English Medium
Academic Year: 2023-2024
Date & Time: 11th March 2024, 10:30 am
Duration: 3h
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General Instructions:
Read the following instructions carefully and follow them:
- This question paper contains 38 questions. All questions are compulsory.
- 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 and 20 are Assertion − Reason based questions of 1 mark each.
- In Section B, question number 21 to 25 are Very short answer (VSA) type questions of 2 marks each.
- In Section C, question number 26 to 31 are Short answer (SA) type questions carrying 3 marks each.
- In Section D, question number 32 to 35 are Long answer (LA) type questions carrying 5 marks each.
- In Section E question number 36 to 38 are Case Study 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 in Section E.
- Draw neat figures wherever required. Take `pi = 22/7` wherever required if not stated.
- Use of calculators is not allowed.
The HCF of the smallest 2-digit number and the smallest composite number is ______.
4
20
2
10
40
Chapter: [0.011000000000000001] Real Numbers
The value of 'k' for which the pair of linear equations x + y − 4 = 0 and 2x + ky − 8 = 0 has infinitely many solutions is ______.
k ≠ 2
k ≠ −2
k = 2
k = −2
Chapter:
Which of the following equations has 2 as a root?
x2 – 4x + 5 = 0
x2 + 3x – 12 = 0
2x2 – 7x + 6 = 0
3x2 – 6x – 2 = 0
Chapter: [0.023] Quadratic Equations
In an A.P., if d =−4 and a7 = 4, then the first term 'a' is equal to ______.
6
7
20
28
Chapter:
The distance of the point (5, 4) from the origin is ______.
41
`sqrt41`
3
9
Chapter:
If sin A = `3/5`, then value of cot A is ______.
`3/4`
`4/3`
`4/5`
`5/4`
Chapter:
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
sec2 A
- 1
cot2 A
tan2 A
Chapter: [0.051] Introduction to Trigonometry
\[\frac{2 \tan 30°}{1 - \tan^2 30°}\] is equal to ______.
cos 60°
sin 60°
tan 60°
sin 30°
Chapter: [0.051] Introduction to Trigonometry [0.052000000000000005] Trigonometric Identities
A quadratic polynomial, the sum of whose zeroes is −5 and their product is 6, is ______.
x2 + 5x + 6
x2 − 5x + 6
x2 − 5x − 6
− x2 + 5x + 6
Chapter:
The zeroes of the polynomial 3x2 + 11x – 4 are ______.
`1/3, -4`
`(-1)/3, 4`
`1/3, 4`
`(-1)/3, -4`
`-1/3, -4`
Chapter: [0.021] Polynomials
The annual rainfall record of a city for 66 days is given in the following table:
| Rainfall (in cm): | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 | 50 − 60 |
| Number of days : | 22 | 10 | 8 | 15 | 5 | 6 |
The difference of upper limits of modal and median classes is ______.
10
15
20
30
Chapter:
If P(A) denotes the probability of an event A, then ______.
P(A) < 0
P(A) > 1
0 ≤ P(A) ≤ 1
–1 ≤ P(A) ≤ 1
Chapter: [0.07200000000000001] Probability
The total surface area of a solid hemisphere of radius 7 cm is ______.
447π cm2
239 π cm2
174 π cm2
147 π cm2
98 π cm2
196 π cm2
`228 2/3 π "cm"^2`
Chapter: [0.062] Surface Areas and Volumes
The difference of the areas of a minor sector of angle 120° and its corresponding major sector of a circle of radius 21 cm is ______.
231 cm2
462 cm2
346.5 cm2
693 cm2
Chapter:
The graph of a pair of linear equations a1x + b1y = c1, and a2x + b2Y = c2 in two variables x and y represents parallel lines, if ______.
`a_1/a_2 ≠ b_1/b_2`
`a_1/a_2 = b_1/b_2 = c_1/c_2`
`a_1/a_2 ≠ b_1/b_2 = c_1/c_2`
`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`
Chapter:
In the given figure, tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°. ∠ABO is equal to ______.
40°
80°
100°
50°
Chapter:
A line intersecting a circle in two distinct points is called a ______.
secant
chord
diameter
tangent
Chapter:
A pole 6 m high casts a shadow `2sqrt(3)` m long on the ground, then the Sun’s elevation is ______.
60°
45°
30°
90°
Chapter: [0.053] Some Applications of Trigonometry
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Assertion (A): A line drawn parallel to any one side of a triangle intersects the other two sides in the same ratio.
Reason (R): Parallel lines cannot be drawn to any side of a triangle.
Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are correct but 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): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
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 (A).
Assertions (A) is true but reason (R) is false.
Assertions (A) is false but reason (R) is true.
Chapter: [0.031] Lines (In Two-dimensions) [0.031] Lines (In Two-dimensions)
Find the HCF of 84 and 144 by prime factorisation method.
