Q1
mcq
1 mark
In the given figure, PA is a tangent from an external point P to a circle with centre O. If POB = 115 , then APO is equal to :
- A. 25
- B. 65
- C. 90
- D. 35
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Q2
mcq
1 mark
A piece of wire 20 cm long is bent into the form of an arc of a circle of radius cm. The angle subtended by the arc at the centre of the circle is :
- A. 30
- B. 60
- C. 90
- D. 50
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Q3
mcq
1 mark
Three numbers in AP have the sum 30. What is its middle term ?
- A. 4
- B. 10
- C. 16
- D. 8
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Q4
mcq
1 mark
An arc of a circle is of length 5 cm and the sector it bounds has an area of 20 cm2. Its radius is :
- A. 10 cm
- B. 1 cm
- C. 5 cm
- D. 8 cm
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Q5
mcq
1 mark
If x = 1 and y = 2 is a solution of the pair of linear equations 2x 3y + a = 0 and 2x + 3y b = 0, then :
- A. a = 2b
- B. 2a = b
- C. a + 2b = 0
- D. 2a + b = 0
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Q6
mcq
1 mark
Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is :
- A. 3
- B. 5
- C. 2
- D. 4
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Q7
mcq
1 mark
If + = 90 and = 2 , then cos2 + sin2 is equal to :
- C. 1
- D. 2
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Q7
mcq
If alpha + beta = 90 and alpha = 2beta, then cos^2 alpha + sin^2 beta is equal to :
- B. 1/2
- C. 1
- D. 2
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Q8
mcq
1 mark
A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is :
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Q9
mcq
1 mark
If and are the zeroes of polynomial 3x2 + 6x + k such that + + = , then the value of k is :
- A. 8
- B. 8
- C. 4
- D. 4
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Q9
mcq
If alpha and beta are the zeroes of polynomial 3x^2 + 6x + k such that alpha^2 + beta^2 + alpha*beta = 8, then the value of k is :
- A. 8
- B. -8
- C. 4
- D. -4
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Q10
mcq
The value of tan^2 theta + 1 / (1 + sin theta)(1 - sin theta) is :
- A. 1
- C. -1
- D. 2
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Q11
mcq
1 mark
Which of the following is a rational number between and ?
- A. 1·4142387954012 ....
- D. 1·857142
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Q12
mcq
1 mark
If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n 7m is :
- B. 28
- C. 98
- D. 198
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Q13
mcq
1 mark
If the length of a chord of a circle is equal to its radius, then the angle subtended by chord at the centre is :
- A. 60
- B. 30
- C. 120
- D. 90
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Q14
mcq
The greatest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is :
- A. 13
- B. 65
- C. 875
- D. 1750
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Q15
mcq
A ladder 14 m long leans against a wall. If the foot of the ladder is 7 m from the wall, then the angle of elevation of the top of the wall is :
- A. 15
- B. 30
- C. 45
- D. 60
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Q16
mcq
In triangles ABC and DEF, angle B = angle E, angle F = angle C and AB = 3 DE. Then, the two triangles are :
- A. congruent but not similar
- B. congruent as well as similar
- C. neither congruent nor similar
- D. similar but not congruent
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Q17
mcq
The mid-point of the line segment joining the points P(-4, 5) and Q(4, 6) lies on :
- A. x-axis
- B. y-axis
- C. origin
- D. neither x-axis nor y-axis
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Q18
mcq
Mode and Mean of a data are 15x and 18x, respectively. Then the median of the data is :
- A. x
- B. 11x
- C. 17x
- D. 34x
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Q19
mcq
Assertion (A): If we join two hemispheres of same radius along their bases, then we get a sphere. Reason (R): Total Surface Area of a sphere of radius r is 3r^2.
- 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.
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Q20
mcq
Assertion (A): The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R): For any event E, if P(E) = 1, then E is called a sure event.
- 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.
