Race IBPS Clerk 2015- Practice Aptitude Questions (Inequality) with Explanations Set-34

  Practice Aptitude Questions (Inequality) Set-34
Race IBPS Clerk 2015- Practice Aptitude Questions (Inequality) with Explanations Set-34:
Dear Readers, Important Practice Aptitude Questions for Upcoming IBPS Clerk V Exam was given here with solutions. Aspirants those who are preparing for the examination can use this

Directions (Q.1-5): In each of these equations, two equations Ⅰ and Ⅱ are given. You have to solve both the equations and give answer


1).Ⅰ.6x+3y=7xy            Ⅱ.3x+9y=11xy

2).Ⅰ.5x+1+52-x=53+1     Ⅱ.y²-2y-3=0

3).Ⅰ.8x²-22x-21=0       Ⅱ.(4/y)-3= 5/ (2y+3)

4).Ⅰ.4√3x²+5x-2√3=0  Ⅱ.y²+5y+6=0 

5).Ⅰ.10x-1/x=3             Ⅱ.30y²+11y+1=0   

Directions (Q.6-8): In each question below two equations are provided On the basis of these, you have to findout the relationbetween p and q. Given answer:











6).Ⅰ.p²+7p=3p+21          Ⅱ.4q²+15q+9=0

7).Ⅰ. √p- (√7/√p) =0       Ⅱ.q- (8/√q) =0

8).Ⅰ.2p²-15p+22=0         Ⅱ.3q²+7q-6=0

Answers:                         
1). a)  2).e ) 3). e)  4). b)  5). e)  6). b)   7). a)   8). d)

Solutions:

1).Given 6x+3y=7xy   …(ⅰ)
On dividing both sides by x y, we get 6/y+3/x=7     …(ⅱ)
Again, 3x+9y=11xy     …(ⅲ)
On dividing both sides in equation (ⅲ) by x y, we get
Or, 3/y+9/x=11 …(ⅳ)
Now, let 1/x=u and 1/y=v
Then, 6v+3u=7      …(ⅴ)
3v+9u=11 …(ⅵ)
Solving (ⅵ)& (ⅵ), we get
∴u=1 and v=2/3
∴ u=1/x=1 so, v=1/y=2/3
Or, x=1                ∴y=3/2=1.5
Hence x< y
Answer: (a)

2). Ⅰ. 5x+1+52-x=53+1
Or, 5x*5+52*5-x=126
Or, 5x×5+ (25/5x) =126
Let 5x= u (say)
Then, 5u2-126u+25=0
Or, 5u2-125u-u+25=0
Or, 5u (u-25)-1 (u-25) =0
Or, (u-25) (5u-1) =0
Or, u=25; u=1/5
Now, u=5x        or, 5x=52              ∴x=2
Again, u=1/5=5-1
∴ 5x=5-1
∴ x=-1
Ⅱ.y2-2y-3=0  or, y2-3y+y-3=0  or, y(y-3) + (y-3) =0  or, (y+1) (y-3)=0
y=-1, 3
Hence relation can’t be established between x and y.
Answer: (e)

3).Ⅰ.8x²-22x-21=0 or, 8x²-28x+6x-21=0 or, 4x (2x-7) +3(2x-7) =0 or, (2x-7) (4x+3) =0
Or, 2x-7=0
Again, 4x+3=0 or, x=7/2   x=-3/4
Ⅱ.(4/y)-3=5/ (2y+3) or, (4-3y)/y=5/ (2y+3) or, (4-3y) (2y+3)=5y or, 6y²+6y-12=0
Or, y²+y-2=0 or, y²+2y-y-2=0 or, y(y+2)-1(y+2) =0 or, y=1, -2
∴ Relation cannot be established between x and y.
Answer: (e)

4).Ⅰ. 4√3 x²+5x-2√3=0
Here 4√3* (-2 √3) =-24 and 8*-3=-24 and 8+ (-3) =5
∴ 4√3 x²+5x-2 √3=0 or, 4√3 x²+8x-3x-2√3=0 or, 4x (√3x+2) -√3 (√3x+2) =0
Or, (4x-√3) (√3x+2) =0
Or, √3x+2=0 And x=(√3/4) or, x=(-2/√3)
II. y²+5y+6 or, y²+3y+2y+6=0 or, y+(y+3)=0 or, y=-2, -3  ∴ x>y
Answer: (b)
5). I.10x-1/x=3
Or, 10 x²-3x-1=0 or, 10 x²-5x+2x-1=0 or, 5x(2x-1)+1(2x-1)=0
Or, x=(1/2,-1/5)
II.30y²+11y+1=0 or, 30 y²+6y+5y+1=0 or, 6y(5y+1)+1(5y+1)=0
or , (5y+1)(6y+1)=0  or, (y=-1/5,-1/6)
∴ No relation can be established between x and y.
Answer: (e)
     
6).Ⅰ.P2+7p=3p+21 
or, p2+7p-3p-21=0 
or, p(p+7)-3 (p+7) =0 
or, (p-3) (p+7) =0
∴ p=3, -7.
Ⅱ. 4q2+15q+9=0 
or, 4q2+12q+3q+9=0 
or, 4q (q+3) +3(q+3) =0 
or, (4q+3) (q+3) =0
∴q=-3/4, -3.
Hence no relation can be established between p and q.
Answer: (b)

7).Ⅰ.√p- (√7/√p) =0  
or, p=√7
Ⅱ.q×√q=8 or, q3/2=8 
or, q=82/3 =641/3 =4
Hence p< q
Answer: (a)

8).Ⅰ.2p²-15p+22=0 
or, 2p²-4p-11p+22=0 
or, 2p (p-2)-11(p-2) =0 
or, (2p-11) (p-2) =0
∴ p=2, 11/2
Ⅱ.3q2+7q-6=0
or, 3q2+9q-2q-6=0 
or, 3q (q+3)-2(q+3) =0
∴ q=-3, +2/3
Hence, p> q

Answer: (d)

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