CBSE 12 Maths Question Paper-2022 Set-3 by Pavan | Practice Test to Test Your Knowledge
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Engineering Courses
Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Certifications
Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

  2. Practice Tests
  3. CBSE 12 Maths Question Paper-2022 Set-3
CBSE 12 Maths Question Paper-2022 Set-3

CBSE 12 Maths Question Paper-2022 Set-3

This mock test includes actual CBSE Class 12 Maths board exam questions from the year 2022 Set-3, helping students understand exam trends and practice real paper format

2025-08-14
Pavan Pavan
CBSE Class 12 2022 Grade 12 Mathematics

Duration

25 min

Questions

22

Marking

Negative

You've not yet enrolled in this practice test. Please login to start practice test.

Questions Preview

If the distance of the point (1, 1, 1) from the plane x-y+z+λ=0 is 5/√3, find the value(s) of λ.

A
4, 6
B
-4, -6
C
5, -5
D
4, -6

Write the projection of the vector (b+c) on the vector a where a=2i-2j+k, b=i+2j-2k and c=2i-j+4k.

A
2
B
3
C
-2
D
6

Find the general solution of the differential equation: dy/dx = (3e^(2x)+3e^(4x))/(e^(x)+e^(-x))

A
y=3e^(2x)+C
B
y=3e^(3x)+C
C
y=3e^(x)+C
D
y=e^(3x)+C

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spade cards.

A
P(X=0) = 9/16, P(X=1) = 6/16, P(X=2) = 1/16
B
P(X=0) = 1/4, P(X=1) = 1/2, P(X=2) = 1/4
C
P(X=0) = 3/4, P(X=1) = 1/4, P(X=2) = 0
D
P(X=0) = 1/16, P(X=1) = 6/16, P(X=2) = 9/16

Find: ∫(dx)/(x^2-6x+13)

A
tan⁻¹((x-3)/2)+C
B
1/2 tan⁻¹((x-3)/2)+C
C
1/2 tan⁻¹((x+3)/2)+C
D
tan⁻¹((x+3)/2)+C

A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number 5 has appeared on atleast one die.

A
1/6
B
2/6
C
1/36
D
2/36

The probability that A hits the target is 2/5 and the probability that B hits it, is 1/3. If both try to hit the target independently, find the probability that the target is hit.

A
7/15
B
1/15
C
2/15
D
13/15

Find the shortest distance between the following lines: r=3i+5j+7k+λ(i-2j+k) and r=(-i-j-k)+μ(7i-6j+k).

A
28√30/15
B
28/15
C
15/28
D
28√30

The two adjacent sides of a parallelogram are represented by vectors 2i-4j+5k and i-2j-3k. Find the unit vector parallel to one of its diagonals. Also, find the area of the parallelogram.

A
Unit vector parallel to diagonal is 1/√11 (3i-6j+2k) and Area is √429 sq. units.
B
Unit vector parallel to diagonal is 1/√14 (3i-6j+2k) and Area is √429 sq. units.
C
Unit vector parallel to diagonal is 1/√14 (3i-6j+2k) and Area is √257 sq. units.
D
Unit vector parallel to diagonal is 1/√11 (3i-6j+2k) and Area is √257 sq. units.

If a=2i+2j+3k, b=-i+2j+k and c=3i+j are such vectors that vector (a+λb) is perpendicular to vector c, then find the value of λ.

A
λ=8
B
λ=6
C
λ=4
D
λ=-8

Find the particular solution of the differential equation x(dy/dx) - y = x²eˣ, given y(1)=0.

A
y = x(eˣ - e)
B
y = x(eˣ - 1)
C
y = x²(eˣ - e)
D
y = xeˣ

Find the general solution of the differential equation x(dy/dx) = y(log y - log x + 1).

A
y = Cx
B
y = xe^(Cx)
C
y = x(e^C)
D
y = xe^(Cy)

Evaluate: ∫(-π/2)^(π/2) (sin|x| + cos|x|) dx

A
2
B
4
C
3
D
0

Find the distance of the point (1, 2, 9) from the point of intersection of the line r=4i+2j+7k+λ(3i+4j+2k) and the plane r⋅(i-j+k)=10.

A
√14
B
2√14
C
√7
D
3√14

Show that the lines: (1-x)/2 = (y-3)/4 = z/-1 and (x-4)/3 = (2y-2)/-4 = z-1 are coplanar.

A
They are not coplanar
B
They are coplanar and intersect at (3, 7, -1)
C
They are coplanar and parallel
D
They are coplanar and intersect at (1, 3, 0)

Find the area of the region bounded by the curve 4x²=y and the line y=8x+12, using integration.

A
128/3 sq. units
B
64/3 sq. units
C
16 sq. units
D
100/3 sq. units

Find: ∫(x²+1)/((x-1)²(x+1)) dx

A
log|x+1| - 2log|x-1| + C
B
log|x+1| - 2log|x-1| - 2/(x-1) + C
C
log|x+1| - 1/(x-1) + C
D
log|x+1| + 2/(x-1) + C

Find the value of λ for which the vectors 2i - λj + k and i + 2j - 3k are orthogonal.

A
λ = 1
B
λ = -1
C
λ = 2
D
λ = -2

Find the general solution of the differential equation: log(dy/dx) = ax+by

A
a e^(ax) + b e^(-by) = C
B
a e^(ax) - b e^(-by) = C
C
(1/a)e^(ax) + (1/b)e^(-by) = C
D
a e^(ax) + b e^(-by) = 0

Find the area of the parallelogram whose adjacent sides are given by the vectors 3i + j + 2k and i - 2j + 4k.

A
√210 sq. units
B
√150 sq. units
C
√190 sq. units
D
√220 sq. units

Find the distance of the point (-2, 4, 5) from the line (x+3)/3 = (y-4)/5 = (z+8)/6.

A
√250
B
√251
C
√253
D
√254

A speaks truth in 75% of the cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

A
30%
B
35%
C
40%
D
45%