PS-Algebra

PS Questions from Algebra

If the equations k(6x2+3)+rx+2x2−1=0k(6x2+3)+rx+2x2−1=0 and 6k(2x2+1)+px+4x2−2=06k(2x2+1)+px+4x2−2=0 have both roots common then the value of (2r−p)(2r−p) is
The two equations can be written as x^2 (6k+2) + rx + (3k-1) = 0 …… (i) & x^2(12k + 4) + px + (6k - 2) = 0 ….. (ii) Divide (ii) by 2 Thus, we get x^...
Tue, 12 Oct, 2021 at 1:03 PM
The table above shows the numbers of hours of television programs that Jane recorded last week and the numbers of hours she spent viewing these recorded programs. No recorded program was viewed more than once. If h is the number of hours of
According to the table, Total RECORDING TIME = 4+2 (Tue+ Thur) = 6 hrs The time of viewing is 1+2=3 hrs and a 3+2=5 hrs and hence the time NOT invested i...
Tue, 12 Oct, 2021 at 1:03 PM
m⊕p=nm⊕p=n n⊕r=mn⊕r=m n⊕q=qn⊕q=q p⊕q=pp⊕q=p q⊕p=rq⊕p=r If the relations shown hold for the operation ⊕ and the numbers m, n, p, q, and r, then [(m⊕p)⊕q]⊕p=[(m⊕p)⊕q]⊕p=
SOLUTION : A NEW OG 2021 QUESTION (m ⊕p)⊕q]⊕p =(n⊕ q]⊕p (Using, m ⊕ p=n) =q ⊕p (Using, n ⊕q=q) =r (Given, q ⊕p=r) (OPTION E)
Tue, 12 Oct, 2021 at 1:03 PM
If z ≠ 0 and z+(1−2z^2/z)=w/z, then w=??
SOLUTION: z+ (1−2z^2/z) = w/z => (z^2 + 1-2z^2 )/z = w/z Cancel out the "w" in the denominators, add the terms in the numerator of the LHS a...
Tue, 12 Oct, 2021 at 1:03 PM
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation (a,b,c)Θ(d,e,f)=ad+be+cf(a,b,c)Θ(d,e,f)=ad+be+cf. What is the value of (1,−2,3)Θ(1,−1/2,1/3) ?
SOLUTION: (a,b,c)Θ(d ,e, f)=ad+ be +cf In the expression (1,−2,3)Θ(1,−1/2,1/3) , a=1 d=1 b=-2 e=-1/2 c=3 f= 1/3 Using this operation, we have, ad+ be +c ...
Tue, 12 Oct, 2021 at 1:04 PM
A Metro train from Mumbai to Gurgaon has capacity to board 900 people. The fare charged (in Rs) is defined by the function: f=(54−x32)2f=(54−x32)2 where x is the number of the people per trip. How many people per trip will make the revenue
CONCEPT: Functions and derivatives At the point maximum, f'(x)=0 SOLUTION: Given, the number of people per trip is x. The fare for each person =[(54−...
Tue, 12 Oct, 2021 at 1:04 PM
If f(x)=x2+3x–4f(x)=x2+3x–4, then f(2+a)=?
CONCEPTS: The question tests on the area of functions. SOLUTION: f(a+2) = (a+2)^2 + 3(a+2) -4 = a^2 +4 +4a + 3a +6 - 4 = a^2 +7a +6 (OPTION A) Alternative...
Tue, 12 Oct, 2021 at 1:04 PM
For all numbers b and c, the operation b&c=(b2)(c2)−3=(b2)(c2)−3 If x=3x=3, what is the value of 5&x?
CONCEPT: The question tests on the basics of custom characters and functions; SOLUTION:   b & c =(b^2)(c^2)−3 5 & X =(5^2)(X^2) - 3  =(5^2)(3^2) - ...
Tue, 12 Oct, 2021 at 1:04 PM
Jane sold cookies at a fair for 96 cents each; she then used that money to buy popsicles for 30 cents each. If she had no money left over, what is the fewest number of cookies she could have sold?
CONCEPT: The question tests on basic application techniques used algebra SOLUTION:   Let Jane sell "a" cookies 96 cents/cookie. Thus total money ...
Tue, 12 Oct, 2021 at 1:05 PM
If the equations k(6x^2+3)+rx+2x^2−1=0 and 6k(2x^2+1)+px+4x^2−2=0 have both roots common then the value of (2r−p)(2r−p) is
CONCEPT: The question is based on the concept of equations. SOLUTION:  The two equations can be written as x^2 (6k+2) + rx + (3k-1) = 0 …… (i) & x^...
Tue, 12 Oct, 2021 at 1:05 PM