30 - 5 - 2 - Maths Standard - 25070913 - 2024 - 02 - 14 - 19 - 35
30 - 5 - 2 - Maths Standard - 25070913 - 2024 - 02 - 14 - 19 - 35
30 - 5 - 2 - Maths Standard - 25070913 - 2024 - 02 - 14 - 19 - 35
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MATHEMATICS (STANDARD)
*
:3 : 80
Time allowed : 3 hours Maximum Marks : 80
NOTE :
(i) - 27
Please check that this question paper contains 27 printed pages.
(ii) - - -
-
Q.P. Code given on the right hand side of the question paper should be written on the title
page of the answer-book by the candidate.
(iii) - 38
Please check that this question paper contains 38 questions.
(iv) -
Please write down the serial number of the question in the answer-book before
attempting it.
(v) - 15 -
10.15 10.15 10.30 -
-
15 minute time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.
SECTION A
This section comprises multiple choice questions (MCQs) of 1 mark each.
1 tan 2 30
1. is equal to :
1 tan 2 30
AB BC
2. . Which of the following makes the two
DE FD
triangles similar ?
(a) A= D (b) B= D
(c) B= E (d) A= F
4. Two dice are rolled together. What is the probability of getting a sum
greater than 10 ?
1 1
(a) (b )
9 6
1 5
(c) (d)
12 18
7. If the mean and the median of a data are 12 and 15 respectively, then its
mode is :
(c) 6 (d) 14
30/5/2 JJJJ Page 5 P.T.O.
8. In the given figure, AB is a tangent to the circle centered at O. If
OA = 6 cm and OAB = 30 , then the radius of the circle is :
(a) 3 cm (b) 3 3 cm
(c) 2 cm (d) 3 cm
(a) 30 (b) 60
(c) 45 (d) 90
(a) 6 (b ) 12·5
(c) 8 (d) 10
13. A quadratic equation whose roots are (2 + 3 ) and (2 3 ) is :
(a) x2 4x + 1 = 0 (b) x2 + 4x + 1 = 0
(c) 4x2 3=0 (d) x2 1=0
5 sin cos
14. If tan = , then the value of is :
12 sin cos
17 17
(a) (b)
7 7
17 7
(c) (d)
13 13
15. If end points of a diameter of a circle are ( 5, 4) and (1, 0), then the
radius of the circle is :
(a) 2 13 units (b) 13 units
(c) 4 2 units (d) 2 2 units
Questions number 19 and 20 are Assertion and Reason based questions carrying
1 mark each. Two statements are given, one labelled as Assertion (A) and the
other is labelled as Reason (R). Select the correct answer to these questions from
the codes (a), (b), (c) and (d) as given below.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the
correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not
the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
n
19. Assertion (A) : The number 5 cannot end with the digit 0, where n is a
natural number.
Reason (R): Prime factorisation of 5 has only two factors, 1 and 5.
20. Assertion (A) : If the points A(4, 3) and B(x, 5) lie on a circle with centre
O(2, 3), then the value of x is 2.
Reason (R) : Centre of a circle is the mid-point of each chord of the
circle.
SECTION B
This section comprises very short answer (VSA) type questions of 2 marks each.
21. Using prime factorisation, find HCF and LCM of 96 and 120.
22. Find the ratio in which line y = x divides the line segment joining the
points (6, 3) and (1, 6).
23. (a) If a cos + b sin = m and a sin b cos = n, then prove that
a2 + b2 = m2 + n2.
OR
30/5/2 JJJJ Page 11 P.T.O.
(b) Prove that :
sec A 1 sec A 1
+ = 2 cosec A
sec A 1 sec A 1
24. (a) The line segment joining the points A(4, 5) and B(4, 5) is divided
by the point P such that AP : AB = 2 : 5. Find the coordinates of P.
OR
(b) Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove
that x = y.
SECTION C
This section comprises short answer (SA) type questions of 3 marks each.
27. A 2-digit number is seven times the sum of its digits. The number formed
by reversing the digits is 18 less than the given number. Find the given
number.
30/5/2 JJJJ Page 13 P.T.O.
28. Prove that :
tan cot
+ = 1 + sec cosec
1 cot 1 tan
OR
(b) The traffic lights at three different road crossings change after
every 48 seconds, 72 seconds and 108 seconds respectively. If they
change simultaneously at 7 a.m., at what time will they change
together next ?
30. In an A.P., the sum of the first n terms is given by Sn = 6n n2. Find its
th
30 term.
OR
This section comprises long answer (LA) type questions of 5 marks each.
OR
34. The angle of elevation of the top of a vertical tower from a point P on the
ground is 60 . From another point Q, 10 m vertically above the first point
P, its angle of elevation is 30 . Find :
(b) The distance of the point P from the foot of the tower.
(c) The distance of the point P from the top of the tower.
OR
15
(b) Two pipes together can fill a tank in hours. The pipe with
8
larger diameter takes 2 hours less than the pipe with smaller
diameter to fill the tank separately. Find the time in which each
pipe can fill the tank separately.
Case Study 1
Making Purple : Spin each spinner once. Blue and red make purple. So, if
(ii) 1
(iii) (a) For each win, a participant gets < 10, but if he/she loses,
he/she has to pay < 5 to the school.
If 99 participants played, calculate how much fund could the
school have collected. 2
OR
(iii) (b) If the same amount of < 5 has been decided for winning or
losing the game, then how much fund had been collected by
school ? (Number of participants = 99) 2
37. A golf ball is spherical with about 300 500 dimples that help increase
its velocity while in play. Golf balls are traditionally white but available
in colours also. In the given figure, a golf ball has diameter
4·2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm.
(ii) Find the volume of the material dug out to make one dimple. 1
(iii) (a) Find the total surface area exposed to the surroundings. 2
OR
(iii) (b) How much distance has the dolphin covered before hitting
the water level again ? 2