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 - Section A, B, C, D and E.
- In Section A, questions numbers 1 to 18 are multiple choice questions (MCQs) and question numbers 19 and 20 are Assertion-Reason based questions of 1 mark each.
- In Section B, question numbers 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each.
- In Section C, question numbers 26 to 31 are short answer (SA) type questions, carrying 3 marks each.
- In Section D, question numbers 32 to 35 are long answer (LA) type questions, carrying 5 marks each.
- In Section E, question numbers 36 to 38 are case-based questions, carrying 4 marks each. Internal choice is provided in 2 marks question 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 of 2 marks in Section E.
- Draw neat diagrams wherever required. Take `π = 22/7` wherever required, if not stated.
- Use of calculator is not allowed.
Which of the following equations is/are quadratic equation(s)?
q1: (y + 1)2 = 2y
q2: (y – 1)2 = y2
q3: (y + 1)3 = (y – 1)3
`q_4: 1 + sqrt(y) = (sqrt(y) + 1)^2`
q1, q2 and q4
q1 and q2
q1, q3 and q4
q1 and q3
Chapter:
The discriminant of the quadratic equation ax2 + x + a = 0 is ______.
`sqrt(1 - 4a^2)`
1 – 4a2
4a2 – 1
`sqrt(4a^2 - 1)`
Chapter:
The end points of the diameter AB of a circle are A(4, 0) and B(0, –4). The length of the diameter is ______.
3 units
8 units
`sqrt(8)` units
`sqrt(32)` units
Chapter:
In the adjoining figure, if ΔAOB ~ ΔCOD, then which of the following is true?
AO.OB = OC.OD
AO.CD = OC.AB
AO.AB = OC.CD
AO.OC = OB.OD
Chapter:
In the adjoining figure, if EA || SR and PE = x cm, then the value of 5x is:
2.4 cm
12 cm
1.35 cm
6.75 cm
Chapter:
Which of the following graphs represents a polynomial with both zeroes being positive?
Chapter:
The system of equations x = 2 and x = 3 has:
unique solution (2, 3)
two solutions (2, 0) and (3, 0)
no solution
infinitely many solutions
Chapter:
If the numbers 2p + 1, 3p + 2, 4p + 3 are in A.P., then the common difference is ______.
p
1
p + 1
0
Chapter:
Which of the following statements is not true?
sin 0° = cos 0°
tan 30° = cot 60°
sin 30° = cos 60°
`sin 45^circ = 1/(sec 45^circ)`
Chapter:
If `2 sin 2θ = sqrt(2)`, then the value of θ is ______.
90°
60°
45°
`(22 1/2)^circ`
Chapter:
In the adjoining figure, the angle of elevation of the point C from the point B, is:
30°
45°
22.5°
67.5°
Chapter:
In the adjoining figure, the slant height of the conical part is:
4 cm
7 cm
5 cm
25 cm
Chapter:
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency | 3 | 5 | 7 | 9 | 11 |
The upper limit of the median class of the above data is:
10
20
30
40
Chapter:
If for a data, median is 5 and mode is 4, then mean is equal to ______.
7
11
`11/2`
`14/3`
Chapter:
The LCM of 22.33 and 32.23 is ______.
1
21.31
23.33
25.35
Chapter:
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A letter is selected from the letters of the word FEBRUARY. The probability that it is a vowel is ______.
`1/8`
`2/8`
`3/8`
`3/7`
Chapter:
Which of the following numbers will not end with 0 for any natural number n?
4n
4n
3n + 1
10n + 1
Chapter:
The system of linear equations px + qy = r and p1x + q1y = r1 has a unique solution, if:
pq ≠ p1q1
pp1 ≠ qq1
pq1 ≠ qp1
pqr ≠ p1q1r1
Chapter:
Assertion (A): 7 × 2 + 3 is a composite number.
Reason (R): A composite number has more than two factors.
Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (А).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Assertion (A): From a bag containing 5 red balls, 2 white balls and 3 green balls, the probability of drawing a non-white ball is `4/5`.
Reason (R): For any event E, P(E) + P(not E) = 1.
Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (А).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
A box consists of 60 wall clocks, out of which 40 are good, 15 have minor defects and the remaining are broken. A trader will reject the box, if the clock taken out from the box is broken. The trader randomly takes out one clock from the box. What is the probability that:
- the box will be rejected?
- the clock taken out of the box has minor defect?
Chapter:
Find the coordinates of the point which divides the line segment joining the points P(–1, 1) and Q(5, –7) in the ratio 2 : 3.
Chapter:
One zero of a quadratic polynomial is twice the other. If the sum of zeroes is (–6), find the polynomial.
Chapter:
If one zero of the polynomial x2 – 5x – c is (–1), find the value of c. Also, find the other zero.
