Give a list of class 10th mathematics most important questions.if anyone gives right questions i will mark him brainest for sure.
Answers
Q. The first and the last terms of an AP are 10 and 361 respectively. If its common difference is 9 then find the number of terms and their total sum?
Sol.
Given, first term, a = 10
Last term, al = 361
And, common difference, d = 9
Now al =a + (n −1)d
⟹ 361 = 10 + (n − 1)9
⟹ 361 = 10 + 9n − 9
⟹ 361 = 9n + 1
⟹ 9n = 360
⟹ n = 40
Therefore, total number of terms in AP = 40
Now, sum of total number of terms of an AP is given as:
Sn = n/2 [2a + (n − 1)d]
⟹ S40 = 40/2 [2 × 10 + (40 − 1)9]
= 20[20 + 39 x 9]
=20[20 + 351]
=20 × 371 = 7420
Thus, sum of all 40 terms of AP = 7420
The taxi charges in a city comprise of a fixed charge together with the charges for the distance covered. For a journey of 10 km the charge paid is Rs. 75 and for a journey of 15 km the charge paid is Rs. 110. What will a person have to pay for travelling a distance of 25 km?
Sol.
Let the fixed charge of taxi be Rs. x per km and the running charge be Rs y per km.
According to the question,
x + 10y = 75
x + 15y = 110
Subtracting equation (ii) from equation (i), we get
– 5y = – 35
⟹ y = 7
Putting y = 7 in equation (i), we get x = 5
∴Total charges for travelling a distance of 25 km = x + 25y
= (5 + 25 × 7)
= (5 + 175)
= Rs 180Q. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms of the AP.
Sol.
Given that sum of the 4th and 8th terms of an AP is 24.
⟹ a + 3d + a + 7d = 24
⟹ 2a + 10d = 24 ...(i)
Also the sum of the 6th and 10th term is 44.
⟹ a + 5d + a + 9d = 44
⟹ 2a + 14d = 44 ...(ii)
Subtracting equation (i) from equation (ii), we get:
4d = 20
⟹ d = 5
Substituting d = 5 in equation (i), we have:
2a + 10d = 24
⟹ 2a + 10 (5) = 24
⟹ 2a + 50 = 24
⟹ 2a = −26
⟹ a = −13
Hence first term of the given AP is - 13
Q. Find the length of the tangent from a point M which is at a distance of 17 cm from the centre O of the circle of radius 8 cm.
Sol.
Consider the figure:
Since, MN is the tangent of the circle,
∠MNO = 90⁰
⟹ MO2 = MN2 + ON2
⟹ 172 = MN2 + 82
⟹ 289 = MN2 + 64
⟹ 289 – 64 = MN2
⟹ MN2 = 225
⟹ MN = 15
Thus, the length of the tangent is 15 cm.
Q. If the common difference of an A.P. is 3, then find a20 – a15.
Sol.
Let the first term of the AP be a.
an = a(n − 1)d
a20 – a15 = [a + (20 – 1)d] – [a + (15 – 1)d]
= 19d – 14d
= 5d
= 5 × 3
Q. Solve the following system of linear equations by substitution method:
2x – y = 2
x + 3y =15
Sol.
Here, 2x – y = 2
⟹ y = 2x – 2
⟹ x + 3y = 15
Substituting the value of y from (i) in (ii), we get
x + 6x – 6 = 15
⟹ 7x = 21
⟹ x = 3
Hope this helps! Have a great week ahead!
Please mark my answer as BRAINLIEST
Some CBSE class 10 Math Important questions have been compiled below:
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).
31. If the polynomials x4 + 2x3 + 8x2 + 12x + 18 is divided by another polynomial x2+ 5, the remainder comes out to be p x +q. Find the values of p and q .
32. Find the values of m and n for which the following system of equations has infinitely many solutions:
3x+4y = 12;
(m + n)x +2(m-n)y=5m-1.
33. Solve for x & y: x/a +y/b =1 ; a(x-a) – b( a + b)=2a2+b2.