Q1
mcq
1 mark
If ax + by = a2 – b2 and bx + ay = 0, then the value of x + y is :
- A. a2 – b2
- B. a + b
- C. a – b
- D. a2 + b2
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Q2
mcq
1 mark
The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is :
- A. 5
- B. 13
- C. 40
- D. 8
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Q3
mcq
1 mark
If a polynomial p(x) is given by p(x) = x2 – 5x + 6, then the value of p(1) + p(4) is :
- B. 4
- C. 2
- D. – 4
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Q4
mcq
1 mark
If the discriminant of the quadratic equation 3x2 – 2x + c = 0 is 16, then the value of c is :
- A. 1
- C. – 1
- D. 2
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Q5
mcq
1 mark
If an arc subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is :
- A. 2 : 3
- B. 1 : 4
- C. 4 : 1
- D. 1 : 3
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Q6
mcq
1 mark
The area of the sector of a circle of radius 12 cm is 60p cm2. The central angle of this sector is :
- A. 120°
- B. 6°
- C. 75°
- D. 150°
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Q7
mcq
1 mark
If the difference of mode and median of a data is 24, then the difference of its median and mean is :
- A. 12
- B. 24
- C. 8
- D. 36
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Q8
mcq
1 mark
Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is :
- A. 6/36
- B. 3/36
- C. 12/36
- D. 9/36
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Q9
mcq
1 mark
The ratio of total surface area of a solid hemisphere to the square of its radius is :
- A. 2p : 1
- B. 4p : 1
- C. 3p : 1
- D. 1 : 4p
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Q10
mcq
1 mark
If sin q = 1, then the value of 1/2 sin^2(q/2) is :
- A. 1/2√2
- B. 1/2
- C. 1/2
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Q11
mcq
1 mark
Two lines are given to be parallel. The equation of one of these lines is 5x – 3y = 2. The equation of the second line can be :
- A. – 15x – 9y = 5
- B. 15x + 9y = 5
- C. 9x – 15y = 6
- D. – 15x + 9y = 5
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Q12
mcq
1 mark
Three numbers in A.P. have the sum 30. What is its middle term ?
- A. 4
- B. 10
- C. 16
- D. 8
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Q13
mcq
1 mark
In ∆ ABC, DE || BC (as shown in the figure). If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is :
- A. 6 cm
- B. 7.5 cm
- C. 9 cm
- D. 5.7 cm
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Q14
mcq
1 mark
At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun’s altitude at that time is :
- A. 30°
- B. 45°
- C. 60°
- D. 90°
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Q15
mcq
1 mark
In the given figure, AB and AC are tangents to the circle. If Ð ABC = 42°, then the measure of Ð BAC is :
- A. 96°
- B. 42°
- C. 106°
- D. 86°
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Q16
mcq
The fourth vertex D of a parallelogram ABCD whose three vertices are A(– 2, 3), B(6, 7) and C(8, 3) is :
- A. (0, 1)
- B. (0, – 1)
- C. (– 1, 0)
- D. (1, 0)
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Q17
mcq
For an event E, if P(E) + P(E) = q, then the value of q2 – 4 is :
- A. – 3
- B. 3
- C. 5
- D. – 5
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Q18
mcq
In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets QR at P. If AP = 4.2 cm, then the length of QR is :
- A. 4.2 cm
- B. 2.1 cm
- C. 8.4 cm
- D. 6.3 cm
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Q19
mcq
Assertion (A) : Mid-point of a line segment divides the line segment in the ratio 1 : 1. Reason (R) : The ratio in which the point (– 3, k) divides the line segment joining the points (– 5, 4) and (– 2, 3) is 1 : 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) : If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference = 2p ´ radius of a circle.
- 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
Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together ?
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Q22
short answer
2 marks
The minute hand of a clock is 14 cm long. Find the area on the face of the clock described by the minute hand in 5 minutes.
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Q23
short answer
2 marks
Find the length of the arc of a circle which subtends an angle of 60° at the centre of the circle of radius 42 cm.
