English Medium
Academic Year: 2022-2023
Date & Time: 21st March 2023, 10:30 am
Duration: 3h
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General Instructions:
- 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 question number 1 to 18 are Multiple Choice Questions (MCQs) and question number 19 & 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 of 2 marks each.
- In Section - C questions number 26 to 31 are Short Answer-II (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/Passage based integrated units and assessment 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 figures wherever required. Take π = `22/7` wherever required if not stated.
- Use of calculator is NOT allowed.
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
x2 + 3x + 2
x2 – 3x + 2
x2 – 3x – 2
x2 + 3x – 2
Chapter: [0.021] Polynomials
(HCF × LCM) for the numbers 70 and 40 is ______.
10
280
2800
70
Chapter: [0.011000000000000001] Real Numbers
If the radius of a semi-circular protractor is 7cm, then its perimeter is ______.
11 cm
14 cm
22 cm
36 cm
Chapter: [0.061] Areas Related to Circles
The number `(5 - 3sqrt(5) + sqrt(5))` is ______.
an integer
a rational number
an irrational number
a whole number
Chapter: [0.011000000000000001] Real Numbers
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
20
0
– 8
8
Chapter: [0.021] Polynomials
Which of the following cannot be the probability of an event?
0.1
`5/3`
3%
`1/3`
Chapter: [0.07200000000000001] Probability
The pair of linear equations x + 2y + 5 = 0 and – 3x – 6y + 1 = 0 has ______.
a unique solution
exactly two solutions
infinitely many solutions
no solution
Chapter:
If ΔABC ~ ΔDEF and ∠A = 47°, ∠E = 83°, then ∠C is equal ______.
47°
50°
83°
130°
Chapter: [0.040999999999999995] Triangles
If the pair of linear equations x – y = 1, x + ky = 5 has a unique solution x = 2, y = 1, then the value of k is ______.
– 2
– 3
3
4
Chapter:
The value of 5 sin2 90° – 2 cos2 0° is ______.
– 2
5
3
– 3
Chapter: [0.051] Introduction to Trigonometry
The length of the arc of a circle of radius 14 cm which subtends an angle of 60° at the centre of the circle is ______.
`44/3` cm
`88/3` cm
`308/3` cm
`616/3` cm
Chapter: [0.061] Areas Related to Circles
The angle of elevation of the top of a 30 m high tower at a point 30 m away from the base of the tower is ______.
30°
45°
60°
90°
Chapter: [0.053] Some Applications of Trigonometry
The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is ______.
2
3
4
5
Chapter: [0.071] Statistics
From a well-shuffled deck of 52 playing cards, a card is drawn at random. What is the probability of getting a red queen?
`1/52`
`1/26`
`1/13`
`12/13`
Chapter: [0.07200000000000001] Probability
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
x2 + 4 = 0
x2 − 4 = 0
4x2 − 1 = 0
x2 − 2 = 0
Chapter: [0.023] Quadratic Equations
Which of the following is not a quadratic equation?
2(x – 1)2 = 4x2 – 2x + 1
2x – x2 = x2 + 5
`(sqrt(2)x + sqrt(3))^2 + x^2 = 3x^2 - 5x`
(x2 + 2x)2 = x4 + 3 + 4x3
Chapter: [0.023] Quadratic Equations
How many tangents can be drawn to a circle from a point on it?
One
Two
Infinite
Zero
Chapter: [0.042] Circles
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The length of the tangent from point A to a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is ______
`sqrt7` cm
7 cm
5 cm
25 cm
Chapter: [0.042] Circles
Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.
Reason (R): The lengths of tangents drawn from an external point to a circle are equal.
Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) does not give 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: [0.042] Circles
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) does not give 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: [0.023] Quadratic Equations
If sin α = `1/2`, then find the value of (3 cos α – 4 cos3 α).
Chapter: [0.051] Introduction to Trigonometry
Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.
Chapter: [0.031] Lines (In Two-dimensions)
If the points A(2, 3), B(–5, 6), C(6, 7) and D(p, 4) are the vertices of a parallelogram ABCD, find the value of p.
Chapter: [0.031] Lines (In Two-dimensions)
Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.
Chapter: [0.023] Quadratic Equations
Find the roots of the quadratic equation x2 – x – 2 = 0.
Chapter: [0.023] Quadratic Equations
In the adjoining figure, PT is a tangent at T to the circle with centre O. If ∠TPO = 30°, find the value of x.
Chapter: [0.042] Circles
In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
Chapter: [0.040999999999999995] Triangles [0.040999999999999995] Triangles [0.040999999999999995] Triangles
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
Chapter: [0.021] Polynomials
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
Chapter: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities
A lending library has a fixed charge for first three days and an additional charge for each day thereafter. Rittik paid 27 for a book kept for 7 days and Manmohan paid ₹ 21 for a book kept for 5 days. Find the fixed charges and the charge for each extra day.
Chapter: [0.022000000000000002] Pair of Linear Equations in Two Variables
Find the values of 'a' and 'b' for which the system of linear equations 3x + 4y = 12, (a + b)x + 2(a – b)y = 24 has infinite number of solutions.
Chapter: [0.022000000000000002] Pair of Linear Equations in Two Variables
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A die is thrown. Find the probability of getting:
an even prime number
Chapter: [0.07200000000000001] Probability
A die is thrown, find the probability of getting:
a number greater than 4
Chapter: [0.07200000000000001] Probability [0.07200000000000001] Probability
A die is thrown once. Find the probability of getting an odd number.
Chapter: [0.07200000000000001] Probability
Find the area of the sector of a circle of radius 7 cm and of central angle 90°. Also, find the area of corresponding major sector.
Chapter: [0.061] Areas Related to Circles
Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Chapter: [0.042] Circles
Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P.
Chapter: [0.042] Circles
The shadow of a tower standing on a level ground is found to be 40 m longer when Sun’s altitude is 30° than when it was 60°. Find the height of the tower.
Chapter: [0.053] Some Applications of Trigonometry
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Chapter: [0.053] Some Applications of Trigonometry
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
Chapter: [0.024] Arithmetic Progressions
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
Chapter: [0.024] Arithmetic Progressions
The following table gives the monthly consumption of electricity of 100 families:
| Monthly Consumption (in units) |
130 – 140 | 140 – 150 | 150 – 160 | 160 – 170 | 170 – 180 | 180 – 190 | 190 – 200 |
| Number of families |
5 | 9 | 17 | 28 | 24 | 10 | 7 |
Find the median of the above data.
Chapter: [0.071] Statistics
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.
Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
Chapter: [0.062] Surface Areas and Volumes
Read the following passage:
|
Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
|
Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
-
- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
Chapter: [0.031] Lines (In Two-dimensions)
Read the following passage:
|
Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 39 apples and 60 bananas and decided to distribute fruits equally among all. |
Based on the above information, answer the following questions:
- How many guests Khushi can invite at the most?
- How many apples and bananas will each guest get?
-
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
OR - If the cost of 1 dozen of bananas is ₹ 60, the cost of 1 apple is ₹ 15 and cost of 1 mango is ₹ 20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes.
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
Chapter: [0.011000000000000001] Real Numbers
Observe the figures given below carefully and answer the questions:
| Figure A |  |
 |
| Figure B |  |
 |
| Figure C |  |
 |
- Name the figure(s) where in two figures are similar.
- Name the figure(s) where in the figures are congruent.
-
- Prove that congruent triangles are also similar but not the converse.
OR - What more is least needed for two similar triangles to be congruent?
- Prove that congruent triangles are also similar but not the converse.
Chapter: [0.040999999999999995] Triangles
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