the missing frequencies in the following frequency distribution table, if N = 100 and median is 32. Marks Number of Students 0-10 10 10-20? 20-30 25 30-40 30 40-50? 50-60 10 Total 100
(B) OR
Find the mean marks per student, using assumed-mean method. Marks Number of Students 0-10 12 10-20 18 20-30 27 30-40 20 40-50 17 50-60 6 SECTION โ D
- Prove that: cosec A cot A cosec A cot A cosec A cot A cosec A cot A
๏ซ ๏ญ ๏จ^ ๏ฉ^
2 2 2 2 2cosec A 1 2 1 cos^ A 1 cos A
๏ฝ ๏ญ ๏ฝ ๏ฆ๏ง^ ๏ซ ๏ถ๏ท
- Find the ratio in which the line 3x + y โ 6 = 0 divides the line segment joining A(1, โ 1) and B(3, 6).
34.(A)
(B)
A 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 depression of 30ยฐ, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60ยฐ. Find the further time taken by the car to reach the foot of the tower from this point OR An airplane when flying at a height of 3000 metres from the ground passes vertically above another airplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60ยฐ and 45ยฐ respectively. Find the vertical distance between the airplanes at the instant [Take 3 = 1.73]
35.(A) The sides of a right-angled triangle are such that the hypotenuse is 6 cm more than the shorter side and the third side is 2 cm less than the hypotenuse. (i) Find the lengths of all sides of the triangle. (ii) Find the numerical difference between its area and perimeter.
- A school auditorium has been designed with rows of seats arranged in an arithmetic progression to ensure clear visibility for everyone. The first row has 20 seats, the second row has 22 seats, the third row has 24 seats, and so on. Based on this arrangement, answer the following: (i) If the auditorium has 30 rows, find the number of seats in the last row. [1 Mark] (ii) Find the total number of seats in the auditorium. [1 Mark]
(iii) Suddenly, school needs to create 4 more rows in the previous arrangement keeping the same arithmetic progression pattern, how many more students can sit now in the auditorium. [2 Marks]
OR If, in the original arrangement of 30 rows, school needs to arrange seats for 510 more students, how many rows need to be added for the same keeping the same arithmetic progression pattern [2 Marks]
- A surveillance drone is flying at a constant height of 100 m above the ground. At a specific moment, the drone camera observes two suspicious vehicles parked on the ground. The angles of depression of the two vehicles from the drone are observed to be 60ยฐ and 30ยฐ. The two vehicles are on the same side of the drone's vertical axis. Based on this situation, answer the following questions: (i) Draw a neat labeled diagram representing the given situation. [1 Mark] (ii) Find the distance of the vehicle with an angle of depression of 60ยฐ from the point on the ground directly below the drone. [1 Mark] (iii) Find the distance between the two vehicles. (Use 3 ๏ฝ 1.73) [2 Marks] OR If the drone moves vertically upwards by another 50 m, what will be the new angle of depression of the first vehicle (which was earlier at 60ยฐ)? Find the value of tan ๏ฑ where ๏ฑ is the new angle of depression.
