Class 10th Real Number PYQ

Maths — Previous Years Questions (PYQ)

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Table of Contents Chapter 1 — Real Number Chapter 2 — Polynomials Chapter 3 — Pair of Linear Equation In Two Variable Chapter 4 — Quadratic Polynomials Chapter 5 — Arithmetic Progression Chapter 6 — Triangle Chapter 7 — Co-ordinate Geometry Chapter 8 — Trigonometry Ratio Chapter 9 — Application of Trigonometry Chapter 10 — Circle Chapter 11 — Area Related to Circle Chapter 12 — Surface Area and Volume Chapter 13 — Statistics Chapter 14 — Probability

Chapter-1: Real Number

1. 1. The sum of powers of prime factors of 400.
   A) 4    B) 9    C) 6    D) 8
2. 2. If HCF = LCM for two rational numbers, then numbers always should be
   A) Composite    B) Equal    C) Prime    D) Co-prime
3. 3. Find the HCF and LCM of 12, 15 and 21 using the prime factorisation method.
4. 1. The HCF of two numbers is 27 and their LCM is 162. If one number is 54, then other number is :
   A) 81    B) 27    C) 54    D) 18
5. 2. If x = 2³ × 3² and y = 2² × 3², then find the least common multiple of x and y.
6. 3. Prove that √5 is an irrational number.
7. 1. The sum of the powers of the prime factors of 196 is
   A) 1    B) 2    C) 4    D) 6
8. 2. Highest Common Factor (HCF) of 95 and 152 is __________.
9. 1. Which of the following is an irrational number?
   A) √2    B) 2.232425….    C) (something missing in source)    D) 2.232...?
10. 2. Find the least common multiple (LCM) of numbers 72 and 120.
11. 3. Find the highest common factor (HCF) of two numbers 616 and 32.
12. 1. If the product of two numbers is 12960 and HCF is 18 then find their LCM.

Chapter-2: Polynomials

1. 1. If 3 is a zero of the polynomial 2x² + x + k, then the value of k will be
   A) -12    B) 21    C) -21    D) 12
2. 2. If the sum and product of the zeros of the quadratic polynomial are 5 and 6 respectively, then the quadratic polynomial is:
   A) x² + 5x + 6    B) x² + 6x + 5    C) x² − 6x + 5    D) x² − 5x + 6
3. 3. If α and β are the zeros of the quadratic polynomial 3x² − 5x + 9, then find (α + β) and αβ.
4. 1. The zeros of the polynomial x² − 2x − 8 are:
   A) 2, 4    B) 2, 5    C) -2, 4    D) -2, 6
5. 2. Find the zeros of the polynomial x² − 3.
6. 3. Find the zeroes of the polynomial 2x² − 2x − 6.
7. 1. If roots of the quadratic equation x² − kx + 8 = 0 are equal, then the value of k will be:
   A) ±1    B) ±2    C) ±3    D) ±4
8. 2. Find the zeroes of the polynomial x² − x − 6.
9. ... (Additional polynomial questions continue in the source PDF)

Chapter-3: Pair of Linear Equation In Two Variable

1. 1. In a two digit number, the unit digit is x and the tens digit is y, then that number is:
   A) 10x + y    B) x + y    C) x + 10y    D) xy
2. 2. For which value of k, linear pair x + y − 4 = 0 and x + ky − 3 = 0 has no solution?
   A) 0    B) 2    C) 6    D) 8
3. 3. Use elimination method to find all possible solutions of:
   3x + 5y = 7 and 6x + y = −4
4. ... (More questions present in the PDF)

Chapter-4: Quadratic Polynomials

1. 1. The difference of squares of two numbers is 180. The square of the smaller number is eight times the larger number. Find both the numbers.
2. 2. Find two consecutive positive integers, whose sum of squares is 365.
3. 3. The difference between two numbers is 26 and one number is three times the other number, then find the numbers.
4. ... (Additional quadratic polynomial problems continue)

Chapter-5: Arithmetic Progression

1. 1. If 18, a, 10 are in arithmetic progression, then a = ________.
2. 2. Find the arithmetic mean of the first ten positive odd natural numbers.
3. 3. Find the number of terms in arithmetic progression 7, 13, 19, …., 205.
4. ... (More AP questions)

Chapter-6: Triangle

1. 1. If ∆ABC ∼ ∆DEF and AB = 10 cm, DE = 8 cm, then BC : EF is:
   A) 8 : 18    B) 4 :5    C) 9 :4    D) 5 :4
2. 2. In the given figure, AB = 2 cm, AC = 4 cm, DE = 3 cm, and DF = 6 cm. If ∠A = 50° and ∠D = 50° and BC = 3 cm, then the measurement of EF is:
   A) 4.5 cm    B) 6 cm    C) 8 cm    D) 5 cm
3. ... (triangle questions continue)

Chapter-7: Co-ordinate Geometry

1. 1. Distance of Point P(-3, 4) from origin O(0, 0) is:
   A) 5    B) ...    C) 7    D) 17
2. 2. The coordinates of the midpoint of point P(7, -3) and point Q(3, 9) is ____.
3. ... (more coordinate geometry questions)

Chapter-8: Trigonometry Ratio

1. 1. cosec²45° − cot²45° equals:
   A) 2    B) 1    C) 0    D) √2
2. 2. sin2A = 2 sinA is true when A equals:
   A) 0°    B) 30°    C) 45°    D) 90°
3. ... (more trigonometry questions)

Chapter-9: Application of Trigonometry

1. 1. The shadow of a vertical pillar is same as the height of pillar, then the angle of elevation of sun is:
   A) 60°    B) 30°    C) 90°    D) 45°
2. 2. A 12 meter long ladder touches the top of a vertical wall. If this ladder makes an angle of 60° with the wall, then find the height of the wall.
3. ... (more application questions)

Chapter-10: Circle

1. 1. From a point P, the length of the tangent to a circle is 24 cm and the distance of P from the centre is 25 cm. The radius of the circle is:
   A) 7 cm    B) 14 cm    C) 3.5 cm    D) 1 cm
2. 2. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
3. ... (more circle questions)

Chapter-11: Area Related to Circle

1. 1. The area of quadrant of a circle whose radius is 7 cm is:
   A) 38.5 cm²    B) 77 cm²    C) 154 cm²    D) 44 cm²
2. 2. The angle subtended at the centre by the minute hand of a clock in 5 minutes is:
   A) 30°    B) 60°    C) 3°    D) 10°
3. ... (more area questions)

Chapter-12: Surface Area and Volume

1. 1. If the radius of a cone is 14 cm and slant height is 10 cm, then the curved surface area of the cone is:
   A) 220 cm²    B) 110 cm²    C) 440 cm²    D) 140 cm²
2. 2. If the diameter of a solid hemisphere is 14 cm, then its total surface area is __________.
3. ... (more surface/volume questions)

Chapter-13: Statistics

1. 1. Find the median of the following frequency distribution:
   x: 3,5,7,9    f: 6,7,5,6
2. 2. If the arithmetic mean of 5, 7, 9, 4, 3, (x+2) is 6, then find the value of x.
3. ... (more statistics questions)

Chapter-14: Probability

1. 1. Which of the following numbers cannot be the probability of any event?
   A) 0.2    B) 0.3    C) 0.7    D) 0.5
2. 2. The mode of the distribution 1, 4, 5, 6, 4, 7, 9, 2, 4, 3, 5 is _________.
3. ... (more probability questions)

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