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 n = wherever required, 7 if not stated.
- Use of a calculator is not allowed.
The number of multiples of 6 lying between 25 and 363 is ______.
56
56.5
57
58
Chapter:
Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by 6, is ______.
`1/6`
`11/36`
`1/12`
`1/4`
Chapter:
In the given figure, Δ ABC is an equilateral triangle. AD is a median of the triangle joining the points `A(0, (5sqrt3)/2), D(0, 0)`. Points B and C are (in same order):
(−5, 0), (5, 0)
`((−5)/2, 0), (5/2, 0)`
(−10, 0), (10, 0)
`(−5sqrt3, 0), (5sqrt3, 0)`
Chapter:
The median and mode of a distribution are 25.2 and 26.1 respectively. The mean of the distribution is ______.
24.75
24.25
24.3
25.5
Chapter:
It is given that ΔABC ~ ΔQRP such that AB = 9 cm, BC = 5 cm and PR = 2 cm. Length of side QR is ______.
0.9 cm
`5/18` cm
`10/9` cm
3.6 cm
Chapter:
A polynomial p(x), which has sum of its zeroes equal to their product, is ______.
3x2 + 2x + 2
3x2 − 2x − 3
3x2 − 2x + 2
x2 − 3x + 2
Chapter:
In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If ∠QPR = 60°, then the length of each tangent is:
`3sqrt3` cm
3 cm
6 cm
`sqrt3` cm
Chapter:
In the given figure, OA x OB = OC x OD. Which of the following options is correct?
∠A = ∠C
∠A = ∠B
∠A = ∠D
AOAD ~ A ОВС
Chapter:
The value of `(1/2 tan^2 45° - cos^2 60°)` is ______.
0
`-1/2`
`1/4`
`-1/4`
Chapter:
A cone of maximum size is carved out from a solid cube of edge length l. The volume of the cone is ______.
`(pil^3)/(12)`
`(pil^3)/(3)`
`l^3(1 - pi/3)`
`(pil^3)/(8)`
Chapter:
(3 × 11 × 13 + 3) is ______.
a prime number
divisible by 13
a composite number
an odd number
Chapter:
Given that sin 2α = `sqrt3/2`, the value of sin 3α is ______.
`(3sqrt3)/4`
`1/2`
1
`sqrt3/4`
Chapter:
If the length of the shadow of a tower is `sqrt(3)` times that of its height, then altitude of the sun is ______.
45°
30°
60°
15°
Chapter:
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Equation of a line coincident with 2.5x − 2y = 3 is ______.
5x − 4y = 3
5x − 4y + 6 = 0
15x − 12y − 3 = 0
5x − 4y − 6 = 0
Chapter:
The nth term of the A.P. `−1/3, 2/3, 5/3, 8/3,` ... is ______.
3n − 4
`n − 4/3`
`(n − 2)/3`
`(n − 4)/3`
Chapter:
In the given figure, PT is a tangent to the circle with centre O and radius r. If ∠POT = 45°, then the length of OP is:
`rsqrt2`
`sqrt2r`
2r
r2
Chapter:
The roots of the quadratic equation (x − 1)2 = 16 are ______.
5, 3
4, −4
5, −3
−5, 3
Chapter:
If the roots of the quadratic equation `sqrt3x^2 - kx + 2sqrt3 = 0` are real and equal, then the value (s) of k is/are ______.
`±sqrt24`
0
4
−5
Chapter:
Assertion (A): tan 2θ is not defined at θ = 45°.
Reason (R): sin90° = cos 90°.
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): Radius is the smallest distance of a tangent from the centre of the circle.
Reason (R): Radius is perpendicular to the tangent.
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:
A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.
Chapter:
In the following figure, if ΔABE ≅ ΔACD, show that ΔADE ∼ ΔABC.
Chapter:
In an A.P., the first term is 4 and the last term is 31. If sum of all the terms is 175, find the number of terms and the common difference.
Chapter:
How many terms of the A.P. 21, 18, 15, … must be added to get the sum 0?
Chapter: [5] Arithmetic Progressions
Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.
Chapter:
Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, −2) and (1, 6) respectively.
- Find the co-ordinates of point P.
- Find the length of the side of the square.
Chapter:
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Find the coordinates of a point on the line x + y = 5 which is equidistant from (6, 4) and (5, 2).
Chapter:
PA and PB are tangents drawn to the circle with centre O as shown in the figure. Prove that ∠APB = 2∠OAB.
Chapter:
In the given figure, PA is the tangent to the circle with centre O such that OA = 10 cm, AB = 8 cm and AB ⊥ OP. Find the length of PB.
Chapter:
Determine the ratio in which the line 3x + y – 9 = 0 divides the line segment joining the points (1, 3) and (2, 5). Find the point of intersection.
Chapter:
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Chapter: [9] Introduction to Trigonometry
Prove that:
(sin A + sec A)2 + (cos A + cosec A)2 = (1 + sec A cosec A)2
Chapter:
In the given figure, chord AB subtends an angle of 120° at the centre of the circle with radius 7 cm. Find (i) perimeter of major sector OACB, and (ii) area of the shaded segment, if area of Δ OAB = 21.2 cm2.
Chapter:
Find two consecutive negative integers, sum of whose squares is 481.
Chapter:
Solve the following system of equations graphically:
x − 2y = 3, 3x − 8y = 7
Chapter:
Five years ago, Adil was thrice as old as Bharat. Ten years later Adil shall be twice as old as Bharat. To know the present ages of Adil and Bharat:
- Form the linear equations representing the above information.
- Show that the system of equations is consistent with unique solution.
- Find the present ages of Adil and Bharat.
Chapter:
Find the mean and the mode of the following frequency distribution:
| Class | Frequency |
| 0 − 15 | 9 |
| 15 − 30 | 15 |
| 30 − 45 | 35 |
| 45 − 60 | 20 |
| 60 − 75 | 11 |
| 75 − 90 | 13 |
| 90 − 105 | 17 |
Chapter:
The angle of elevation of the top of a building from a point A, on the ground, is 30°. On moving a distance of 24 m towards its base to the point B, the angle of elevation changes to 60°. Find the height of the building and distance of point A from the base of the building. (Take `sqrt3` = 1.73)
Chapter:
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