Q1
mcq
1 mark
The pair of linear equations $x+y=10$ and $x-y=4$ has
- A. unique solution
- B. exactly two solutions
- C. infinitely many solutions
- D. no solution
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Q1
mcq
1 mark
Which of the following rational numbers is a terminating decimal expansion?
- A. ui/eSB32rDSg/ri3
- B. exactly g:r32rDSg/ri23
- C. /i./i/gBDw3uAiw32rDSg/ri23
- D. ir32rDSg/ri3
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Q2
mcq
1 mark
The common difference of the A.P. $\frac{1}{2x}$, $1-4x$, $1-8x$,... is:
- A. –2x
- B. –2
- C. 2
- D. 2x
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Q3
mcq
1 mark
Two dice are thrown at the same time. The probability of getting two numbers whose product is even is:
- A. 1
- B. 5/6
- C. 1/3
- D. 2/3
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Q4
mcq
1 mark
If the probability of winning a game is $\frac{x}{6}$, and the probability of losing the game is $\frac{2}{3}$, then the value of x is:
- A. 2
- B. 3
- C. 4
- D. 6
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Q5
mcq
1 mark
If A=2^x \times 3^2, B=2^2 \times 3 \times 5, C=2^2 \times 3 \times 5 and LCM (A, B, C) = 3780, then x is:
- A. 1
- B. 2
- C. 3
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Q6
mcq
1 mark
Zeros of the quadratic polynomial 2x^2-3x-7 are:
- A. hf-3/2
- B. –hf-3/2
- C. –hf3/2
- D. 3, 3/2
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Q7
mcq
1 mark
From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is 60°. The height of the tower is:
- A. 10
- B. 30
- C. 60
- D. 30
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Q8
mcq
1 mark
If cos q=3/2 and sin q=1/2, then tan q is:
- A. 3
- B. 1/3
- C. 1
- D. not defined
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Q9
mcq
1 mark
Maximum number of common tangents that can be drawn to two circles which intersect at two distinct points is:
- A. 4
- B. 3
- C. 2
- D. 1
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Q10
mcq
1 mark
In the given figure, PT is a tangent to a circle with centre O and angle TPO=60°, then angle x is:
- A. 110°
- B. 115°
- C. 120°
- D. 125°
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Q10
mcq
1 mark
If $PT$ is a tangent to a circle with centre $O$ and $\angle TPO = 30^{\circ}$, then $\angle x$ is:
- A. 110°
- B. 115°
- C. 120°
- D. 125°
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Q11
mcq
1 mark
If the diagonals of a quadrilateral divide each other proportionally, then it is a:
- A. parallelogram
- B. rectangle
- C. square
- D. trapezium
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Q12
mcq
1 mark
In the given figure, DE || BC. If AD = 2 cm, BD = 3 cm, BC = 7.5 cm, then the length of DE (in cm) is:
- A. 2.5
- B. 3
- C. 5
- D. 6
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Q12
mcq
1 mark
If $AD = 2$ cm, $BD = 3$ cm, $BC = 7.5$ cm, then the length of $DE$ (in cm) is:
- A. 2.5
- B. 3
- C. 5
- D. 6
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Q13
mcq
1 mark
Given HCF (2520, 6600) = 40 and 6600 = 2520 k + 40, then the value of k is:
- A. 1650
- B. 1600
- C. 165
- D. 1625
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Q13
mcq
1 mark
Given HCF (2520, 6600) = 40, the value of $k$ is:
- A. 1650
- B. 1600
- C. 1653
- D. 1625
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Q14
mcq
1 mark
H(sA/E)r. /EEAg/riAD iSuOBE23:Pr2B3omlpA963013O3mO60lcO.3cABVTm3013:
- A. (16, 4)
- B. (5, 2)
- C. (3, 27)
- D. (36, 2)
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Q15
mcq
1 mark
If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9; then gPB3sErOAO/D/gw3gPAg3gP/23T/~/g3/23Ai3rTT3sE/uB3iSuOBE3/23c3
- A. 1/3
- B. 2/3
- C. 4/9
- D. 5/9
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Q16
mcq
1 mark
mPB3uBAi3r.3five3rO2BENAg/ri23/23tdR3=.3gPB3uBAi3r.3./E2g3gPEBB3rO2BENAg/ri23/23 t)3 AiT3 gPAg3 r.3 gPB3 DA2g3 gPEBB3 rO2BENAg/ri23 /23 t5f3 gPBi3 gPB3 gP/ET3 rO2BENAg/ri3/23
- A. 20
- B. 19
- C. 18
- D. 17
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Q17
mcq
1 mark
Perimeter of a sector of a circle whose central angle is 90° AiT3EAT/S237 cm is:
- A. 35 cm
- B. 11 cm
- C. 22 cm
- D. 25 cm
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Q18
mcq
1 mark
In the given figure, O is the centre of the circle. MN is 62T392lmp3Ocp362T3 gAi~Big36–3Ag3sr/ig363uAaB23Ai3Ai~DB3r.35n°3with MN.3mPB3uBA2SEB3r.3ÐMON3is:
- A. 120°
- B. 140°
- C. 70°
- D. 90°
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Q19
short answer
The point which divides the line segment joining the points $A (x_1, y_1)$ and $B (x_2, y_2)$ in the ratio $m_1 : m_2$ are $\left[ \frac{m_1x_2 + m_2x_1}{m_1+m_2}, \frac{m_1y_2 + m_2y_1}{m_1+m_2} \right]$
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Q20
short answer
In a cricket match, a batsman hits a boundary 9 times out of 30 balls. Find the probability that she did not hit a boundary.
