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 natural number 1 is ______.
a prime number.
a composite number.
prime as well as composite.
neither prime nor composite.
Chapter:
For any natural number n, 5n ends with the digit:
0
5
3
2
Chapter:
The graph of y = f(x) is given. The number of distinct zeroes of y = f(x) is:
0
1
2
3
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:
If the pair of linear equations: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 is consistent and dependent, then
`(a_1)/(a_2) ≠ (b_1)/(b_2)`
`(a_1)/(a_2) ≠ (b_1)/(b_2) = (c_1)/(c_2)`
`(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`
`(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`
Chapter:
Which of the following sequence is not an A.P.?
`2, 5/2, 3, 7/2, ...`
–1.2, –3.2, –5.2, –7.2, ...
`sqrt(2), sqrt(8), sqrt(18), ...`
12, 32, 52, 72, ...
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:
The distance of the point A(4a, 3a) from x-axis is ______.
3a
– 3a
4a
– 4a
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
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If 2 sin A = 1, then the value of tan A + cot A is ______.
`sqrt(3)`
`4/sqrt(3)`
`sqrt(3)/2`
1
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:
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:
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:
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:
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:
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:
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:
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:
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:
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If α, β are the zeroes of the quadratic polynomial px2 + qx + r, then find the value of α3β + β3α.
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:
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:
If `tan θ + 1/tan θ = 2`, find the value of `tan^2 θ + 1/(tan^2 θ)`.
Chapter:
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Chapter: [9] Introduction to Trigonometry
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 coordinates of the points of trisection of the line segment joining the points A(–1, 4) and B(–3, –2).
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:
If `(sec α)/("cosec" β) = p` and `(tan α)/("cosec" β) = q`, then prove that (p2 – q2) sec2α = p2.
Chapter:
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