Maths · CBSE

Board exam

2024Class 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.

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Source: CBSE Board Examination 2024, Class 12 Mathematics (041), paper 65/1/1, published by CBSE. CBSE's ZIP of every set

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9 questions

Q1Section A1 mark
$A function f : R⁺ \to R (where R⁺ is the set of all non-negative real numbers) defined by f(x) = 4x + 3 is :$
1. A $one-one but not onto$
2. B $onto but not one-one$
3. C $both one-one and onto$
4. D $neither one-one nor onto$
Q2Section A1 mark
$If a matrix has 36 elements, the number of possible orders it can have, is :$
1. A $13$
2. B $3$
3. C $5$
4. D $9$
Q9Section A1 mark
$If the direction cosines of a line are \sqrt3 k, \sqrt3 k, \sqrt3 k, then the value of k is :$
1. A $\pm1$
2. B $\pm\sqrt3$
3. C $\pm3$
4. D $\pm1/3$
Q10Section A1 mark
$A linear programming problem deals with the optimization of a/an :$
1. A $logarithmic function$
2. B $linear function$
3. C $quadratic function$
4. D $exponential function$
Q15Section A1 mark
$The vector with terminal point A (2, -3, 5) and initial point B (3, -4, 7) is :$
1. A $î - ĵ + 2k̂$
2. B $î + ĵ + 2k̂$
3. C $-î - ĵ - 2k̂$
4. D $-î + ĵ - 2k̂$
Q16Section A1 mark
$The distance of point P(a, b, c) from y-axis is :$
1. A $b$
2. B $b²$
3. C $\sqrt(a² + c²)$
4. D $a² + c²$
Q18Section A1 mark
$If A and B are two non-zero square matrices of same order such that (A + B)² = A² + B², then :$
1. A $AB = O$
2. B $AB = -BA$
3. C $BA = O$
4. D $AB = BA$
Q22Section B2 marks
$Show that the function f(x) = 4x³ - 18x² + 27x - 7 has neither maxima nor minima.$
Q26Section C3 marks
1. a $A relation R on set A = {1, 2, 3, 4, 5} is defined as R = {(x, y) : |x² - y²| < 8}. Check whether the relation R is reflexive, symmetric and transitive. OR$
2. b $A function f is defined from R \to R as f(x) = ax + b, such that f(1) = 1 and f(2) = 3. Find function f(x). Hence, check whether function f(x) is one-one and onto or not.$