1
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A plane $\pi_1$ passing through the point $3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is perpendicular to the vector $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and another plane $\pi_2$ passing through the point $2 \hat{\mathbf{i}}+7 \hat{\mathbf{k}}-8 \hat{\mathbf{k}}$ is perpendicular to the vector $3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$. If $p_1$ and $p_2$ are the perpendicular distances from the origin to the planes $\pi_1$ and $\pi_2$ respectively, then $p_1-p_2=$
A
1
B
2
C
3
D
4
2
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$A(2,3, k), B(-1, k,-1)$ and $C(4,-3,2)$ are the vertices of $\triangle A B C$. If $A B=A C$ and $k>0$, then $\triangle A B C$ is
A
an equilateral triangle
B
a right-angled isosceles triangle
C
an isosceles triangle but not right angled
D
an obtuse angled isosceles triangle
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $a, b$ and $c$ are the intercepts made on $X, Y, Z$-axes respectively by the plane passing through the points $(1,0,-2),(3,-1,2)$ and $(0,-3,4)$, then $3 a+4 b+7 c=$
A
-5
B
5
C
-15
D
15
4
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\hat{\mathbf{i}}+\hat{\mathbf{j}}, \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{k}}+\hat{\mathbf{i}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are the position vectors of the points $A, B, C, D, E$ respectively, then the point of intersection of the line $A B$ and the plane passing through $C, D, E$ is.
A
$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$
B
$\frac{1}{2} \hat{\mathbf{i}}+\hat{\mathrm{j}}+\frac{1}{2} \hat{\mathbf{k}}$
C
$\left.\frac{1}{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\right)$
D
$\frac{1}{2} \hat{i}-\hat{j}+\frac{1}{2} \hat{k}$
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