CBSE Class 10 Mathematics Exam 2019: Important 3 Marks Questions with Solutions
Q. Demonstrate that √3 is nonsensical.Sol.
Let √3 be an objective number
√3 = a/b (an and b are whole numbers and co-primes and b ≠ 0)
On squaring both the sides, 3 = a2/b2
⟹ 3b2 = a2
⟹ a2 is separable by 3
⟹ an is separable by 3
We can compose a = 3c for some whole number c.
⟹ a2 = 9c2
⟹ 3b2 = 9c2
⟹ b2 = 3c2
⟹ b2 is distinguishable by 3
⟹ b is distinguishable by 3
From (I) and (ii), we get 3 as a factor of 'an' and 'b' which is repudiating the way that aand b are co-primes. Thus our supposition that√3 is a discerning number is false. So √3 is a silly number.
Q. For any positive number n, demonstrate that n3 ‒ n is distinguishable by 6.
Sol.
Let x = n3‒ n
⟹ a = n(n2‒1)
⟹ x = (n ‒ 1) ×(n+ 1) [∵ (a2 ‒ b2)=(a‒b)(a + b)]
x = (n ‒1) × n × (n+ 1) ... (I)
We realize that, in the event that a number is totally distinct by 2 and 3, at that point it is additionally separable by 6.
Distinctness test for 3:
In the event that the aggregate of digits of any number is distinguishable by 3, at that point it is distinct by 3:
Entirety of the digits = (n ‒ 1) + (n) + (n + 1) = 3
⟹ Number is detachable by 3.
Detachability test for 2:
In the event that n is odd, at that point (n ‒ 1) and (n + 1) will be all things being equal, (n ‒1) × n × (n + 1) will be distinct by 2.
In the event that n is even, at that point, (n ‒1) × n × (n + 1) will be distinct by 2.
In this way, for any positive necessary estimation of n, n3 ‒ n is detachable by 6.
Q. At present Asha's age (in years) is 2 more than the square of her little girl Nisha's age. At the point when Nisha develops to her mom's present age, Asha's age would be one year under multiple times the present period of Nisha. Locate the present times of both Asha and Nisha.
Sol.
Give, Nisha's present age a chance to be = x year
In this manner, as per the primary condition, Asha's present age = x2 + 2
Nisha develops to her mom's present age after [(x2 + 2) – x] years.
At that point, Asha's age will move toward becoming (x2 + 2) + [(x2 + 2) – x] year.
As indicated by the inquiry,
(x2 + 2) + [(x2 + 2) – x] = 10x – 1
⟹ 2x2 – x + 4 = 10x – 1
⟹ 2x2 – 11x + 5 = 0
⟹ 2x2 – 10x – x + 5= 0
⟹ 2x (x – 5) – 1(x – 5) = 0
⟹ (x – 5) (2x – 1) = 0
⟹ (x – 5) = 0 or (2x – 1) = 0
⟹ x = 5 or 1/2
Overlooking x = 1/2 since then Asha's age = x2 + 2 =which is preposterous.
Thus, present time of Nisha = 5year
What's more, present time of Asha = x2 + 2 = (5)2 + 2 = 25 + 2 = multi year.
Our subject specialists have arranged these inquiries by dissecting patterns followed in earlier years' board tests and following the most recent schedule. Understudies must practice these imperative inquiries to familiarize with the vital subjects of class 10 Maths and track their readiness for the board test 2019. In addition, the arrangements gave here will give understudies a thought regarding how to compose legitimate answers for inquiries asked in board test in order to score high stamps
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