KCET Maths Answer Key 2024 (Out): Maths Questions with Solutions

Karnataka CET Maths exam is over. Now, students are looking for KCET Math answer key 2024. This paper’s unofficial KCET answer key and solution is available in this article.

KCET Maths Answer Key 2024 with Questions

KCET paper all sets had same questions, only questions were shuffled. So, here are the direct questions and answers without any mentioning of sets. Hense, all set students can refer these questions and answers.

Below, we have tabulated the KCET maths exam solution along with questions

Sr. No.QuestionKCET 2024 Maths Answer Key
1Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0.5). Let x = 4x + 6y be the objective function. The minimum value of z occurs atAny point on the line segment joining the points (0, 2) and (3, 0)
2A the is thrown 10 times. The probability that an odd number will come up at least once is1023/1024
3A random variable X has the following probability distribution:X012P(X)25/36k1/36If the mean of thee random variable X is 1/3 then the variance is5/18
4If a random variable X follows the binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3) then p is equal to1/10
5If a, b, c are three non-coplanar vectors and p, q, r are vectors defined by
p = ( b × c ) / [ a    b    c ], 
q = ( c × a ) / [ a    b    c ], 
r = ( a × b ) / [ a    b    c ], then, 
( a + b ) . p + ( b + c ) . q + ( c + a ) . r is
3
6If lines (x – 1)/-3 = (y – 2)/2k = (z – 3)/2 and (x – 1)/3k = (y – 5)/1 = (z – 6)/-5 are mutually perpendicular, then k is equal to-10/7
7The distance between the two planes 2x + 3y + 4z = 4 and 4x + 6y + z = 12 is2/√29
8The sine of the angle between the straight line (x – 2)/3 = (y – 3)/4 = (4 – z)/-5 and the plane 2x – 2y + z = 5 is1/5√2
9The equation xy = 0 in three-dimensional space representsa pair of planes at right angles
10The plane containing the point (3, 2, 0) and the line (x – 3)/1 = (y – 6)/5 = (z – 4)/4 is x – y + z = 1
11Two finite sets have m and n elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are6, 3
12If [ x ]– 5 [ x ] + 6 = 0, where [ x ] denotes the greatest integer function, thenx ∈ [2, 3]
13If in two circles, arcs of the same length subtend angles 30° and 78° at the centre, then the ratio of their radii is13/5
14If Δ ABC is right-angled at C, then the value of tan A + tan B isc2/ab
15The real value of ‘α’ for which [ (1 – i sinα) / (1 + 2i sinα) ] is purely real is nπ, n ∈ N
16The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm, thenBreadth ≥ 15 cm
17The value of 49C3 + 48C3 + 47C3 + 45C3 + 45C4 is50C4
18In the expansion (1 + x)n
C1/C0 + 2C2/C1 + 3C3/C2 + … + nCn/Cn-1 is equal to 
n(n + 1)/2
19If Sn stands for sum to n-terms of a G.P. with 4 ‘a’ as the first term and ‘r’ as the common ratio then Sn / S2n is1/(rn + 1)
20If A.M. and G.M. of roots of a quadratic equation are 5 and 4 respectively, then the quadratic equation isx2 – 10x + 16 = 0
21The angle between the line x + y = 3 and the line joining the points (1, 1) and (-3, 4) istan-1(1/7)
22The equation of parabola whose focus is (6,0) and directrix is x = – 6 isy2 = 24x
23lim (x → π/4) [ (√2 cosx – 1) / (cotx – 1) ] is equal to 1/2
