1
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$O A B C$$ is a tetrahedron. If $$D, E$$ are the mid-points of $$O A$$ and $$B C$$ respectively, then $$\mathbf{D E}=$$

A
$$\frac{1}{2}(O A+O B+O C)$$
B
$$\frac{1}{2}(O A+O B-O C)$$
C
$$\frac{1}{2}(O A-O B+O C)$$
D
$$\frac{1}{2}(-O A+O B+O C)$$
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$\mathbf{a}+\mathbf{b}+\mathbf{c}=0$$ and $$|\mathbf{a}|=7,|\mathbf{b}|=5,|\mathbf{c}|=3$$ then the angle between $$\mathbf{b}$$ and $$\mathbf{c}$$ is

A
$$30^{\circ}$$
B
$$45^{\circ}$$
C
$$60^{\circ}$$
D
$$90^{\circ}$$
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$P$$ and $$Q$$ are two points on the curve $$y=2^{x+2}$$ in the rectangular cartesian coordinate system such that $$\mathbf{O P} \cdot \hat{i}=-1, \mathrm{OQ} \cdot \hat{i}=2$$, then $$\mathrm{OQ}-4 \mathrm{OP}=$$

A
$$3 \hat{i}+8 \hat{j}$$
B
$$4 \hat{i}+6 \hat{j}$$
C
$$6 \hat{i}+8 \hat{j}$$
D
$$4 \hat{i}+3 \hat{j}$$
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

In quadrilateral $$A B C D, \mathbf{A B}=\mathbf{a}, \mathbf{B C}=\mathbf{b}$$. $$\mathbf{D A}=\mathbf{a}-\mathbf{b}, M$$ is the mid-point of $$B C$$ and $$X$$ is a point on DM such that, $$\mathbf{D X}=\frac{4}{5}$$ DM. Then, the points $$A, X$$ and $$C$$.

A
form an equilateral triangle.
B
are collinear
C
form an isosceles triangle
D
form a right angled triangle
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