1
KCET 2025
MCQ (Single Correct Answer)
+1
-0

The system of equations $4 x+6 y=5$ and $8 x+12 y=10$ has

A
No solution
B
Infinitely many solutions
C
A unique solution
D
Only two solutions
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is

A
1
B
$\pm 1$
C
-1
D
0
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If $|\overrightarrow{\mathrm{a}}|=10,|\overrightarrow{\mathrm{~b}}|=2$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=12$, then the value of $|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|$ is
A
5
B
10
C
14
D
16
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0

Consider the following statements :

Statement (I) : If either $|\vec{a}|=0$ or $|\vec{b}|=0$, then $\vec{a} \cdot \vec{b}=0$

Statement (II) : If $\vec{a} \times \vec{b}=\overrightarrow{0}$, then a is perpendicular to $b$. Which of the following is correct?

A
Statement (I) is true but Statement (II) is false
B
Statement (I) is false but Statement (II) is true
C
Both Statement (I) and Statement (II) is true
D
Both Statement (I) and Statement (II) is false
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12