List of top B.Ed. Mathematics Questions on Vectors

Which of the following statements are true? A. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}+\vec{b}|\leq |\vec{a}|+|\vec{b}|\).
B. Scalar product of two non-zero vectors might be zero.
C. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}\cdot \vec{b}|\leq |\vec{a}||\vec{b}|\).
D. Cross product of two vectors is not a vector.
E. Dot product of two vectors is a scalar.

Given below are two statements:

Assertion (A):
The function \(f(x)=x|x|\) is continuous at \(x=0\) and derivative of \(f\) also exists at \(x=0\).
Reason (R):
It is necessary and sufficient that every continuous function is derivable at any point.

Which of the following statements are true? A. \(2^{4n}-1\) is divisible by \(15\).
B. \(5,12\) and \(13\) is Pythagorean triplet.
C. \(n^7-n\) is divisible by \(42\).
D. \(1^2+2^2+3^2+\cdots+n^2=\left[\dfrac{n(n+1){2}\right]^2\).}

Which of the following statements are true? A. \(2^{4n}-1\) is divisible by \(15\).
B. \(5,12\) and \(13\) is Pythagorean triplet.
C. \(n^7-n\) is divisible by \(42\).
D. \(1^2+2^2+3^2+\cdots+n^2=\left[\dfrac{n(n+1){2}\right]^2\).}

Which of the following statements are true? A. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}+\vec{b}|\leq |\vec{a}|+|\vec{b}|\).
B. Scalar product of two non-zero vectors might be zero.
C. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}\cdot \vec{b}|\leq |\vec{a}||\vec{b}|\).
D. Cross product of two vectors is not a vector.
E. Dot product of two vectors is a scalar.

Given below are two statements:

Assertion (A):
The function \(f(x)=x|x|\) is continuous at \(x=0\) and derivative of \(f\) also exists at \(x=0\).
Reason (R):
It is necessary and sufficient that every continuous function is derivable at any point.