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Questions and Answers
What is the product of the integers a and b divided by LCM(a, b) if a = x³y² and b = xy³?
What is the product of the integers a and b divided by LCM(a, b) if a = x³y² and b = xy³?
How many zeros does the linear polynomial y = f(x) have?
How many zeros does the linear polynomial y = f(x) have?
In which case do the lines representing a pair of linear equations not intersect?
In which case do the lines representing a pair of linear equations not intersect?
What is the nature of the roots for the quadratic equation 9x² - 6x - 2 = 0?
What is the nature of the roots for the quadratic equation 9x² - 6x - 2 = 0?
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If two arithmetic progressions (APs) have the same common difference but different first terms of -1 and -8, what determines the first term of the second AP?
If two arithmetic progressions (APs) have the same common difference but different first terms of -1 and -8, what determines the first term of the second AP?
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Which of the following is a characteristic of linear polynomials?
Which of the following is a characteristic of linear polynomials?
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In the context of the given APs, what can be inferred if the common differences remain the same?
In the context of the given APs, what can be inferred if the common differences remain the same?
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What is the significance of internal choice in the mathematics examination sections?
What is the significance of internal choice in the mathematics examination sections?
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What is the difference between the fourth terms?
What is the difference between the fourth terms?
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In what ratio is the line segment joining (2,-3) and (5, 6) divided by the x-axis?
In what ratio is the line segment joining (2,-3) and (5, 6) divided by the x-axis?
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How many points (x,y) are located 5 units from the origin in the third quadrant?
How many points (x,y) are located 5 units from the origin in the third quadrant?
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If DE is parallel to AB in triangle ABC, and given AB = a, DE = x, BE = b, and EC = c, how is x expressed?
If DE is parallel to AB in triangle ABC, and given AB = a, DE = x, BE = b, and EC = c, how is x expressed?
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What is the angle subtended by chord PQ at the center O if it makes a 50° angle with tangent PR?
What is the angle subtended by chord PQ at the center O if it makes a 50° angle with tangent PR?
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What is the length of SP in the quadrilateral PQRS circumscribing a circle if PQ = 12 cm, QR = 15 cm, and RS = 14 cm?
What is the length of SP in the quadrilateral PQRS circumscribing a circle if PQ = 12 cm, QR = 15 cm, and RS = 14 cm?
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If sin θ = 3/5, how can cos θ be expressed?
If sin θ = 3/5, how can cos θ be expressed?
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What is the result of (sec A + tan A)(1 - sin A)?
What is the result of (sec A + tan A)(1 - sin A)?
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What is the radius of a circle if its perimeter and area are numerically equal?
What is the radius of a circle if its perimeter and area are numerically equal?
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What is the radius of a new circular park equal in area to two smaller parks with diameters of 16 m and 12 m?
What is the radius of a new circular park equal in area to two smaller parks with diameters of 16 m and 12 m?
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If a square board with side '2a' units circumscribes a circle, what is the probability of placing a dot on the shaded area?
If a square board with side '2a' units circumscribes a circle, what is the probability of placing a dot on the shaded area?
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What is the probability of drawing a black card from a pack of cards after 2 hearts and 4 spades are removed?
What is the probability of drawing a black card from a pack of cards after 2 hearts and 4 spades are removed?
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What is the upper limit of the modal class from the given height distribution of girls?
What is the upper limit of the modal class from the given height distribution of girls?
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What can be stated about the assertion that the total surface area of the top consists of the hemispherical and conical curved surfaces?
What can be stated about the assertion that the total surface area of the top consists of the hemispherical and conical curved surfaces?
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Is the sequence -5, __, 0, __, ... considered an arithmetic progression?
Is the sequence -5, __, 0, __, ... considered an arithmetic progression?
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What is the result of a geometric series where the first term is 1 and the second term is 2?
What is the result of a geometric series where the first term is 1 and the second term is 2?
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What is the diameter of the pipe through which water is flowing?
What is the diameter of the pipe through which water is flowing?
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What is the height of the cylindrical part of the tent?
What is the height of the cylindrical part of the tent?
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What increase in throw distance does Sanjitha achieve each week?
What increase in throw distance does Sanjitha achieve each week?
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How many throws did Sanjitha start with on the first day of the special camp?
How many throws did Sanjitha start with on the first day of the special camp?