Chapter:
In the adjoining figure, DE || BC and `(DE)/(BC) = 1/3`. If AD = 1.5 cm, then find the length of BD.
Chapter:
If sin (A + 2B) = 2 cos 60° and A = 3B, find the measures of A and B.
Chapter:
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Chapter:
In the adjoining figure, AB is the diameter of the circle with centre O. Two tangents p and g are drawn to the circle at points A and B respectively. Prove that p || q. Further, a line CD touches the circle at E and ∠BCD = 110°. Find the measure of ∠ADC.
Chapter:
Given that `sqrt(2)` is an irrational number, prove that `5 - 2sqrt(2)` is also an irrational number.
Chapter:
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Solve the following system of equations graphically:
x + 3y = 6 and 2x – 3y = 12
Also, find the area of the triangle formed by the lines x + 3y = 6, x = 0 and y = 0.
Chapter:
One of the supplementary angles exceeds the other by 120°. Express the given information as a system of linear equations in two variables. Hence, find the measure of both the angles.
Chapter:
If the point A(x, y) is equidistant from the points B(–2, 0) and C(2, 0), prove that the point A lies on y-axis. Also, find the coordinates of the point A, if ΔABC is an equilateral triangle.
Chapter:
Prove that: `(sin A - tan A)/(sin A + tan A) = (1 - sec A)/(1 + sec A)`
Chapter:
If sin x = p, then prove that `cot x = sqrt(1 - p^2)/p`.
Chapter:
If sin x = p, then prove that `(1 + tan^2 x)/(1 + cot^2 x) = p^2/(1 - p^2)`.
Chapter:
In the adjoining figure, ΔOAB is an equilateral triangle and the area of the shaded region is 750 π cm2. Find the perimeter of the shaded region.
Chapter:
O and O’ are the centres of the circles of radius r as shown in figures (i) and (ii) respectively.
 |
 |
| (i) | (ii) |
Find the ratio of area of shaded region in figure (i) to that of area of shaded region in figure (ii).
Chapter:
Find the mean and the mode for the following data:
| Class | Frequency |
| 5 – 10 | 5 |
| 10 – 15 | 6 |
| 15 – 20 | 15 |
| 20 – 25 | 10 |
| 25 – 30 | 5 |
| 30 – 35 | 4 |
| 35 – 40 | 2 |
| 40 – 45 | 2 |
Chapter:
Express `24/(18 - x) - 24/(18 + x) = 1` as a quadratic equation in standard form and find the discriminant of the quadratic equation, so obtained. Also, find the roots of the equation.
Chapter:
The sum of squares of two positive numbers is 100. If one number exceeds the other by 2, find the numbers.
Chapter:
In the adjoining figure, AB || EF || CD, CD = 12 cm, AB = 7.2 cm and DF = 4.8 cm. Prove that `(CF)/(FB) = (DF)/(FA)`. Also, find the value of y, if x = 4.5 cm.
Chapter:
|
A flagstaff, 7.32 m long is fitted at the top of 10 m tall building. The flagstaff is supported by the ropes which are tied to the point P on the ground which is x m away from the base of the building. It is given that `l_1` is the length of rope from point P to the base of the flagstaff and `l_2` is the length of rope from point P to the top of flagstaff. Rope `l_1` makes an angle of 30° with the horizontal and θ be the angle which rope `l_2` makes with the horizontal as shown in the figure.
|
Based on the given information, answer the following questions:
(Use `sqrt(2) = 1.4` and `sqrt(3) = 1.732`)
(i) Find the value of x. [1]
(ii) Find the measure of angle θ. [1]
(iii) (a) Find the total length of ropes needed to support the flagstaff. [2]
OR
(iii) (b) Which rope is longer `l_1` or `l_2` and by how much? [2]
Chapter:
|
A watermelon vendor arranged the watermelons similar to shown in the adjoining picture:
|
Based on the above information, answer the following questions:
(i) Find the value of ‘d’. [1]
(ii) How many watermelons will be there in the 15th row from the bottom? [1]
(iii) (a) Find the total number of watermelons from bottom to top. [2]
OR
(iii) (b) If the number of watermelons in the nth row from top is equal to number of watermelons in the nth row from bottom, find the value of n. [2]
Chapter:
|
As a part of school project, Mishika and Sahaj created a bird-bath from the cylindrical log of wood by scooping out the hemispherical depression from one end of the cylinder as shown in the figure given. Cylinder has a length 2 m out of which 0.6 m is in earth and the diameter is 1.4 m.
|
On the basis of the above information, answer the following questions:
(i) Write the radius of the hemispherical depression. [1]
(ii) Find the volume of water that can be filled in the hemispherical depression in terms of π. [1]
(iii) (a) Find the total surface area of log of wood above the ground after making the bird-bath. [2]
OR
(iii) (b) Compute the volume of log of wood above the ground after making the bird-bath. [2]
Chapter:
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