Math important questions #shortvideo #viral#shorts

Solve for
𝑥
x:
2
𝑥
+
5
=
15
2x+5=15.
Factorize the quadratic equation:
𝑥
2
−
5
𝑥
+
6
x
2
−5x+6.
Simplify the expression:
(
3
𝑥
2
+
2
𝑥
−
5
)
−
(
𝑥
2
−
4
𝑥
+
3
)
(3x
2
+2x−5)−(x
2
−4x+3).
Geometry
Find the area of a triangle with base 10 cm and height 5 cm.
Prove that the sum of the interior angles of a triangle is 180°.
Calculate the volume of a cylinder with radius 4 cm and height 10 cm.
Calculus
Differentiate
𝑓
(
𝑥
)
=
3
𝑥
2
+
2
𝑥
+
1
f(x)=3x
2
+2x+1.
Find the integral of
𝑓
(
𝑥
)
=
5
𝑥
3
f(x)=5x
3
.
Solve the limit:
lim
⁡
𝑥
→
∞
1
𝑥
lim
x→∞


x
1

.
Trigonometry
Prove that
sin
⁡
2
𝜃
+
cos
⁡
2
𝜃
=
1
sin
2
θ+cos
2
θ=1.
Find the value of
sin
⁡
4
5
∘
sin45
∘
.
Solve for
𝜃
θ:
tan
⁡
𝜃
=
3
4
tanθ=
4
3

.
Statistics and Probability
Find the mean of the data set: 3, 7, 9, 12, 15.
Calculate the probability of rolling a 6 on a standard die.
What is the median of the following numbers: 1, 3, 3, 6, 7, 8, 9?
Number Theory
Determine if 97 is a prime number.
Find the greatest common divisor (GCD) of 60 and 48.
Solve the Diophantine equation:
2
𝑥
+
3
𝑦
=
17
2x+3y=17.
Linear Algebra
Solve the system of equations:
2
𝑥
+
3
𝑦
=
5
2x+3y=5
4
𝑥
−
𝑦
=
1
4x−y=1
Find the determinant of the matrix:
(
1
2
3
4
)
(
1
3


2
4

)
Calculate the eigenvalues of the matrix:
(
2
1
1
2
)
(
2
1


1
2

)
Discrete Mathematics
Prove by induction:
1
+
2
+
3
+
…
+
𝑛
=
𝑛
(
𝑛
+
1
)
2
1+2+3+…+n=
2
n(n+1)

.
How many ways can you arrange the letters in the word "MATH"?
Find the shortest path in a graph using Dijkstra’s algorithm.
Each question tests foundational concepts and problem-solving skills in mathematics.