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Which statement is true regarding the terms of an Arithmetic Progression?
Which statement is true regarding the terms of an Arithmetic Progression?
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What can be concluded if the Assertion (A) is true but Reason (R) is false?
What can be concluded if the Assertion (A) is true but Reason (R) is false?
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What is the base cost of the canvas per square meter needed for the tent?
What is the base cost of the canvas per square meter needed for the tent?
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What is the length of the tent when the conical top is included?
What is the length of the tent when the conical top is included?
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Which of the following is a method to prove √2 is irrational?
Which of the following is a method to prove √2 is irrational?
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In a parallelogram, if point P divides AB in a ratio of 2:3, what is the significance of this ratio in terms of the segments AP and PB?
In a parallelogram, if point P divides AB in a ratio of 2:3, what is the significance of this ratio in terms of the segments AP and PB?
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What is the median value of the data set provided?
What is the median value of the data set provided?
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What is the relationship between tangents PA and PB to the circle with center O?
What is the relationship between tangents PA and PB to the circle with center O?
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How long will it take for the water level to rise by 21 cm at a flow rate of 15 km/h?
How long will it take for the water level to rise by 21 cm at a flow rate of 15 km/h?
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If tan(A + B) = √3, what can be deduced about the sum of angles A and B?
If tan(A + B) = √3, what can be deduced about the sum of angles A and B?
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When arcs are drawn with a radius of 14 cm around the vertices of ΔABC, what region is formed?
When arcs are drawn with a radius of 14 cm around the vertices of ΔABC, what region is formed?
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Which group has the most significant interest among students in the National Art convention?
Which group has the most significant interest among students in the National Art convention?
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What is the total number of students in a group if the maximum number of groups with equal sizes is needed?
What is the total number of students in a group if the maximum number of groups with equal sizes is needed?
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What is the value of the sum of the zeroes 𝛼 and β of the polynomial 5x² + 5x + 1?
What is the value of the sum of the zeroes 𝛼 and β of the polynomial 5x² + 5x + 1?
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If the difference between the digits of a two-digit number is 2 and their sum with the reversed number is 66, what digit is in the ten's place?
If the difference between the digits of a two-digit number is 2 and their sum with the reversed number is 66, what digit is in the ten's place?
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In a circle, if the length of the chord AB is 6 cm and it makes an angle of 30° with the radius at the point of contact, what trigonometric function can be used to find OA?
In a circle, if the length of the chord AB is 6 cm and it makes an angle of 30° with the radius at the point of contact, what trigonometric function can be used to find OA?
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Which equation can be derived from the following relationship: 1 + sin²θ = 3sinθ cosθ?
Which equation can be derived from the following relationship: 1 + sin²θ = 3sinθ cosθ?
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When measuring the length of leaves that are represented in a given frequency table, what is the highest frequency recorded?
When measuring the length of leaves that are represented in a given frequency table, what is the highest frequency recorded?
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If a motor boat takes 1 hour more to travel upstream 24 km than to return downstream, what can be inferred about the speed of the stream?
If a motor boat takes 1 hour more to travel upstream 24 km than to return downstream, what can be inferred about the speed of the stream?
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If two water taps together fill a tank in 9 hours and one tap takes 10 hours less than the other to fill separately, how long does the smaller tap take to fill the tank?
If two water taps together fill a tank in 9 hours and one tap takes 10 hours less than the other to fill separately, how long does the smaller tap take to fill the tank?
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Study Notes
General Instructions
- This question paper has 5 sections (A, B, C, D, and E).
- Section A has 20 multiple choice questions (MCQs), each worth 1 mark.
- Section B has 5 questions, each worth 2 marks.
- Section C has 6 questions, each worth 3 marks.
- Section D has 4 questions, each worth 5 marks.
- Section E has 3 case-based integrated units of assessment (each worth 4 marks).
- All questions are compulsory.
- Internal choices are provided in some questions (5 marks, 3 marks, and some 2 marks questions).
- Draw neat figures wherever required. Use π = 22/7 unless otherwise stated.
SECTION A
- Question 1: If integers a and b are expressed as a = x³y² and b = xy³, where x and y are prime numbers, the result of dividing the product of a and b by LCM(a,b) is xy.
- Question 2: The given linear polynomial y = f(x) has one zero, and the zero is 3.