Chapter:
The sum of two natural numbers is 70 and their difference is 10. Find the natural numbers.
Chapter:
15 defective pens are accidentally mixed with 145 good ones. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
Chapter:
In the given figure, OA·OB = OC·OD, Prove that ΔAOD ∼ ΔCOB.
Chapter:
In the given figure, ∠D = ∠E and `"AD"/"DB" = "AE"/"EC"` Prove that ΔABC is isosceles.
Chapter:
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Chapter: [0.042] Circles
Two dice are tossed simultaneously. Find the probability of getting an even number on both the dice.
Chapter:
Two dice are tossed simultaneously. Find the probability of getting the sum of two numbers more than 9.
Chapter:
In two concentric circles, a chord of length 24 cm of larger circle touches the smaller circle, whose radius is 5 cm. Find the radius of the larger circle.
Chapter:
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.
Chapter: [0.042] Circles
Prove that `7 - 3sqrt5` is an irrational number, given that `sqrt5` is an irrational number.
Chapter:
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Zeroes of the quadratic polynomial x2 − 3x + 2 are α and β. Construct a quadratic polynomial whose zeroes are 2α + 1 and 2β + 1.
Chapter:
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Chapter: [0.021] Polynomials
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ
Chapter: [0.051] Introduction to Trigonometry
A car has two wipers that do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the blades. `("Take" π =22/7)`
Chapter: [0.061] Areas Related to Circles
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Chapter: [0.023] Quadratic Equations
A TV tower stands vertically on a bank of a river/canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From a point 20 m away this point on the same bank, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the river/canal.
Chapter: [0.053] Some Applications of Trigonometry
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔAEP ∼ ΔCDP
Chapter: [0.040999999999999995] Triangles
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔABD ∼ ΔCBE
Chapter: [0.040999999999999995] Triangles
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔAEP ∼ ΔADB
Chapter: [0.040999999999999995] Triangles
If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR, prove that `("AB")/("PQ") = ("AD")/("PM")`.
Chapter: [0.040999999999999995] Triangles
A textile industry runs in a shed. This shed is in the shape of a cuboid surmounted by a half-cylinder. If the base of the industry is of dimensions 14 m × 20 m and the height of the cuboidal portion is 7 m, find the volume of air that the industry can hold. Further, suppose the machinery in the industry occupies a total space of 400 m3. Then, how much space is left in the industry?
Chapter:
From a solid cylinder of height 8 cm and radius 6 cm, a conical cavity of the same height and same radius is carved out. Find the total surface area of the remaining solid. (Take π = 3.14)
Chapter:
|
Saving money is a good habit and it should be inculcated in children right from the beginning. Rehan's mother brought a piggy bank for Rehan and put one ₹ 5 coin of her savings in the piggy bank on the first day. She increases his savings by one ₹ 5 coin daily.
|
Based on the above information, answer the following questions:
- How many coins were added to the piggy bank on 8th day? (1)
- How much money will be there in the piggy bank after 8 days? (1)
-
- If the piggy bank can hold one hundred twenty ₹ 5 coins in all, find the number of days she can contribute to put ₹ 5 coins into it. (2)
OR - Find the total money saved when the piggy bank is full. (2)
- If the piggy bank can hold one hundred twenty ₹ 5 coins in all, find the number of days she can contribute to put ₹ 5 coins into it. (2)
Chapter:
Heart Rate : The heart rate is one of the 'vital signs' of health in the human body. It measures the number of times per minute that the heart contracts or beats. While a normal heart rate does not guarantee that a person is free of health problems, it is a useful benchmark for identifying a range of health issues.
Thirty women were examined by doctors of AIIMS and the number of heart beats per minute were recorded and summarized as follows:
| Number of heart beats per minute | Number of Women |
| 65 − 68 | 2 |
| 68 − 71 | 4 |
| 71 − 74 | 3 |
| 74 − 77 | 8 |
| 77 − 80 | 7 |
| 80 − 83 | 4 |
| 83 − 86 | 2 |
Based on the above information, answer the following questions:
- How many women are having heart beat in the range 68 − 77? (1)
- What is the median class of heart beats per minute for these women? (1)
-
- Find the modal value of heart beats per minute for these women. (2)
OR - Find the median value of heart beats per minute for these women. (2)
- Find the modal value of heart beats per minute for these women. (2)
Chapter:
The top of a table is hexagonal in shape.
On the basis of the information given above, answer the following questions:
- Write the coordinates of A and B. (1)
- Write the coordinates of the mid-point of the line segment joining C and D. (1)
-
- Find the distance between M and Q. (2)
OR - Find the coordinates of the point which divides the line segment joining M and N in the ratio 1:3 internally. (2)
- Find the distance between M and Q. (2)
Chapter:
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