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 number 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 number 21 to 25 are Very Short Answer (VSA) type questions, carrying 2 marks each.
- In Section-C, questions number 26 to 31 are Short Answer (SA) type questions, carrying 3 marks each.
- In Section-D, questions number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
- In Section-E, questions number 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 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.
If PQ and PR are tangents to the circle with centre O and radius 4 cm such that ∠QPR = 90°, then the length OP is
4 cm
`4sqrt(2)` cm
8 cm
`2sqrt(2)` cm
Chapter:
An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is `r/2`, then h : 2r equals
1 : 8
1 : 2
1 : 1
2 : 1
Chapter:
Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If `hat(PQ)` = 11 cm, then the value of θ is ______.
10°
60°
45°
100°
Chapter:
`(1 + tan^2A)/(1 + cot^2 A)` equals to ______.
tan2 A
–1
– tan2 A
cot2 A
Chapter:
Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is
2πr3
3πr3
5πr3
4πr3
Chapter:
Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is ______.
`2/9`
`7/36`
`1/4`
`2/3`
Chapter:
ABCD is a parallelogram such that AF = 7 cm, FB = 3 cm and EF = 4 cm, length FD = equals
`21/4 cm`
`28/3 cm`
`12/7 cm`
5.5 cm
Chapter:
PQ is tangent to a circle with centre O. If ∠POR = 65°, then m∠PTR is
65°
58.5°
57.5°
45°
Chapter:
A circle centred at (–1, 2) passes through the point (0, 3). Radius of the circle is ______.
`2sqrt(2)`
`sqrt(2)`
`sqrt(26)`
1
Chapter:
It is given that ΔABC ~ ΔEDF. Which of the following is not true?
`("Perimeter of" ΔABC)/("Perimeter of" ΔEDF) = (AB)/(ED)`
`(AB)/(ED) = (AC)/(EF)`
∠A = ∠D, ∠C = ∠F
`(AB + BC)/(AC) = (DE + DF)/(EF)`
Chapter:
If roots of the quadratic equation `x^2 - ksqrt(3)x + 2 = 0` are real and equal, then value of k is ______.
–2
`sqrt(8/3)`
1
2
Chapter:
Observe the graph of polynomial p(x). Number of zeroes of p(x) is
5
4
6
3
Chapter:
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is ______.
34
43
38.5
41.5
Chapter:
Area of sector of a circle with radius 18 cm is 198 cm2. The measure of central angle is ______.
70°
14°
140°
210°
Chapter:
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If 2 tan A = 3, then value of sec A equals
`sqrt(13/2)`
`sqrt(13)/4`
`2/sqrt(13)`
`sqrt(13)/2`
Chapter:
The value of k for which the system of linear equations `x/2 + y/3 = 5` and 2x + ky = 7 is inconsistent, is ______.
`3/4`
`4/3`
`1/3`
3
Chapter:
In an A.P., a = –3 and S17 = 357. The value of a17 is ______.
47
39
45
42
Chapter:
In the given figure, a circle is centred at (1, 2). The diameter of the circle is
4
`2sqrt(2)`
`sqrt(5)`
`2sqrt(5)`
Chapter:
Assertion (A): `(sqrt(3) + sqrt(5))` is an irrational number.
Reason (R): Sum of the any two irrational numbers is always irrational.
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 Assertion (А).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Assertion (A): If probability of happening of an event is 0.2p, p > 0, then p can’t be more than 5.
Reason (R): `P(barE) = 1 - P(E)` for an event E.
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 Assertion (А).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Given that `sqrt(5)` is an irrational number, prove that `2 + 3sqrt(5)` is an irrational number.
Chapter:
If the HCF of 210 and 55 is expressed as 210 × 5 + 55m, then find the value of m.
Chapter:
In the given figure, DE || AC and DF || AE. Prove that : `(BF)/(FE) = (BE)/(EC)`.
Chapter:
Verify that roots of the quadratic equation (p – q)x2 + (q – r)x + (r – p) = 0 are equal when q + r = 2p.
