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Question Bank [2022] Maths - Question Bank [2022]

Maharashtra Board - STD 12 - Maths (MSBSHSE - Semi English Medium). 638 questions in this chapter.

Question types

Question Bank [2022] question types

638 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

638
Questions
5
Question groups
5
Question types
Sample Questions

Question Bank [2022] questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The coordinates of the foot of perpendicular drawn from the origin to the plane 2x + y − 2z = 18 are ______
  • A
    (4,2,4)
  • B
    (-4,2,4)
  • C
    (-4,-2,4)
  • ✓
    (4,2,-4)

Answer: D.

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Q 2MCQ1 Mark
The perpendicular distance of the origin from the plane $x-3 y+4 z=6$ is_____
  • A
    6
  • ✓
    $\frac{6}{\sqrt{26}}$
  • C
    36
  • D
    $\frac{1}{\sqrt{26}}$

Answer: B.

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Q 3MCQ1 Mark
If the foot of the perpendicular drawn from the origin to the plane is $(4, −2, -5),$ then the equation of the plane is ______
  • A
    $4 x+y+5 z=14$
  • ✓
    $4 x-2 y-5 z=45$
  • C
    $x-2 y-5 z=10$
  • D
    $4 x+y+6 z=11$

Answer: B.

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Q 4MCQ1 Mark
The direction cosines of the normal to the plane $2 x-y+2 z=3$ are______
  • ✓
    $\frac{2}{3}, \frac{-1}{3}, \frac{2}{3}$
  • B
    $\frac{-2}{3}, \frac{1}{3}, \frac{-2}{3}$
  • C
    $\frac{2}{3}, \frac{1}{3}, \frac{2}{3}$
  • D
    $\frac{2}{3}, \frac{-1}{3}, \frac{-2}{3}$

Answer: A.

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Q 5MCQ1 Mark
If the planes $2 x-m y+z=3$ and $4 x-y+2 z=5$ are parallel then $m=$____
  • A
    -2
  • B
    2
  • C
    $\frac{-1}{2}$
  • ✓
    $\frac{1}{2}$

Answer: D.

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Q 15Solve the Following Question.(2 Marks)2 Marks
Find the position vector of point $R$ which divides the line joining the points $P$ and $Q$ whose position vectors are $2 \hat{ i }-\hat{ j }+3 \widehat{ k }$ and $-5 \hat{ i }+2 \hat{ j }-5 \widehat{ k }$ in the ratio $3: 2$
(i) internally
(ii) externally
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