important ques of maths for class 10th board
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Top 30 Questions of 10th Board
1. Prove that 1/(2+√3) is an irrational number.
2. Prove that √5 is an irrational number.
3. Show that any positive odd integer is of the form (6p+1), (6p+3) or (6p+5), where p is some integer.
4. Find the HCF and LCM of 306 and 54. Verify that HCF × LCM = Product of the two numbers.
5. A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?
6. Use Euclid’s Lemma to show that square of any positive integer is of form 4 m or 4m+1 for some integer m.
7. If the ratio of the corresponding sides of two similar triangles is 2:3, then what is the ratio of their corresponding height?
8. The areas of two similar triangles and are 25cm2 and 49 cm2 respectively. If QR = 9.8 cm, find BC.
9. DE is parallel to BC. If AD = 12.4 cm, DB = 6.2cm, AE = 2x and EC = 6x – 2. Find the value of x.
10. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
11. In the given figure, in ABC, DE || BC so that AD = 2.4cm, AE = 32cm and EC=4.8cm. Find AB.class 10 math important questions
12. State and prove Basic Proportionality Theorem. Using the above theorem, if ABCD is a trapezium whose diagonals intersect each other at O show that AO/OC = BO/OD.
13. It the given figure, if Δ ABE ≅ Δ ACD, prove that ΔADE ~ ΔABC.
class 10 math important questions
14. Prove that the square of the hypotenuse is equal to the sum of the squares of the other two sides.Using the above result show that sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
15. Prove that the ratio of areas of 2 similar triangles is equal to the ratio of squares of their corresponding sides. Using the above result prove that area of an equilateral triangle described on one side of a square is half the area of triangle described on one of its diagonals.
16. Find the missing frequencies f1 and f2 in the following frequency distribution table, it is given that the mean of the distribution is 56.
C.I 0 – 20 20 – 40 40 – 60 60 – 80 80 –100 100 – 120 Total
F 16 f1 25 f2 12 10 90
17. Find the value of k, for which given value is a zero of the given quadratic polynomial
(a) (x2+2kx-3); x = -1/2 (b) x2+4ax-k; x= -a
18. Verify that -1, 1, 2 are zeros of a cubic polynomial x3 – 2x2 – x+2 & verify the relationship between the zeros & its coefficients.
19. Form a quadratic polynomial whose (i) zeros are 2 & -3 (ii) zeros are -4/5 & 1/3.
20. Solve the equations 15x -6y = 30 ; 17x + 10y =118.
21. Solve the equations ax + by = c; bx – ay = 0.
22. A fraction becomes 9/11, if 2 is added to both the numerator & denominator. If 3 is added to both the numerator & denominator it becomes 5/6. Find the fraction.
23. Solve (By cross multiplication) 2/u + 3/v = 13 ; 5/u – 4/v = -2.
24. Find the values of p & q for which the following system has infinite solutions.
2x + 3y = 7 ;
(p + q)x + (2p – q)y = 21.
25. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. How old I am and how old is my son?
26. A and B are friends and their ages differ by two years. A’s father D is twice as old as A, & B is twice as old as his sister C. The ages of D and C differ by 40 years. Find the ages of A and B?
27. Five years hence father’s age will be three times age of his son. Five years ago father was seven times as old as his son. Find their present ages.
28. Five years ago, Neeta was thrice as old as Gita. Ten years later, Neeta will be twice as old Gita. How old are Gita & Neeta now?
29. If two zeroes of the polynomials are x4 – 6x3 – 26x2 + 138x – 35 are 2±√3, find the other zeroes.
30. On dividing x3 – 3x2 + x + 2 by polynomials g(x), the quotient & remainder were x – 2 & – 2x+4 respectively. Find g(x).
1. Prove that 1/(2+√3) is an irrational number.
2. Prove that √5 is an irrational number.
3. Show that any positive odd integer is of the form (6p+1), (6p+3) or (6p+5), where p is some integer.
4. Find the HCF and LCM of 306 and 54. Verify that HCF × LCM = Product of the two numbers.
5. A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?
6. Use Euclid’s Lemma to show that square of any positive integer is of form 4 m or 4m+1 for some integer m.
7. If the ratio of the corresponding sides of two similar triangles is 2:3, then what is the ratio of their corresponding height?
8. The areas of two similar triangles and are 25cm2 and 49 cm2 respectively. If QR = 9.8 cm, find BC.
9. DE is parallel to BC. If AD = 12.4 cm, DB = 6.2cm, AE = 2x and EC = 6x – 2. Find the value of x.
10. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
11. In the given figure, in ABC, DE || BC so that AD = 2.4cm, AE = 32cm and EC=4.8cm. Find AB.class 10 math important questions
12. State and prove Basic Proportionality Theorem. Using the above theorem, if ABCD is a trapezium whose diagonals intersect each other at O show that AO/OC = BO/OD.
13. It the given figure, if Δ ABE ≅ Δ ACD, prove that ΔADE ~ ΔABC.
class 10 math important questions
14. Prove that the square of the hypotenuse is equal to the sum of the squares of the other two sides.Using the above result show that sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
15. Prove that the ratio of areas of 2 similar triangles is equal to the ratio of squares of their corresponding sides. Using the above result prove that area of an equilateral triangle described on one side of a square is half the area of triangle described on one of its diagonals.
16. Find the missing frequencies f1 and f2 in the following frequency distribution table, it is given that the mean of the distribution is 56.
C.I 0 – 20 20 – 40 40 – 60 60 – 80 80 –100 100 – 120 Total
F 16 f1 25 f2 12 10 90
17. Find the value of k, for which given value is a zero of the given quadratic polynomial
(a) (x2+2kx-3); x = -1/2 (b) x2+4ax-k; x= -a
18. Verify that -1, 1, 2 are zeros of a cubic polynomial x3 – 2x2 – x+2 & verify the relationship between the zeros & its coefficients.
19. Form a quadratic polynomial whose (i) zeros are 2 & -3 (ii) zeros are -4/5 & 1/3.
20. Solve the equations 15x -6y = 30 ; 17x + 10y =118.
21. Solve the equations ax + by = c; bx – ay = 0.
22. A fraction becomes 9/11, if 2 is added to both the numerator & denominator. If 3 is added to both the numerator & denominator it becomes 5/6. Find the fraction.
23. Solve (By cross multiplication) 2/u + 3/v = 13 ; 5/u – 4/v = -2.
24. Find the values of p & q for which the following system has infinite solutions.
2x + 3y = 7 ;
(p + q)x + (2p – q)y = 21.
25. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. How old I am and how old is my son?
26. A and B are friends and their ages differ by two years. A’s father D is twice as old as A, & B is twice as old as his sister C. The ages of D and C differ by 40 years. Find the ages of A and B?
27. Five years hence father’s age will be three times age of his son. Five years ago father was seven times as old as his son. Find their present ages.
28. Five years ago, Neeta was thrice as old as Gita. Ten years later, Neeta will be twice as old Gita. How old are Gita & Neeta now?
29. If two zeroes of the polynomials are x4 – 6x3 – 26x2 + 138x – 35 are 2±√3, find the other zeroes.
30. On dividing x3 – 3x2 + x + 2 by polynomials g(x), the quotient & remainder were x – 2 & – 2x+4 respectively. Find g(x).
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