Chapter:
α, β are zeroes of the polynomial p(x) = 3x2 – 6x – 5. Find the value of `1/α^2 + 1/β^2`.
Chapter:
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Chapter: [9] Introduction to Trigonometry
Evaluate: `(3 cos^2 30^circ - 6 "cosec"^2 30^circ)/(tan^2 60^circ)`
Chapter:
A trader has three different types of oils of volume 870 `l`, 812 `l` and 638 `l`. Find the least number of containers of equal size required to store all the oil without getting mixed.
Chapter:
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To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are 14 m × 25 m × 16 m.
Chapter:
The internal and external radii of a hollow hemisphere are `5sqrt(2)` cm and 10 cm respectively. A cone of height `5sqrt(7)` cm and radius `5sqrt(2)` cm is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of π. (Use `sqrt(2) = 1.4`)
Chapter:
In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.
Chapter:
Solve the linear equations 3x + y = 14 and y = 2 graphically.
Chapter:
A bag contains 30 balls out of which ‘m’ number of balls are blue in colour.
- Find the probability that a ball drawn at random from the bag is not blue.
- If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be `5/4` times the probability of drawing a blue ball in the first case. Find the value of m.
Chapter:
Prove that: `1/(sec x - tan x) - 1/(cos x) = 1/(cos x) - 1/(sec x + tan x)`
Chapter:
The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also find the value of θ.
Chapter:
A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30°. From the bottom of the same building, the angle of elevation of kite is 45°. Find the length of the string and height of roof from the ground. (Use `sqrt(3) = 1.73`)
Chapter:
Find mean and mode of the following frequency distribution:
| Class: | 5 – 15 | 15 – 25 | 25 – 35 | 35 – 45 | 45 – 55 | 55 – 65 |
| Frequency: | 11 | 20 | 25 | 22 | 12 | 10 |
Chapter:
The median of the following data is 32.5, find the missing frequencies x and y:
| Class: | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 –50 | 50 – 60 | 60 – 70 | Total |
| Frequency: | x | 5 | 9 | 12 | y | 3 | 2 | 40 |
Chapter:
A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.
Chapter:
The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered 2 m extra cloth for free thus reducing the price of cloth per metre by ₹ 120. What was the original per metre price of cloth and its length?
Chapter:
In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B respectively. It is given that MQ = 13 cm, NB = 8 cm, BQ = 35 cm and TP = 80 cm.
- Name the quadrilateral MQBN. [1]
- Is MN parallel to PA? Justify your answer. [1]
- Find length TB. [1]
- Find length MN. [2]
Chapter:
|
‘Kolam’ is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below.
|
Based on the above, answer the following questions:
(i) Show that number of dots given above form an A.P. Write the first term and common differencе. [1]
(ii) Write nth term of the A.P. formed. [1]
(iii) (a) The pattern is expanded on a large ground. If total 220 dots are used, then find the number of squares formed. [2]
OR
(b) Is it possible to complete n number of squares using 100 dots? If yes, then find the value of n.
Chapter:
|
Point A: (–4, 2) Rajasthan High Court Point B: (4, –4) Birla Mandir Point C: (4, 3) Heera Bagh Point D: (–5, –2) Amar Jawan Jyoti |
Based on the above, answer the following questions:
(i) Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home? [1]
(ii) There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio. [1]
(iii) (a) Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti? Justify your answer. [2]
OR
(b) Using section formula, show that points A, O and B are not collinear.
Chapter:
Carom cm. It board has is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR = x, ∠PRQ = α and ∠CRB = θ. |
Based on the above information, answer the following questions:
(i) Using law of reflection i.e. ∠PRT = ∠CRT, prove that θ = α. [1]
(ii) Prove that ΔPQR ~ ΔCBR given that PQ is perpendicular to АВ. [1]
(ii) (a) Find the value of x using similarity of triangles. [2]
OR
(b) If `(Area ΔPQR)/(Area ΔCBR) = (PQ^2)/(CB^2)`, then find the value of x.
Chapter:
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