English Medium
Academic Year: 2025-2026
Date: March 2026
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General Instructions:
Read the following instructions carefully and follow them:
- This question paper contains 38 questions. All Questions are compulsory.
- This Question Paper is divided into 5 Sections A, B, C, D and E.
- In Section A, Question numbers 1 - 18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion- Reason based questions of 1 mark each.
- In Section B, Question numbers 21 - 25 are very short answer (VSA) type questions, carrying 02 marks each.
- In Section C, Question numbers 26 - 31 are short answer (SA) type questions, carrying 03 marks each.
- In Section D, Question numbers 32 - 35 are long answer (LA) type questions, carrying 05 marks each.
- In Section E, Question numbers 36 - 38 are case study-based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively.
- There is no overall choice. However, an internal choice in 2 questions of Section B, 2 questions of Section C and 2 questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E.
- Draw neat and clean figures wherever required. Take `pi = 22/7` wherever required if not stated.
- Use of calculators is not allowed.
If a = 22 × 3x, b = 22 × 3 × 5, c = 22 × 3 × 7 and LCM (a, b, c) = 3780, then x is equal to ______.
1
2
3
0
Chapter:
The shortest distance (in units) of the point (2, 3) from y-axis is ______.
2
3
5
1
Chapter:
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are not parallel, then k has to be ______.
`15/4`
`≠15/4`
any rational number
any rational number having 4 as denominator
Chapter:
A quadrilateral ABCD is drawn to circumscribe a circle. If BC = 7 cm, CD = 4 cm and AD = 3 cm, then the length of AB is ______.
3 cm
4 cm
6 cm
7 cm
Chapter:
If sec θ + tan θ = x, then sec θ – tan θ will be ______.
x
x2
`2/x`
`1/x`
Chapter:
Which one of the following is not a quadratic equation?
(x + 2)2 = 2(x + 3)
x2 + 3x = (–1)(1 – 3x)2
x3 – x2 + 2x + 1 = (x + 1)3
(x + 2)(x + 1) = x2 + 2x + 3
Chapter:
Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1 cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1 cm. Total area of all the dotted regions assuming the thickness of the rings to be negligible is:
`4(pi/12-sqrt3/4)"cm"^2`
`(pi/6-sqrt3/4)"cm"^2`
`4(pi/6-sqrt3/4)"cm"^2`
`8(pi/6-sqrt3/4)"cm"^2`
Chapter:
A pair of dice is tossed. The probability of not getting the sum eight is ______.
`5/36`
`31/36`
`5/18`
`5/9`
Chapter:
If 2 sin 5x = `sqrt(3)`, 0° ≤ x ≤ 90°, then x is equal to ______.
10°
12°
20°
50°
Chapter:
The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such numbers are ______.
2
3
4
5
Chapter:
If the area of the base of a right circular cone is 51 cm2 and it’s volume is 85 cm2, then the height of the cone is given as ______.
`5/6` cm
`5/3` cm
`5/2` cm
5 cm
Chapter:
If zeroes of the quadratic polynomial ax2 + bx + c (a, c ≠ 0) are equal, then ______.
c and b must have opposite signs
c and a must have opposite signs
c and b must have same signs
c and a must have same signs
Chapter:
The area (in cm2) of a sector of a circle of radius 21 cm cut off by an arc of length 22 cm is ______.
441
321
231
221
Chapter:
If ∆ABC ~ ∆DEF, AB = 6 cm, DE = 9 cm, EF = 6 cm and FD = 12 cm, then the perimeter of ∆ABC is ______.
28 cm
28.5 cm
18 cm
23 cm
Chapter:
If the probability of the letter chosen at random from the letters of the word “Mathematics” to be a vowel is `2/(2x + 1)`, then x is equal to ______.
`4/11`
`9/4`
`11/4`
`4/9`
Chapter:
The points A(9, 0), B(9, –6), C(–9, 0) and D(–9, 6) are the vertices of a ______.
Square
Rectangle
Parallelogram
Trapezium
Chapter:
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The median of a set of 9 distinct observations is 20.5. If each of the observations of a set is increased by 2, then the median of a new set ______.
is increased by 2
is decreased by 2
is two times the original number
remains same as that of original observations
Chapter:
The length of a tangent drawn to a circle of radius 9 cm from a point at a distance of 41 cm from the centre of the circle is ______.
40 cm
9 cm
41 cm
50 cm
Chapter:
Assertion (A): The number 5n cannot end with the digit 0, where n is a natural number.
Reason (R): A number ends with 0, if its prime factorization contains both 2 and 5.
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 and reason (R) is not the correct explanation of assertion (A).
Assertion (A) is true but reason (R) is false.
Assertion (A) is false but reason (R) is true.
Chapter:
Assertion (A): If cos A + cos2A = 1, then sin2A + sin4A = 1.
Reason (R): sin2A + cos2A = 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 and reason (R) is not the correct explanation of assertion (A).
Assertion (A) is true but reason (R) is false.
Assertion (A) is false but reason (R) is true.
Chapter:
The A.P. 8, 10, 12, ....... has 60 terms. Find the sum of the last 10 terms.
Chapter:
Find the middle term of A.P. 6, 13, 20, ......., 230.
Chapter:
If sin(A + B) = 1 and cos(A – B) = `sqrt(3)/2`, 0° < A + B ≤ 90° and A > B, then find the measures of angles A and B.