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Q21
short answer
2 marks
If the zeroes of the polynomial x^2 + ax + b are in the ratio 3 : 4, then prove that 12a^2 = 49b.
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Q22
short answer
2 marks
A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that his distances from the points A and B on the ground are 10 m (PA and PB are tangents to the circle). Find the radius of the circular ground.
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Q23
short answer
2 marks
If ABC ~ PQR in which AB = 6 cm, BC = 4 cm, AC = 8 cm and PR = 6 cm, then find the length of (PQ + QR).
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Q24
short answer
2 marks
If x cos 60 + y cos 0 + sin 30 cot 45 = 5, then find the value of x + 2y.
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Q25
short answer
2 marks
The coordinates of the centre of a circle are (2a, a - 7). Find the value(s) of a if the circle passes through the point (11, -9) and has diameter 10 units.
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Q26
short answer
3 marks
If the radii of the bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3, find the ratio of their volumes.
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Q27
short answer
3 marks
Three sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. The number of Physics books is 144, the number of Chemistry books is 180 and the number of Mathematics books is 192. Assuming that the books are of same thickness, determine the number of stacks of Physics, Chemistry and Mathematics books.
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Q28
short answer
3 marks
Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.
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Q30
short answer
In the given figure, QR/QS = QT/PR and ∠1 = ∠2, show that ΔPQS ~ ΔTQR.
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Q31
short answer
Evaluate: (tan θ / (1 - cot θ)) + (cot θ / (1 - tan θ)) = 1 + sec θ cosec θ
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Q31
short answer
3 marks
Find the ratio in which the y-axis divides the line segment joining the points (5, 6) and (-1, -4). Also find the point of intersection.
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Q33
long answer
5 marks
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mean and mode of the data: Monthly Consumption (units): 65-85 (4), 85-105 (5), 105-125 (13), 125-145 (20), 145-165 (14), 165-185 (8), 185-205 (4).
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Q34
short answer
3 marks
Prove that: (sin A + cos A) / (sin A - cos A) + (sin A - cos A) / (sin A + cos A) = 2 / (sin^2 A - cos^2 A)
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Q34
long answer
5 marks
Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received 1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received 20 more as annual interest. How much money did he invest in each scheme?
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Q35
short answer
3 marks
In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠BAC + ∠ACD = 90°.
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Q36
short answer
3 marks
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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Q38
long answer
5 marks
The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove that DF/EF = FB/FA.
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Q39
long answer
5 marks
In ABC, if AD perpendicular BC and AD^2 = BD * DC, then prove that ∠BAC = 90°.
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Q42
long answer
5 marks
A two-digit number is such that the product of its digits is 12. When 36 is added to this number, the digits interchange their places. Find the number.
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Q43
long answer
5 marks
A student scored a total of 32 marks in class tests in Mathematics and Science. Had he scored 2 marks less in Science and 4 marks more in Mathematics, the product of his marks would have been 253. Find his marks in the two subjects.
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A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs. One such brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure.
Q44
short answer
1 mark
Find the central angle of each sector.
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Q46
short answer
2 marks
Find the area of each sector of the brooch.
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Q47
short answer
2 marks
Find the total length of the silver wire used.
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Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be 60. Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be 45.
Q48
short answer
1 mark
Find the value of CD in terms of h, assuming BD is base length.
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Q50
short answer
2 marks
Find the height CE of the lighthouse [Use = 1.73]
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A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds around a track, with each round being 300 metres. To make the event more challenging and engaging, the organizers decide to increase the distance of each subsequent round by 50 metres. For example, the second round will be 350 metres, the third round will be 400 metres and so on. The total number of rounds planned is 10.
Q52
short answer
1 mark
Write the fourth, fifth and sixth term of the Arithmetic Progression so formed.
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Q53
short answer
1 mark
Determine the distance of the 8th round.
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Q54
short answer
2 marks
Find the total distance run after completing all 10 rounds.
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Q55
short answer
2 marks
If a runner completes only the first 6 rounds, what is the total distance run by the runner ?
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