Solve the following quadratic inequality: x2−x - 4 ≤ 2
−3<x<2
−2≤x≤3
x≤−2,x≤3
−2<x<3
Correct answer is B
x2−x−4≤2
Subtract two from both sides to rewrite it in the quadratic standard form:
= x2−x−4−2≤2−2
= x2−x−6≤0
Now set it = 0 and factor and solve like normal.
= x2−x - 6=0
= (x−3)(x+2)=0
x + 2 = 0 or x - 3 = 0
x = -2 or x = 3
So the two zeros are -2 and 3, and will mark the boundaries of our answer interval. To find out if the interval is between -2 and 3, or on either side, we simply take a test point between -2 and 3 (for instance, x = 0) and evaluate the original inequality.
= x2−x−4≤2
= (0)2−(0)−4≤2
= 0−0−4≤2
−4≤2
Since the above is a true statement, we know that the solution interval is between -2 and 3, the same region where we picked our test point. Since the original inequality was less than or equal, we include the endpoints.
∴ −2≤x≤3.
Let a binary operation '*' be defined on a set A. The operation will be commutative if
a*b = b*a
(a*b)*c = a*(b*c)
(b ο c)*a = (b*a) ο (c*a)
None of the above
Correct answer is A
A binary operation '*' defined on a set A is said to be commutative only if a*b=b*a, ∀a, b∈A. If (a*b)*c=a*(b*c), then the operation is said to associative ∀ a, b∈ A. If (b ο c)*a=(b*a) ο (c*a), then the operation is said to be distributive ∀ a, b, c ∈ A.
If −2x3+6x2+17x - 21 is divided by (x+1), then the remainder is
32
30
-30
-32
Correct answer is C
Let p(x)=−2x3+6x2+17x−21
Using the remainder theorem
Let x+1=0
∴ x=−1
Since, (x+1) divides p(x), then, remainder will be p(-1)
⇒ p(-1) = -2(-1)3+6(−1)2 + 17(-1) - 21
∴ p(-1) = -30
How many students scored at least 25%
16
19
3
8
Correct answer is A
Number of students who scored atleast 25% = 5 + 3 + 8 = 16
A [012−1] = [2−110]
[21−1/2−1/2]
[011/21/2]
[210−1]
[211/2−2]
Correct answer is B
Let A = [abcd]
i.e [abcd] [012−1] = [2−110]
⟹[a(0)+b(2)a(1)+b(−1)c(0)+d(2)c(1)+d(−1)] = [2−110]
⟹[2ba−b2dc−d] = [2−110]
By comparing
2b = 2
a - b = -1
2d = 1 and
c - d = 0
∴ b = 2/2 = 1
a - b = -1
⇒ a - 1 = -1
∴ a = 0
∴ d = 1/2
⇒ c = d
∴ c = 1/2
∴The matrice A = [011/21/2]