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Q24
short answer
2 marks
Evaluate : (5 cos^2 60° + 4 sec^2 30° – tan^2 45°) / (sin^2 30° + sin^2 60°)
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Q24
short answer
In the given figure, O is the centre of the circle. If Angle AOB = 145°, then find the value of x.
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Q25
short answer
2 marks
If sin (A – B) = 1/2, cos (A + B) = 1/2 ; 0 < A + B ≤ 90°, A > B; find ∠ A and ∠ B.
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Q25
short answer
In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC.
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Q26
short answer
2 marks
Evaluate: (sin^2 30 + sin^2 60) / (cos^2 60 + 4 sec^2 30 - tan^2 45)
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Q26
short answer
3 marks
Prove that: (sec theta - tan theta) / (sin theta + cos theta - 1) = 1 / (sin theta - cos theta + 1)
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Q28
short answer
3 marks
Rehana went to a bank to withdraw 2,000. She asked the cashier to give her 50 and 100 notes only. Rehana got 25 notes in all. Find how many notes of 50 and 100 did she receive.
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Q30
short answer
3 marks
Three coins are tossed simultaneously. What is the probability of getting at least one head?
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Q30
short answer
3 marks
Prove that 5 / 2 - 3 is an irrational number, given that 3 is an irrational number.
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Q31
short answer
3 marks
A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a 2-digit number less than 40.
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Q31
short answer
3 marks
Prove that the parallelogram circumscribing a circle is a rhombus.
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Q32
long answer
5 marks
Two poles of equal heights are standing opposite each other on either side of the road, which is 100 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of each pole and the distances of the point from the poles. (Use 3 = 1.732)
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Q32
long answer
5 marks
Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60° and 30°. Find the length of each pillar and distance of the point on the road from the pillars. (Use √3 = 1·732)
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Q33
short answer
3 marks
Find the zeroes of the polynomial 4x^2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial.
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Q34
short answer
3 marks
If a and b are the zeroes of the polynomial x^2 + x – 2, then find the value of (a/b) + (b/a).
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Q35
long answer
5 marks
The following table shows the ages of the patients admitted in a hospital during a year : Age (in years) 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 Number of patients 6 11 21 23 14 5 Find the mode and mean of the data given above.
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Q38
long answer
5 marks
E is a point on side AD produced of a parallelogram ABCD such that BE intersects CD at F. Show that triangle ABE ~ triangle CFB.
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Q39
long answer
5 marks
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Prove that triangle ABC ~ triangle PQR.
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Q40
long answer
5 marks
A train travels a distance of 90 km at a uniform speed. If the speed had been 15 km/h more, it would have taken 30 minutes less for the journey. Find the original speed of the train.
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Q41
long answer
5 marks
Find the value of 'c' for which the quadratic equation (c + 1)x^2 – 6(c + 1)x + 3(c + 9) = 0; c != –1 has real and equal roots.
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Q43
long answer
5 marks
Sides AB, BC and the median AD of ∆ ABC are respectively proportional to sides PQ, QR and the median PM of another ∆ PQR. Prove that ∆ ABC ~ ∆ PQR.
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Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below : Based on the above, answer the following questions :
Q45
short answer
1 mark
Find the mid-point of the segment joining F and G.
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Q46
short answer
2 marks
What is the distance between the points A and C ?
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Q47
short answer
2 marks
Find the coordinates of the point which divides the line segment joining the points A and B in the ratio 1 : 3 internally.
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Q48
short answer
1 mark
What are the coordinates of the point D ?
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Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize. While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the nth spot is 20 + 4n, then answer the following questions to help the players in spotting the clues :
Q51
short answer
2 marks
What is the sum of all the numbers on the first 10 spots ?
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Q52
short answer
1 mark
Which number is on the (n – 2)th spot ?
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Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals. 500 mL milk is packed in a cuboidal container of dimensions 15 cm ´ 8 cm ´ 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm ´ 32 cm ´ 15 cm. Based on the above given information, answer the following questions :
Q53
short answer
1 mark
Find the volume of the cuboidal carton.
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Q54
short answer
2 marks
Find the total surface area of a milk packet.
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Q55
short answer
2 marks
How many milk packets can be filled in a carton ?
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Q56
short answer
1 mark
How much milk can the cup (as shown in the figure) hold ?
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