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BHADRACHALAM PUBLIC SCHOOL & JR COLLEGE
PRE-MIDEXAMINATION – JULY 2025
Class: X Subject: Mathematics (041) Time Allowed: 3 Hrs Maximum Marks: Name: ____________________ Section:_____ Roll Number:_____ General Instructions:
- 15 minutes reading time is allotted for Question Paper reading.
- This Question Paper has 5 Sections A, B, C, D and E.
- Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
- Section B has 5 Short Answer - I (SA - I) type questions carrying 2 marks each.
- Section C has 6 Short Answer - II (SA - II) type questions carrying 3 marks each.
- Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
- Section E has Case Based integrated units of assessment (4 marks each) with sub - parts of the values of 1, 1 and 2 marks each respectively.
- All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks and 2 Qs of 5 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E. Q. No SECTION - A Marks 1 The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is 1
a)7 b) 11 c) 12 d) 7 + √ 5
2 In what ratio does the point (–2, 3) divide the line-segment joining the points (–3, 5) and (4, –9)?
a) 2:3 b) 1:6 c) 6:1 d) 2: 3 If (
a
, 4) is the midpoint of the line segment joining A(–6, 5) and B(–2, 3), then what is the value of ‘a’?
a) - 4 b) -12 c) 12 d) - 14 4 Sin 2A = 2 Sin A is true when A = 1 a) 0^0 b) 30^0 c) 45^0 d) 60^0 5 If (Sec^2 θ) (1 + Sinθ) (1 – Sinθ) = k, then find the value of k. 1 a) Sinθ b) Cosθ c) Cotθ d) 6 A man while walking on a hot day noticed how the length of his shadow changes with the sun’s altitude. If the height and length of the shadow of a man are the same, the angle of elevation of the sun is
a) 45^0 b) 60^0 c) 90^0 d) 30^0
7 The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:
a) 30m b) 10m c)
√^3
d)
√^3
8 The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is
a) corresponding angle b) angle of elevation c) angle of depression d) complete angle 9 The class mark of a class is 25 and if the upper limit of that class is 40, then its lower limit is ___________
a) 10 b) 20 c) 30 d) 40 10 A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of numbers is
a) 6 b) 7 c) 8 d) 9 11 In the following distribution Monthly income range (in Rs.) No. of families Income more than Rs.10000 100 Income more than Rs.13000 85 Income more than Rs.16000 69 Income more than Rs.19000 50 Income more than Rs.22000 33 Income more than Rs.25000 15 the number of families having income range (in Rs.) 16000 – 19000 is
a) 69 b) 50 c) 18 d) 19 12 For the following grouped frequency distribution Class (^) 3-6 6-9 9-12 12-15 15-18 18-21 21- Frequency (^2 5 10 25 21 12 ) Consider the following: i. Lower limit of model class is 12 ii. Frequency of the class preceding the model class = iii. Class mark of model class is 16.
c) A is true but R is false. d) A is false but R is true. SECTION-B 21 The vertices of triangles A(3,0), B (6,4) and C (-1,3) are vertices of a triangle ABC. Find length of its median BE.
22 a) If x = a sinθ and y = b cosθ, then find b^2 x^2 + a^2 y^2 (OR) b) Evaluate: sin^2 600 2 cos^2 450 +
cosec^2 .
(^23) The length of the shadow of a tower on the plane ground is √3 𝑚 times the height of the tower. Find the angle of elevation of the Sun.
24 a) The mean of the numbers 25, 26, 29, 30, 33, 32, and 35 is 30. However, a student made a mistake and took 32 instead of 23 while calculating the mean. What is the correct mean of the numbers? (OR) b)Find the mean of the class marks of 12-18 and 24-30.
25 A box contains cards numbered 5 to 60. A card is drawn at random from the box. Find the probability that the drawn card has a number which is a perfect square.
SECTION-C
26 The four vertices of a parallelogram ABCD are A (2, -3),B(6,5) and C(-2,1). Find the coordinates of the point where both the diagonals AD and BC intersect.
a) Prove that:
tan θ
1 −cot θ
cot θ
1 −tan θ
= 1+ secθ cosec θ (OR) b) Prove that:
1 −cos θ
1 +cos θ
= (cosec θ- cot θ)^2
28 A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground, then find the height of the pole, if the angle made by the rope with the ground level is 30°.
29 From the top of 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°, and then finds the height of the tower.
30 a) Find the median of the following data. Class 4-7 8-11 12-15 16- Frequency 5 4 9 10 (OR) b)Yoga is an ancient practice which is form of medicine and exercise. By practicing yoga, we not even make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on21 st June every year since 2015. To promote Yoga, Green Park Society in Pune organized a 7-day Yoga camp in their society. The number of people of different age groups who enrolled for this ca is given as follows: Find the mean of the age of people enrolled for the camp using assumed mean method.
(^31) If mode of the following frequency distribution is 55, then find the value of ‘x’ Class 0-15 15-30 30-45 45-60 60-75 75- Frequency 10 7 x 15 10 12
SECTION-D
32 A 1 ) Find the ratio in which the y-axis divides the line segment join the points (6, -4) and (-2, -7). A 2 ) The mid points of the line segment join the points A (3,4) and B(k,6) is P (x, y) and x+y-10=0, find the value of k. (OR) B 1 ) Do the points P (1,5), Q (1,4) and R (8,5) form a triangle? B 2 ) Find the coordinates of the points of trisection of the line segment joining the points P (2, −1) and Q(8,5).
33A 1 ) If sin A =
, then find
( sec
2
A ̶ 1 )cos
2
A
sin A
33A 2 ) Prove that: 1 +tan 2 A 1 +cot 2 A
= sec 2 A 1
(OR)
33B 1 ) For A = 30^0 and B = 60^0 , verify that : sin (A + B) = sin A cos B + cos A sin B
Age group No. of people 15-25 8 25-35 10 35-45 15 45-55 25 55-65 40 65-75 24 75-85 18
(OR)
d) Evaluate: (sin^2 C + Cos^2 C) (Sin B) (cosec^2 A cot^2 A) 38 One weekend Rashmika was playing card with her family. The deck has 52 cards, if her brother drew one card.
a) Find the probability of getting a king of yellow colour. b) If the probability of getting black-Ace is 0.729, then find the probability of getting non- black Ace. c) Find the probability of red face card. d) Rashmika secretly removed two King cards from a standard deck of 52 playing cards without informing her brother. If her brother now draws one card at random from the remaining deck, what is the probability that he picks a Red Queen?
