English Medium
Academic Year: 2025-2026
Date & Time: 17th February 2026, 10:30 am
Duration: 3h
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General Instructions:
Read the following instructions very carefully and strictly follow them:
- This question paper contains 38 questions. All questions are compulsory.
- This question paper is divided into five Sections - A, B, C, D and E.
- In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and questions number 19 and 20 are Assertion-Reason based questions of 1 mark each.
- In Section B, Questions no. 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each.
- In Section C, Questions no. 26 to 31 are short answer (SA) type questions, carrying 3 marks each.
- In Section D, Questions no. 32 to 35 are long answer (LA) type questions carrying 5 marks each.
- In Section E, Questions no. 36 to 38 are case study based questions carrying 4 marks each. Internal choice is provided in 2 marks questions in each case study.
- There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions in Section E.
- Draw neat diagrams wherever required. Take `π = 22/7` wherever required, if not stated.
- Use of calculator is not allowed.
The graph of y = f(x) is given. The number of distinct zeroes of y = f(x) is:
0
1
2
3
Chapter:
There 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 minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B?
144
2
420
272
Chapter:
The pair of linear equations `(3x)/2 + (5y)/3 = 7` and 9x + 10y = 14, is ______.
consistent
inconsistent
consistent with one solution
consistent with many solutions
Chapter:
The natural number 1 is ______.
a prime number.
a composite number.
prime as well as composite.
neither prime nor composite.
Chapter:
The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an A.P., is ______.
6
– 6
18
–18
Chapter:
For any natural number n, 5n ends with the digit:
0
5
3
2
Chapter:
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R, then AB : AC is equal to ______.
PQ : PR
PQ : QR
QR : QP
PR : QR
Chapter:
If α and β are two zeroes of a polynomial (fx) = px2 – 2x + 3p and α + β = αß, then value of p is ______.
`(-2)/3`
`2/3`
`1/3`
`(-1)/3`
Chapter:
The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is ______.
43.4
42.4
44.2
49.3
Chapter:
If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.
±4
4
–4
0
Chapter: [6] Coordinate Geometry
A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in cm3) is ______.
182 π
`182/3 π`
`682/3 π`
`364/3 π`
Chapter:
If cos A = `4/5`, then the value of tan A is ______.
`3/5`
`3/4`
`4/3`
`5/3`
`1/8`
Chapter: [9] Introduction to Trigonometry
Area of a segment of a circle of radius ‘r’ and central angle 60° is ______.
`(πr^2)/2 - 1/2 r^2`
`(2πr)/4 - sqrt(3)/4 r^2`
`(πr^2)/6 - sqrt(3)/4 r^2`
`(2πr)/4 - r^2 sin 60^circ`
Chapter:
If 2 sin A = 1, then the value of tan A + cot A is ______.
`sqrt(3)`
`4/sqrt(3)`
`sqrt(3)/2`
1
Chapter:
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In the given figure, PA and PB are tangents to a circle centred at O. If ∠OAB = 15°, then ∠APB equals:
30°
15°
45°
10°
Chapter:
From 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 the tower is found to be 45°. The height (in metres) of the tower is ______.
`10sqrt(3)`
`30sqrt(3)`
60
30
Chapter:
The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is ______.
`15/25`
`10/25`
`11/25`
`9/25`
Chapter:
In the given figure, PA and PB are tangents to a circle centred at O. If ∠AOB = 130°, then ∠APB is equal to:
130°
50°
120°
90°
Chapter:
Assertion (A): The mean of first 'n' natural numbers is `(n - 1)/2`.
Reason (R): The sum of first 'n' natural numbers is `(n(n + 1))/2`.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Assertion (A): The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm2.
Reason (R): The surface area of a cuboid of dimensions I × b × h is (lb + bh + hl).
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
In the given figure, ΔАНK ~ ΔABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find the length of AС.
Chapter:
In the given figure, XY || QR, `(PQ)/(XQ) = 7/3` and PR = 6.3 cm. Find the length of YR.
Chapter:
Evaluate:
`(5 cos^2 60^circ + 4 sec^2 30^circ - tan^2 45^circ)/(sin^2 30^circ + cos^2 30^circ)`
Chapter:
Prove that `1 + (cot^2 α)/(1 + "cosec" α) = "cosec" α`
Chapter:
In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.
Chapter:
Find the value of p, for which one zero of the quadratic polynomial px2 – 14x + 8 is 6 times the other.
Chapter:
If 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 find the values of m and n.
Chapter:
Prove that: `(sec^3 θ)/(sec^2 θ - 1) + ("cosec"^3 θ)/("cosec"^2 θ - 1) = sec θ . "cosec" θ (sec θ + "cosec" θ)`
Chapter:
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If `(sec α)/("cosec" β) = p` and `(tan α)/("cosec" β) = q`, then prove that (p2 – q2) sec2α = p2.
Chapter:
Find 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]`
Chapter:
Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5 and (ii) difference of the numbers on the two dice is 3.
Chapter:
Find the coordinates of the points of trisection of the line segment joining the points A(–1, 4) and B(–3, –2).
Chapter:
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Chapter:
If a regular hexagon ABCDEF circumscribes a circle, then prove that AB + CD + EF = BC + DE + FA.
Chapter:
If the median of the following distribution is 32.5, then find the values of x and y.
| Class | Frequency |
| 0 – 10 | x |
| 10 – 20 | 5 |
| 20 – 30 | 9 |
| 30 – 40 | 12 |
| 40 – 50 | y |
| 50 – 60 | 3 |
| 60 – 70 | 2 |
| Total | 40 |
Chapter:
Aarush bought 2 pencils and 3 chocolates for ₹ 11 and Tanish bought 1 pencil and 2 chocolates for ₹ 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
Chapter:
In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.
Chapter:
Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the nine of larger diameter to fill the pool.
Chapter:
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
Chapter:
A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/sec. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
Chapter:
|
Tejas is standing at the top of a building and observes a car at an angle of depression of 30° as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to 60° and at that moment, the car is 25 m away from the building.
|
Based on the information given above, answer the following questions:
(i) What is the height of the building? [1]
(ii) What is the distance between the two positions of the car? [1]
(iii) (a) What would be the total time taken by the car to reach the foot of the building from the starting point? [2]
OR
(iii) (b) What is the distance of the observer from the car when it makes an angle of 60°? [2]
Chapter:
|
On 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 cube and a strawberry ice-cream for you.
|
Based on the information given above, answer the following questions:
(i) Find the length of the diagonal of Rubik’s cube if each edge measures 6 cm. [1]
(ii) Find the volume of Rubik’s cube if the length of the edge is 7 cm. [1]
(iii) (a) What is the curved surface area of hemisphere (ice-cream) if the base radius is 7 cm? [2]
OR
(iii) (b) If two cubes of edges 4 cm are joined end-to-end, then find the surface area of the resulting cuboid. [2]
Chapter:
| Your 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 ₹ 1,18,000 by paying every month, starting with the first instalment of ₹ 1,000 and he increases the instalment by ₹ 100 every month. |
Based on the information given above, answer the following questions:
(i) Find the amount paid by him in the 30th instalment. [1]
(ii) If the total number of instalments is 40, what is the amount paid in the last instalment? [1]
(iii) (a) What amount does he still have to pay after the 30th instalment? [2]
OR
(iii) (b) Find the ratio of the tenth instalment to the last instalment. [2]
Chapter:
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