Q1
mcq
1 mark
In the figure, if PT is a tangent to a circle with centre O and $ÐTPO = 30°$, then the measure of $Ðx$ is:
- A. 110°
- B. 115°
- C. 120°
- D. 125°
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Q1
mcq
1 mark
In the given figure, 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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Q2
mcq
1 mark
The probability of guessing the correct answer to a certain test question is $x/6$. If the probability of not guessing the correct answer is $2/3$, then $x$ is:
- A. 2
- B. 3
- C. 4
- D. 6
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Q3
mcq
1 mark
A point on the ground, which is at a distance of $30$ m from the foot of a tower, has an elevation angle of the top of the tower of $60°$, then the height of the tower (in meters) is:
- A. 10
- B. 30
- C. 60
- D. 30
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Q3
mcq
1 mark
A point on the ground, which is 30 m away from the foot of a vertical tower, has an angle of elevation of the top of the tower as 60°, then the height of the tower is:
- A. 10
- B. 30
- C. 60
- D. 30\sqrt{3}
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Q4
mcq
1 mark
In the given figure, MN is the chord and the circle makes an angle of 70° with it. The value of $\angle MON$ is:
- A. 120°
- B. 140°
- C. 70°
- D. 90°
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Q5
mcq
1 mark
If a pair of linear equations in two variables is consistent, then the lines represented by the equations are:
- A. always intersecting
- B. parallel
- C. always coincident
- D. intersecting or coincident
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Q6
mcq
1 mark
If the area of a sector of a circle is $\frac{20}{7}$ of the area of the circle, then the angle at the centre is equal to:
- A. 110°
- B. 130°
- C. 100°
- D. 126°
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Q7
mcq
1 mark
If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9; then the probability of choosing an odd prime number is:
- A. \frac{1}{3}
- B. \frac{2}{3}
- C. \frac{4}{9}
- D. \frac{5}{9}
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Q8
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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Q9
mcq
1 mark
If $a = 2^3 \times x$, $b = 2^3 \times 3 \times 5$, $c = 2^2 \times 3 \times 7$ and $\text{LCM} (a, b, c) = 3780$, then $x$ is:
- A. 1
- B. 2
- C. 3
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Q10
mcq
1 mark
Two coins are tossed simultaneously. The probability of getting at most one tail is:
- A. \frac{1}{2}
- B. \frac{1}{4}
- C. \frac{3}{4}
- D. 1
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Q11
mcq
1 mark
If the mean of five observations $x, x+3, x+5, x+7$ and $x+10$ is 11, then the value of $x$ is:
- A. 4
- B. 7
- C. 11
- D. 6
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Q12
mcq
1 mark
The zeroes of the quadratic polynomial $2x^2 - 3x - 5$ are:
- A. 1, -\frac{5}{2}
- B. -1, -\frac{5}{2}
- C. -1, \frac{5}{2}
- D. 3, \frac{3}{2}
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Q13
mcq
1 mark
Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:
- A. 4
- B. 3
- C. 2
- D. 1
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Q14
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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Q15
mcq
1 mark
If $\cos \theta = 1/2$ and $\sin \theta = 1/2$, then $\tan \theta$ is:
- A. 3
- B. $1/3$
- C. 1
- D. not defined
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Q16
mcq
1 mark
Given $HCF (2520, 6600) = 40$, $LCM (2520, 6600) = 252 \times k$, then $k$ is:
- A. 1650
- B. 1600
- C. 165
- D. 1625
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Q17
mcq
1 mark
The sum of first $n$ terms of an AP is $n^2 + 4n$ and its common difference is:
- A. 7
- B. 4
- C. 6
- D. 3
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Q18
mcq
1 mark
What should be subtracted from $x^2 - 16x + 30$ to get a quadratic polynomial that is a perfect square?
- A. 30
- B. 14
- C. 15
- D. 16
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Q19
mcq
1 mark
In a cricket match, a batsman hits a boundary 9 times out of 30 balls played. Find the probability that he did not hit a boundary is $4/5$.
- 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
1 mark
The point which divides the line segment joining the points $(-1, 3)$ and $(2, -1)$ internally in the ratio $1:3$ is $(-1/4, 2)$.
- 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
short answer
The coordinates of the point which divides the line segment joining the points A $(x_1, y_1)$ and B $(x_2, y_2)$ in the ratio $m_1 : m_2$ is $\left( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} \right)$
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Q21
short answer
2 marks
Evaluate : $\frac{\sec^2 45° - \tan^2 45°}{\sin^2 45°}$
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Q25
short answer
2 marks
Find points P(x, y) on the x-axis such that the distance from the point (7, 6) is 10 units. Find x and y.
