# Class 10 maths term 2 important questions with solutions standard - Questions Bank

Class 10 maths term 2 important questions with solutions. We hope this blog will help the learners as well as those candicate who will appear in the boards exams 2023-2024 because we provide here all possible solutions of queries by our users. Class 10 maths term 2 important questions with solutions standard - Questions Bank (Class 10 maths term 2 important questions with solutions) for Examination Year 2023-2024

## Class 10 maths term 2 important questions with solutions standard

Source:www.questionsbanks.com Last updated: 2022-10-09 03:34:26

Class 10 maths term 2 important questions with solutions standard

Math Final Term Board Exam Class 10

Q1. Let a and b be two positive integers such that a = p3q4 and b = p2q3 , where p and q are prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs, then (m+n)(r+s)=
(a) 15
(b) 30
(c) 35
(d) 72

Solution:  HCF(a,b) = pmq = p2q

Therefore, m = 2 and n = 3

LCM(a,b) = prq = p3q

Therefore, r = 3 and s = 4

Now (m+n)(r+s) = (2 + 3) (3 + 4) = 5 x 7 = 35

Q2. Let p be a prime number. The quadratic equation having its roots as factors of p is
(a) x2 –px +p=0
(b) x2–(p+1)x +p=0
(c) x2+(p+1)x +p=0
(d) x2 –px+p+1=0

Solutions: (b) x2– (p+1)x +p = 0

Q3. If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is
(a)-2/3
(b) 2/3
(c) 1/3
(d) -1/3

Solutions: Given that α + β = αβ

Here α + β = - b/a

= - (-2) / p = 2/p

αβ = c/a = 3p/p = 3

Now α + β = αβ

=> 2/p = 3

=> p = 2/3

Q4. If the system of equations 3x + y = 1 and (2k-1)x + (k-1)y = 2k+1 is inconsistent, then k =
(a) -1
(b) 0
(c) 1
(d) 2

Solution:

3x + y = 1   ................. (i)

(2k-1)x + (k-1)y = 2k+1  ............ (ii)

a1/a2 = 3/(2k-1)

b1/b2 = 1/(k-1)

c1/c2 = 1/2k+1

For a pair of linear equation to be inconsistent

a1/a2 = b1/b2

3/(2k-1)  = 1/(k-1)

3(k - 1) = 2k - 1

3k - 2 = 2k -1

3k - 2k = - 1 + 2

k = 1

Q5. If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), then the coordinates of its fourth vertex S are
(a) (-2,-1)
(b) (-2,-3)
(c) (2,-1)
(d) (1,2)

Solution:

Now the mid-point of PR where PR and QS are two diagonals pf ||gm PQRS.

P(3,4) and R(-3,-2)

x = (3 + -3 )/ 2 = 0

y = (4 + - 2) / 2 = 1

The coordinates of mid point of PR is O(0, 1)

Mind that diagonals PR and OS bisect each other at point O(0, 1)

Q(-2,3) and let S(x, y)  and O(0, 1) is also mid point of QS

Then, using mid-point formula

x = (-2 + x) / 2

0 = - 2 + x

gives x = 2

y = (3 + y)/ 2

1 = (3 + y)/ 2

1 x 2 = 3 + y

y = 2 - 3

y = - 1

The coordinates of  S(2, - 1)

Correct Answer: (c) (2, - 1)

## Chapter: Class 10 maths term 2 important questions with solutions standard | Topic: Math Final Term Board Exam Class 10

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### Chapter: Class 10 maths term 2 important questions with solutions standard (Math Final Term Board Exam Class 10)

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# Class 10 maths term 2 important questions with solutions standard - Questions Bank

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