11th Grade > Mathematics
INEQUALITIES MODULUS AND LOGARITHMS MCQs
:
C
m=x2(x2−1)2+3=+ive i.e.≥0
Again m=1x2+4x2−2=1(x−2x)2+2≤12
mϵ[0,12]
:
D
ab=log4 5. log5 6=log4 6=12log2 6
ab=12(1+log2 3)⇒2ab−1=log2 3
∴ log3 2=12ab−1
To pass a bill in the Lower house, the Indian government requires at least 23 majority in the house. There are 545 seats in the lower house. 248 members are in favor of passing a particular bill. Which of the following inequality represents the number of additional lower house members, p, who would support the bill, to achieve the required majority ? Round off your answer to nearest tenth digit.
:
D
Step 1 : Underline the key words.
To pass a bill in the Lower house, the Indian government requires at least 23 majority in the house. There are 545 seats in the lower house. 248 members are in favor of passing a particular bill. Which of the following inequality represents the number of additional lower house members, p, who would support the bill, to achieve the required majority.
Step 2 : Recognize the variable
Additional members required to support the bill
Step 3 : Decipher the relation
Given, there are 248 members already supporting the bill and we require 'p' members more.
Thus, 248 + p is required to pass the bill
Step 4 : decide the inequality
Look out for cues :at least 23 majority. We also, know there are 545 seats.
Therefore, 248+p≥(23) 545.
Since, the answer options are simplified. Simplify the given inequation :
p≥115.333
Hence, option D is correct.
:
C
log5 a.loga x=2⇒log5x=2⇒x=52=25
A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let x be the number of 40-pound boxes and y be the number of 65-pound boxes. The forklift can carry up to either 45 boxes or a weight of 2,400 pounds. Which of the following systems of inequalities represents this relationship?
:
A
The first constraint is on the weight of the boxes. The total weight of the boxes cannot exceed 2400. Since there are x 40 pound boxes and y 65 pound boxes, total weight is (40x + 65 y). So,
40x+65y≤2400
The total number of boxes cannot exceed 45. Total number of boxes is (x + y). So,
x+y≤45
Hence, A is the correct choice.
:
A
−2x+5≤10
Subtract 5 on both side
−2x+5−5≤10−5
−2x≤5
Divide by -2 on both side
−2x−2≥5−2
x≥−52
The correct answer is option A
:
C
3<p<7 and −9<q<−4
Multiply the second inequality with - 1. This causes the sign to flip.
So, 3<p<7 and 4<−q<9
Adding these two inequalities, we get
7<p−q<16
:
B
−8>2x+10+6x>−20
−8>8x+10>−20
Dividing by 2 on each side −82>8x+102>−202
−4>4x+5>−10
:
A
−1<2x+3≤10
Subtract 3 from each sides
−1−3<2x+3−3≤10−3
−4<2x≤7
Divide by 2 each side
−42<2x2≤72
−2<x≤3.5
From here we can say that x will that all the value between -2 to 3.5 [including 3.5 because ≤ sign].
Now lets look at options
A) {1,2,3}
B) {1,2,3,4} → not possible because 4 is not in the range
C) {2,3,4} → same reason
D) {2,3,4,5} → Same reason
:
B and D
(x−3)(x2−1)=(x−3)(x−1)(x+1)Let P=(x−3)(x−1)(x+1)
Find the points on the number line where P=0
P=0⇒x ϵ {−1,1,3}
Split the number line into 4 using these points.
(−∞,−1), (−1,1), (1,3) & (3,∞)(−∞,−1): (x−3)<0, (x−1)<0 & (x+1)<0⇒P<0(−1,1): (x−3)<0, (x−1)<0 & (x+1)>0⇒P>0(1,3): (x−3)<0, (x−1)>0 & (x+1)>0⇒P<0(3,∞): (x−3)>0, (x−1)>0 & (x+1)>0⇒P>0
∴ P>0, when x ϵ (−1,1)∪(3,∞)