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Q25
short answer
2 marks
In the given figure, $\frac{EA}{EC} = \frac{EB}{ED}$, prove that $\Delta EAD \sim \Delta EBC$.
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Q26
short answer
2 marks
Points A(-1, y) and B(5, 7) lie on a circle with centre O(2, -3y) such that AB is a diameter of the circle. Find the value of y. Also, find the radius of the circle.
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Q26
short answer
Solve the following system of linear equations graphically: $x - y = 1$ and $x + y = 3$.
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Q27
short answer
One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is a red face card.
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Q27
short answer
Prove that $\frac{\sin A + \cos A}{\sin A - \cos A} + \frac{\sin A - \cos A}{\sin A + \cos A} = \frac{2}{\sin^2 A - 1}$
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Q28
short answer
2 marks
If $x + y = 7$ and $(x - y) = 1$, find the value of $(x - y)$.
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Q29
short answer
2 marks
Sum of two numbers is 105 and their difference is 45. Find the numbers.
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Q29
short answer
Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord.
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Q30
short answer
Find the zeroes of the quadratic polynomial $x^2 - 3$ and verify the relationship between the zeroes and the polynomial coefficients.
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Q33
short answer
In what ratio does the X-axis divide the line segment joining the points (0, -6) and (5, 6)? Also, find the coordinates of the point of intersection.
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Q34
short answer
Find the area of $\Delta ABC$ having vertices A(0, -2), B(5, 2) and C(0, 3).
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Q34
long answer
5 marks
In $\triangle ABC$, the coordinates of the vertices A, B, and C are given. A line BM is drawn intersecting AC in L and AD produced in E. Prove that $EL = BL$.
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Q35
long answer
5 marks
The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 3600$\sqrt{3}$ m, find the speed of the jet plane.
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Q37
short answer
In an A.P. the sum of its first $n$ terms is $3n^2 + 5n$ and its $m^{th}$ term is 164, find the value of $m$.
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Q38
short answer
Find the sum of the $n^{th}$ term and $m^{th}$ term of an A.P. if the sum of its first six terms is 42. Find the first term and the common difference of A.P.
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Q39
long answer
5 marks
A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another cylinder of height 50 cm and radius 7 cm. Find the mass of the pole, given that 1 cm$^3$ of iron has approximately 8 g mass.
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Q40
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 4 mm, find its surface area. Also, find its volume.
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Q41
long answer
5 marks
Due to bad weather, an aircraft was slowed down. Its average speed is reduced by 100 km/h and by doing so, the time of flight is increased by 30 minutes. Find the original speed of the aircraft.
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Q42
long answer
5 marks
The numerator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is $2 \frac{16}{21}$, find the fraction.
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Students of a school are standing in a straight line for the assembly and the drill. In this process, the teacher asked the students of the class to create an algebraic expression for the expressions of the students. The first student is asked to multiply the expression $x$ by some algebraic number to get the second expression. The second expression is multiplied by some algebraic number to get the third expression. In this way, algebraic numbers are multiplied to get the final expression.
Q45
short answer
1 mark
What is the highest common factor used by the expressions?
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Teaching Mathematics through activities is a powerful approach that enhances students’ understanding and engagement. Keeping this in mind, 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 AgST1ig3 BDAr3 uSDg/sD/1T3 /g3 Ow3 B3 sE/u13 iSuO1E3 BiT3 sBAA1T3 /g3 gr3 gP/ET3 AgST1igR3)i3gP/A3:Bw3Ow3uSDg/sDw/i~3gr3B3sE/u13iSuO1Ef3gP13DBAg3AgST1ig3 ~rg3t=hMdnR3
Q46
short answer
1 mark
What is the least prime number used by students ?
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Q47
short answer
2 marks
How many students are in the class ?
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Q48
short answer
1 mark
Which prime number has been used maximum times ?
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Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self-reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training: Age (in years): 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54 Participants: 62, 132, 96, 37, 13, 11, 10, 4
Q49
short answer
1 mark
What is the lower limit of the modal class of the above data ?
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Q51
short answer
2 marks
Find the number of participants of age less than 50 years who undergo vocational training.
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Q52
short answer
1 mark
Give the empirical relationship between mean, median and mode.
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