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 follow them strictly:
- 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, Question numbers 1 to 18 are Multiple Choice Questions (MCQs) and Questions 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 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.
A bag contains some red and some white balls. A ball is drawn at random from the bag. If the probability of getting a red ball is `2/7`, then the probability of getting a white ball is ______.
`1/14`
`5/7`
`1/7`
`2/7`
Chapter:
If the zeroes of the polynomial p(x) = 2x2 – 7x + 6 are α and β, then the value of `1/α + 1/β` is ______.
`7/2`
`6/7`
`(-7)/6`
`7/6`
Chapter:
The probability of getting sum greater than 10, when two dice are rolled together, is ______.
`1/9`
`1/18`
`1/12`
1
Chapter:
The total surface area of a solid cone of radius 7 cm and slant height 25 cm, is ______.
724 cm2
704 cm2
550 cm2
616 cm2
Chapter:
The length of a pendulum is 70 cm and it describes an arc of length 88 cm when swings. The angle subtended by the arc at the centre is ______.
36°
70°
72°
80°
Chapter:
The distance between the points (–4, 5) and (–1, 2) is ______.
5
`3sqrt(2)`
6
`2sqrt(3)`
Chapter:
nth term of the A.P.: `(-1)/3, 4/3, 3,` ... is ______.
`(5n - 9)/3`
`(5n - 6)/3`
`(3n - 4)/3`
`(3n + 2)/3`
Chapter:
In the given figure, DE || BС. If AD : AB = 1 : 3 and AE = 2.5 cm, then AC equals
7.5 cm
5 cm
10 cm
2.5 cm
Chapter:
A cylinder of radius r is surmounted on a hemisphere of same radius. If total height of the object is 13 cm, then its inner surface area is
2πr(r + 13)
13πr
2π(13 + r)2
26πr
Chapter:
Which of the following statements is not always true?
Two circles are similar.
Two isosceles right triangles are similar.
Two rectangles are similar.
Two equilateral triangles are similar.
Chapter:
7 × 11 × 13 + 5 is ______.
a prime number.
an odd number.
a composite number.
a multiple of 5.
Chapter:
The roots of the quadratic equation x2 + 9 = 0 are
real and equal
not real
real and negative of each other
rational numbers
Chapter:
A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a queen of spade is ______.
`1/26`
`1/52`
0
`1/4`
Chapter:
If `sin θ = 1/sqrt(11)`, then cot θ equals
`sqrt(11)/sqrt(10)`
`sqrt(10)/sqrt(11)`
`sqrt(10)`
`sqrt(11)`
Chapter:
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The graph of a polynomial p(x) is shown here. The number of zeroes of the polynomial p(x) is
5
1
0
4
Chapter:
A chord QR subtends an angle of 105° at the centre O of the circle. The measure of ∠RQP is
`(75^circ)/2`
`(105^circ)/2`
75°
15°
Chapter:
If `(-20)/9, (-2)/9, 16/9,` .... are in A.P., then next term of the sequence is ______.
`32/9`
`46/9`
`2/9`
`34/9`
Chapter:
PQ is tangent to a circle at a point P on the circle. The number of tangents which can be drawn to the circle parallel to PQ, is ______.
2
1
many
zero
Chapter:
Assertion (A): Median of a data is the value of `N/2`, where N represents sum of all frequencies.
Reason (R): Median divides the whole distribution in two equal parts.
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): For an acute angle θ, cos θ is always less than 1.
Reason (R): In a right-angled triangle, hypotenuse is the longest side and `cos θ = "Base"/"Hypotenuse"`.
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:
If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b.
Chapter:
In the given figure, ΔODC ~ ΔOBA. If ∠BOC = 110°, ∠ODC = 45° and AB = 2CD, then find (i) m∠OAB (ii) OB : OD.
Chapter:
Evaluate: `(5 sin^2 45^circ - 3 tan^2 30^circ)/(2 sec^2 30^circ)`
Chapter:
For A = 60° and B = 30°, verify that tan (A – B) = `(tan A - tan B)/(1 + tan A tan B)`.
Chapter:
If H.C.F. of 135x2 and 189x3 is 108, then find the value of x.
Chapter:
Find the probability that a number selected at random from the numbers 30, 31, 32, 33, ....., 60 is (i) a prime number (ii) a multiple of 6.
Chapter:
Slips of letters of the word ‘BACKGROUND’ are put in a bowl and thoroughly mixed. One slip is picked up at random. Find the probability that picked up slip’s letter is (i) a vowel (ii) present in the word ‘BALL’.
Chapter:
Find the zeroes of the polynomial p(x) = 4x2 – 8x + 3 and verify the relationship between its zeroes and co-efficients.
Chapter:
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Form a polynomial whose zeroes are α2 and β2, where α and β are zeroes of the polynomial `p(x) = x^2 - 3sqrt(2)x + 4`.
Chapter:
How many terms of the A.P. 3, 5, 7, 9, ... must be added to get the sum 80?
Chapter:
Find three consecutive terms in A.P. whose sum is 21 and their product is 231.
Chapter:
Chord AB of a circle subtends an angle of 120° at the centre O of the circle. Find the length of arc AB, if radius of the circle is 21 cm.
Chapter:
Prove that: tan2 θ + cot2 θ + 2 = sec2 θ cosec2 θ.
Chapter:
Points P(6, 0), Q(2, 8) and R(–2, 4) are vertices of ΔPQR. It is given that MN || QR such that `(PM)/(MQ) = 1/3`. Using distance formula and ratio formula, show that `(MN)/(QR) = 1/4`.
Chapter:
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30º, respectively. Find the height of poles and the distance of the point from the poles.
Chapter:
Find mean and mode of the following data:
| Class | 0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 – 75 | 75 – 90 | 90 – 105 |
| Frequency | 4 | 6 | 8 | 10 | 12 | 7 | 3 |
Chapter:
In the given figure, ΔABC is right angled triangle with ∠A = 90°. AD is perpendicular to BC.
Prove that:
- ΔDBA ∼ ΔDAC
- DA2 = DB × DC
- Find the area of ΔABC when DB = 9 cm and DC = 16 cm.
Chapter:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
Chapter:
ABCD is a rectangle of dimensions 80 cm × 60 cm. Another rectangle PQRS is drawn inside ABCD leaving space of equal width x cm along the edges of ABCD. If area PQRS is half of the area ABCD, then find the value of x.
Chapter:
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
Chapter: [4] Quadratic Equations
In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle. |
Based on above information, answer the following questions:
(i) Find m∠AOP. [1]
(ii) Prove that ΔOAР ≅ ΔОВР. [1]
(iii) (a) Find the length of fencing required to protect the statue. (Take `sqrt(3) = 1.73`) [2]
OR
(b) Find area of quadrilateral OAPB. (Take `sqrt(3) = 1.73`)
Chapter:
|
|
To find the number of calories burned per minute on each machine, answer the following:
(i) Represent the above situation in terms of a pair of linear equations in two variables.
(ii) Show that the equations have unique solution.
(iii) (a) Solve both equations to find the values of the variables using elimination method.
OR
(b) Solve both equations to find the values of the variables using substitution method.
Chapter:
|
|
Considering mushroom a solid object, answer the following questions:
(i) What is the total height of a mushroom?
(ii) Find the volume of the stem.
(iii) (a) Determine the volume of 7 such mushrooms.
OR
(b) Find the total surface area of 7 such mushrooms.
Chapter:
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