SECTION B
- Question 21: Prove that √2 is an irrational number.
- Question 22: Given ABCD is a parallelogram, P divides AB in a 2:3 ratio and Q divides DC in a 4:1 ratio. Prove that OC is half of OA.
- Question 23: From an external point P, two tangents PA and PB are drawn to a circle with center O. A tangent is drawn at a point E on the circle intersecting PA at C and PB at D. If PA = 10 cm, find the perimeter of APCD.
- Question 24: Given tan(A + B) = √3 and tan(A - B) = 1/√3, where 0° < A + B < 90° and A > B. Find A and B. OR, find x if 2 cosec²30° + x sin²60° / tan²30° = 10.
- Question 25: With vertices A, B, and C of triangle ABC as centers, arcs are drawn with radii 14 cm. The three portions of the triangle are removed. Calculate the total area removed. OR, Calculate the area of the unshaded region in a given figure.
SECTION C
- Question 26: National Art convention registrations: 60 interested in music, 84 in dance, 108 in handicrafts. Find the number of students in each group and the number of groups for each art form. How many rooms are required if one group gets one room.
- Question 27: If α and β are zeroes of the quadratic polynomial 5x² + 5x + 1, find α² + β² and α⁻¹ + β⁻¹.
- Question 28: The sum of a two-digit number and its reverse is 66. If the digits differ by 2, find the number. How many such numbers are there? OR, solve: √x/2 + 3/√x =2 and √x/2 = -1, x, y > 0.
- Question 29: PA and PB are tangents drawn to a circle with center O, and chord AB makes a 30° angle with the radius at the point of contact. If the length of the chord is 6cm, find the length of tangent PA and radius OA. OR, two tangents TP and TQ are drawn from an external point T, touching a circle. Prove that ∠PTQ = 2∠ OPQ.
- Question 30: Given 1 + sin²θ = 3sinθcosθ, prove that tanθ = 1 or -1/2.
- Question 31: The length of 40 leaves of a plant are measured, and the data is given in a table. Find the mean length of the leaves.
SECTION D
- Question 32: A motorboat takes 1 hour longer for 24 km upstream than downstream to the same spot. The motorboat speed is 18 km/h in still water. What is the speed of the stream? OR, Two water taps together can fill a tank in 9 hours. The tap with a larger diameter takes 10 hours less than the other tap to fill the tank separately. Calculate the time each tap takes to fill the tank individually.
- Question 33: (a) State and prove the Basic Proportionality Theorem. (b) Given ∠CEF = ∠CFE and F is the midpoint of DC. Prove that AB/BD = AE/FD.
- Question 34: Water flows at 15 km/h through a 14cm diameter pipe into a 50m long, 44m wide pond. In what time will the water level rise by 21cm? What should be the speed if the level rises in 1 hour? OR, A tent is shaped like a cylinder surmounted by a conical top. The cylindrical portion has height 3m and radius 14m, and the total height of the tent is 13.5m. Calculate the area of canvas needed and the cost if canvas costs ₹500/m².
SECTION E
- Question 35: Given a frequency distribution table related to marks obtained by students. Median is 50. Find the values of p and q. Also find the mode of the data.
- Question 36: Manpreet Kaur, a national record holder in shot put, is a role model for Sanjitha. (a) How many throws did Sanjitha practice on the 11th day? (b) Find Sanjitha's throw distance after 6 weeks. (c) How many throws did she do in the entire 15-day camp? OR, When will Sanjitha be able to achieve a throw of 11.16m?
- Question 37: Details of a football tournament from 20th July to 20th August 2023. Players are represented as points on a coordinate plane.
- Question 38: Midfielders and forwards formed a parallelogram. (1) Find the position of the central midfielder (D). (2) Check if the goalkeeper, sweeper, and wing-back are collinear. (3) Determine the positions of the defensive midfielder, attacking midfielder and striker. OR (details of birds and balls trajectories given in tree). (1) At what distance was the observer from the tree? (2) How far did the bird fly? (3) What is the speed of the bird in m/min?
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Description
Test your understanding of key mathematics concepts including products of integers, roots of quadratic equations, and characteristics of linear polynomials. This quiz covers various topics useful in algebra and arithmetic progressions. Challenge yourself and reinforce your knowledge in these fundamental areas.
