Maths · CBSE

Board exam

2023Class 12Set 65/1/180 marks38 questions

9 of its 38 questions are here. The rest have a figure or are still being checked, so for now they're only in the official PDF.

Sit this paper against the clock, marked by its official answers, or get a new paper like it. Sign in first; practising is part of Pro.

Source: CBSE Board Examination 2023, Class 12 Mathematics (041), paper 65/1/1, published by CBSE. CBSE's ZIP of every set

Download PDF

9 questions

Q1Section A1 mark
$If for a square matrix A, A² - 3A + I = O and A⁻¹ = xA + yI, then the value of x + y is :$
1. A $-2$
2. B $2$
3. C $3$
4. D $-3$
Q3Section A1 mark
$Let A be a 3 \times 3 matrix such that |adj A| = 64. Then |A| is equal to :$
1. A $8 only$
2. B $-8 only$
3. C $64$
4. D $8 or -8$
Q9Section A1 mark
$The value of (î \times ĵ) \cdot ĵ + (ĵ \times î) \cdot k̂ is :$
1. A $2$
2. B $0$
3. C $1$
4. D $-1$
Q10Section A1 mark
$If a⃗ + b⃗ = î and a⃗ = 2î - 2ĵ + 2k̂, then |b⃗| equals :$
1. A $\sqrt14$
2. B $3$
3. C $\sqrt12$
4. D $\sqrt17$
Q17Section A1 mark
$The corner points of the feasible region in the graphical representation of a linear programming problem are (2, 72), (15, 20) and (40, 15). If z = 18x + 9y be the objective function, then :$
1. A $z is maximum at (2, 72), minimum at (15, 20)$
2. B $z is maximum at (15, 20), minimum at (40, 15)$
3. C $z is maximum at (40, 15), minimum at (15, 20)$
4. D $z is maximum at (40, 15), minimum at (2, 72)$
Q18Section A1 mark
$The number of corner points of the feasible region determined by the constraints x - y \geq 0, 2y \leq x + 2, x \geq 0, y \geq 0 is :$
1. A $2$
2. B $3$
3. C $4$
4. D $5$
Q22Section B2 marks
$Find all the vectors of magnitude 3\sqrt3 which are collinear to vector î + ĵ + k̂.$
Q34Section D5 marks
1. a $Find the vector and the Cartesian equations of a line passing through the point (1, 2, -4) and parallel to the line joining the points A(3, 3, -5) and B(1, 0, -11). Hence, find the distance between the two lines. OR$
2. b $Find the equations of the line passing through the points A(1, 2, 3) and B(3, 5, 9). Hence, find the coordinates of the points on this line which are at a distance of 14 units from point B.$
Q35Section D5 marks
$Find the area of the region bounded by the curves x² = y, y = x + 2 and x-axis, using integration.$

Board exam

2023Class 12Set 65/1/180 marks38 questions

9 of its 38 questions are here. The rest have a figure or are still being checked, so for now they're only in the official PDF.

Sit this paper against the clock, marked by its official answers, or get a new paper like it. Sign in first; practising is part of Pro.

Source: CBSE Board Examination 2023, Class 12 Mathematics (041), paper 65/1/1, published by CBSE. CBSE's ZIP of every set