Chapter:
If AP and DQ are medians of triangles ABC and DEF respectively, where ∆ABC ~ ∆DEF, then prove that `(AB)/(DE) = (AP)/(DQ)`.
Chapter:
A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35 m, 40 m and 50 m. Find the area of grass field that can be grazed by them.
Chapter:
Find the area of the major segment (in terms of π) of a circle of radius 5 cm, formed by a chord subtending an angle of 90° at the centre.
Chapter:
A ∆ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that ar(∆ABC) = 90 cm2.
Chapter:
In the given figure, XY and X’Y’ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C, intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°.
Chapter:
In a workshop, the number of teachers of English, Hindi and Science are 36, 60 and 84 respectively. Find the minimum number of rooms required if in each room the same number of teachers are to be seated and all of them being of the same subject.
Chapter:
Find the zeroes of the quadratic polynomial `2x^2 - (1 + 2sqrt(2))x + sqrt(2)` and verify the relationship between the zeroes and coefficients of the polynomial.
Chapter:
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If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Chapter: [9] Introduction to Trigonometry
Prove that `(cosA - sinA + 1)/(cosA + sinA - 1)` = cosec A + cot A
Chapter:
On a particular day, Vidhi and Unnati couldn’t decide on who would get to drive the car. They had one coin each and flipped their coin exactly three times.
The following was agreed upon:
- If Vidhi gets two heads in a row, she would drive the car.
- If Unnati gets a head immediately followed by a tail, she would drive the car.
Who has greater probability to drive the car that day? Justify your answer.
Chapter:
The monthly income of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in ratio 5 : 7. If each saves ₹ 15,000 per month, find their monthly incomes.
Chapter:
Solve the following system of equations graphically:
2x + y = 6, 2x – y – 2 = 0. Find the area of the triangle so formed by two lines and x-axis.
Chapter:
A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original average speed?
Chapter:
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Hence in ΔPQR, prove that a line ℓ intersects the sides PQ and PR of a ∆PQR at L and M, respectively, such that LM || QR. If PL = 5.7 cm, PQ = 15.2 cm and MR = 5.5 cm, then find the length of PM (in cm).
Chapter:
From a solid right circular cone, whose height is 6 cm and radius of base is 12 cm, a right circular cylindrical cavity of height 3 cm and radius 4 cm is hollowed out such that bases of cone and cylinder form concentric circles. Find the surface area of the remaining solid in terms of π.
Chapter:
An empty cone of radius 3 cm and height 12 cm is filled with ice-cream such that the lower part of the cone which is `(1/6)^"th"` of the volume of the cone is unfilled (empty) but a hemisphere is formed on the top. Find the volume of the ice-cream.
Chapter:
If the mode of the following distribution is 55, then find the value of x. Hence, find the mean.
| Class interval | 0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 – 75 | 75 – 90 |
| Frequency | 10 | 7 | x | 15 | 10 | 12 |
Chapter:
A survey regarding heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:
| Heights (in cm) | Number of girls |
| less than 140 | 04 |
| less than 145 | 11 |
| less than 150 | 29 |
| less than 155 | 40 |
| less than 160 | 46 |
| less than 165 | 51 |
Find the median height of girls. If the mode of the above distribution is 148.05, find the mean using the empirical formula.
Chapter:
| In class, the teacher asks every student to write an example of an A.P. Two boys, Aryan and Roshan, write the progressions as −5, −2, 1, 4, ... and 187, 184, 181, ... respectively. Now the teacher asks his various students the following questions on progression. |
Help the students to find answers for the following:
- Find the sum of the common difference of two progressions. (1)
- Find the 34th term of the progression written by Roshan. (1)
-
- Find the sum of the first 10 terms of the progression written by Aryan. (2)
OR - Which term of the progression will have the same value? (2)
- Find the sum of the first 10 terms of the progression written by Aryan. (2)
Chapter:
|
A group of class X students goes to a picnic during winter holidays. The positions of three friends Aman, Kirti and Chahat, are shown by the points P, Q and R.
|
- Find the distance between P and R. (1)
- Is Q the midpoint of PR? Justify by finding the midpoint of PR. (1)
-
- Find the point on the x-axis which is equidistant from P and Q. (2)
OR - Let S be a point which divides the line joining PQ in the ratio 2 : 3. Find the coordinates of S. (2)
- Find the point on the x-axis which is equidistant from P and Q. (2)
Chapter:
|
India gate (formerly known as the All India war memorial) is located near Karthavya path (formerly Rajpath) at New Delhi. It stands as a memorial to 74187 soldiers of the Indian Army, who gave their life in the first world war. This 42 m tall structure was designed by Sir Edwin Lutyens in the style of Roman triumphal arches. A student named Shreya, who is 1 m tall, visited India Gate as part of her study tour.
|
- What is the angle of elevation from Shreya’s eye to the top of India Gate if she is standing at a distance of 41 m away from the India Gate? (1)
- If Shreya observes the angle of elevation from her eye to the top of India Gate to be 60°, then how far is she standing from the base of the India Gate? (1)
-
- If the angle of elevation from Shreya’s eye changes from 45° to 30°, when she moves some distance back from the original position. Find the distance she moves back. (2)
OR - If Shreya moves to a point which is at a distance of `41/sqrt(3)` m from the India Gate, then find the angle of elevation made by her eye to the top of the India Gate. (2)
- If the angle of elevation from Shreya’s eye changes from 45° to 30°, when she moves some distance back from the original position. Find the distance she moves back. (2)
Chapter:
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