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پی ڈی ایف میں ڈنلوڈ کرنے کے لیےاس لنک پر کلک کریں۔
Basic Math PDF File
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چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔
Semi group
Monoid
Abelian group
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
A commutative group is a group where the operation satisfies commutativity: a ⋅ b = b ⋅ a a cdot b = b cdot a for all elements. Such a group is called an Abelian group, named after Niels Henrik Abel .
p(x) = (x - r)q(x)k
p(x) = (x - r)q(x) + k
p(x) = (x - r)q(x) - k
p(x) = (x + r)q(x) + k
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
By the polynomial division algorithm, any polynomial p ( x ) p(x) can be expressed as:
p(x)=(x−r)q(x)+k
p ( x ) = ( x − r ) q ( x ) + k where q ( x ) q(x) is the quotient and k k is the remainder.
If r r is a root of p ( x ) p(x) , then k = 0 k = 0 , making p ( x ) p(x) completely factored.
Not a function
One-one and onto function
One-to-one function
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
A function must assign each element of A a unique value in B, but f(b) is not defined, so it fails to be a function. Since not all elements of A have an image in B, it does not satisfy the definition of a function.
Composite functions
Multilinear function
Linear function
None of these
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Explanation
A tensor is a multilinear function. It maps vectors and their duals (covectors) to scalars , satisfying linearity in each argument. Tensors generalize the concept of scalars, vectors, and matrices in various dimensions. This making them essential in fields like physics and engineering.
Cyclic
Abelian
Finite
None of these
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Explanation
If every element of a group G G is its own inverse, then g 2 = e g^2 = e for all g ∈ G g in G , meaning all elements are of order 2. Such a group is Abelian because the group operation commutes: ( g h ) 2 = e (gh)^2 = e implies g g and h h must commute.
4
8
6
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
The identity element e should satisfy ae = ea = a for all a in G.
Here, e = 6 works since 26=2, 46=4, 66=6 , 86=8.
Solvable
Abelian
Prime
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
A polynomial is solvable by radicals if and only if its Galois group is solvable . A solvable group has a series of subgroups where each quotient is abelian.
The even numbers
The odd numbers
The negative numbers
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
An ideal in the ring of integers ℤ must be closed under addition and multiplication by any integer. The set of even numbers forms an ideal since the sum and product of any even numbers remain even.
18
144
156
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
When throwing a die, there are 6 possible outcomes (1, 2, 3, 4, 5, 6).
When drawing a letter at random from the English alphabet, there are 26 possible outcomes (A, B, C, ..., Z).
Since the two events are independent, the total number of points in the sample space is the product of the two:
6 (die outcomes) × 26 (letter outcomes) = 156
Ø
-3
3
None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
Since f(x) = x^2 is always non-negative, there is no real x such that f(x) = -9.
So, the inverse image of -9 is the empty set:
f^(-1)(-9) = Ø