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Q24
short answer
2 marks
In the given figure, $\frac{EA}{EC} = \frac{EB}{ED}$, prove that $\Delta BIE \sim \Delta DECD$.
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Q25
short answer
2 marks
One card is drawn at random from a well shuffled deck of 52 cards. Find the probability of: (i) a red face card;
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Q25
short answer
2 marks
Evaluate: $\frac{\cos 45^\circ + \sin 60^\circ}{\sec 30^\circ + \operatorname{cosec} 30^\circ}$
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Q26
short answer
2 marks
If $2x + y = 35$ and $3x + 4y = 65$, then find the value of $(x - y)$.
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Q27
short answer
2 marks
Sum of two numbers is 105 and their difference is 45. Find the numbers.
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Q27
short answer
3 marks
Find the zeroes of the quadratic polynomial $x^2 - 3$. Verify the relationship between the zeroes and the coefficients of the polynomial.
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Q28
short answer
2 marks
Find a relation between $x$ and $y$ such that the point $(x, y)$ is equidistant from the points $(7, 1)$ and $(3, 5)$.
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Q28
short answer
3 marks
Solve the following system of linear equations graphically: $x - y = 1$; $x + y = 3$.
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Q29
short answer
2 marks
Points $(–2, 5)$ and $(3, –1)$ lie on a circle with centre $O(2, –3y)$ such that $PQ$ is a diameter of the circle. Find the value of $y$. Also, find the radius of the circle.
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Q30
short answer
3 marks
Prove that: $\frac{\sin \theta - 2\sin^3 \theta}{2\cos^3 \theta - \cos \theta} = \tan \theta$.
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Q30
short answer
Prove that: $\frac{\sin \theta}{1 + \cos \theta} + \frac{1 + \cos \theta}{\sin \theta} = 2 \operatorname{cosec} \theta$.
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Q31
short answer
3 marks
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
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Q31
short answer
Find the area of the shaded region in the figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC = 40^\circ$.
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Q32
short answer
3 marks
If the 5th term of an A.P. is 7 and its 15th term is 27, find the 20th term.
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Q33
short answer
3 marks
The 10th and 30th terms of an A.P. is 3 and the sum of its first six terms is 42. Find the first term and the common difference of A.P.
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Q33
long answer
5 marks
State and prove Basic Proportionality theorem.
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Q34
long answer
5 marks
From a point on a ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45^\circ$ and $60^\circ$ respectively. Find the height of the tower.
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Q36
short answer
3 marks
Find the ratio in which the line segment joining the points $(5, 1)$ and $(-1, 1)$ is divided by Y-axis.
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Q37
short answer
3 marks
P(-2, 5) and Q(3, 2) are two points. Find the coordinates of point R on line PQ such that PR = 2QR.
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Q40
short answer
If the sum of first p terms of an A.P. is $ap^2 + bp$, find its common difference.
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Q43
long answer
5 marks
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains.
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Q44
long answer
5 marks
The sum of a fraction and its reciprocal is $2 \frac{16}{21}$, find the fraction.
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Q47
long answer
5 marks
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm$^3$ of iron has approximately 8 g mass.
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Q48
long answer
5 marks
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm, find its surface area. Also, find its volume.
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A stable owner has four horses. He usually tie these horses with 5 m ropes to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he proposes to change the arrangement for grazing.
Q49
short answer
1 mark
Find the area of the square field in which these horses can graze.
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Q50
short answer
2 marks
(b) If the length of the rope of each horse is increased from 7 m to 10 m, find the area grazed by one horse. (Use π = 3.14)
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Q51
short answer
1 mark
What is area of the field that is left ungrazed, if the rope of each horse is 7 cm?
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Vocational training complements traditional education by providing skill-based learning and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability. Keeping this in view, a teacher made the following table showing the frequency distribution of students/adults undergoing vocational training.
Q52
short answer
1 mark
What is the lower limit of the modal class of the above data?
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Q53
short answer
2 marks
(a) Determine the modal class of the above data.
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Q54
short answer
2 marks
(b) Determine the class size of the above data (Age in years) using modal class.
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Q55
short answer
1 mark
Give the empirical relationship between mean, median and mode.
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Age (in years): 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54 Number of participants: 6, 13, 23, 9, 6, 3, 11, 10, 4
Q56
short answer
2 marks
Find the cumulative frequency of the modal class.
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Q57
short answer
2 marks
Find the cumulative frequency of less than 30 years age group.
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Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement. Based on this, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student again multiply it by a prime number and pass it to third student. In this way she continues multiplying to a prime number and the last student gets the result.
Q58
short answer
1 mark
What is the least prime number used by students?
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Q59
short answer
2 marks
How many students are in the class?
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Q60
short answer
1 mark
Which prime number has been used maximum times?
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