24The negation of the statement
“For every real number x; x2 + 5 is positive”
is
There exists at least one real number x such that x2 + 5 is not positive.
25Let a, b, c, d and e be the observations with mean m and standard deviation S. The standard deviation of the observations a + k b – k r + k d + k and e + k isS
26Let f : R → R be given by f(x) = tan x. Then f-1(1) is{nπ + π/4; n ∈ Z}
27Let f : R → R be defined by f(x) = x2 + 1 Then the pre-images of 17 and -3 respectively are{4, -4}, Φ
28Let (gof) (x) = sin x and (fog) (x) = (sin√x)2. Thenf(x) = sin2x, g(x) = √x
29Let A= {2, 3, 4, 5 ,………….16, 17, 18}. Let R be the relation on the set A of ordered pairs of positive integers defined by (a, b) R (c, d) if and only if ad = bc for all (a, b) (c, d) in A × A.Then the number of ordered pairs of the equivalence class of (3, 2) is6
30If cos-1x + cos-1y + cos-1z = 3, then x (y + z) + y (z + x) + z (x + y) equals to6
31If 2sin-1x – 3cos-1x = 4, x ∈ [-1,1] then 2sin-1x + 3cos-1x is equal to(6π – 4)/5
32If A is a square matrix such that A2 = A, then (I + A)3 is equal to7A + I
33If A = ( ( 1    1 ), ( 1    1 ) ), then A10 is equal to 29A
34If f(x) = | ( x – 3    2x2 – 18    2x3 – 81), (x – 5    2x2 – 50    4x3 – 500), (1    2    3) |, then f(1) . f(3) + f(3) . f(5) + f(5) . f(1) is0
35If P = [ ( 1    α    3 ), ( 1    3    3 ), ( 2    4    4 ) ] is the adjoint of a 3 x 3 matrix A and | A | = 4, then α is equal to11
36If A = | ( x    1 ), ( 1    x ) | and B = | ( x    1    1 ), ( 1    x    1 ), ( 1    1    x ) |, then dB/dx is3A
37Let f(x) = | ( cosx    x    1 ), ( 2sinx    x    2x ), ( sinx    x    x ) |. Then lim (x → 0) f(x)/x2 = -1
38Which one of the following observations is correct for the features of the logarithm function to any base b > 1 ?The point (1, 0) is always on the graph of the logarithm function.
39The function f(x) = |cos x| iseverywhere continuous but not differentiable at odd multiples of π/2
40If y = 2x3x, then dy/dx at x = 1 is6
41Let the function satisfy the equation f(x + y) = f(x) f(y) for all x, y ∈ R where f(0) ≠ 0. If f(5) = 3 and f'(0) = 2 then f'(5) is6
42The value of C in (0; 2) satisfying the mean value theorem for the function f(x) = x (x – 1)2, x ∈ [0, 2] is equal to4/3
43d/dx [ cos2 (cot-1((2 + x)/(2 – x))1/2) ] is1/2
44For the function f(x) = x3 – 6x2 + 12x – 3; x = 2 isnot a critical point
45The function xx ; x > 0 is strictly increasing atx > 1/e
46The maximum volume of the right circular cone with slant height 6 units is16√3
47If f(x) = x ex(1 – x) then f(x) isincreasing on [-1/2, 1]
48∫ [ sinx / (3 + 4cos2x ] dx = ?-1/2√3 [ tan-1(2cosx/√3) + C
49π ( 1 – x2 ) sinx cos2x dx = ?0
50∫ { 1 / (x [6 (log x)2 + 7 log x + 2 ] } dx = ?log | (2 log x + 1) / (3 log x + 2 ) | + C
51∫ [ sin(5x/2) / sin(x/2) ] dx = ?x + 2 sin x + sin 2x + C
5215 ( | x – 3 | + | 1 – x | ) dx = ?12
53lim (x → ∞) [ ( n2 / (n2 + 12)) + ( n2 / (n2 + 22)) + ( n2 / (n2 + 32)) + … + ( 1 / 5n) ] = tan-12
54The area of the region bounded by the line y = 3x and the curve y = x2 in sq. units is9/2
55The area of the region bounded by the line y = x and the curve v = x3 is0.5 sq. units.
56The solution of edy/dx = x + 1, y(0) = 3 isy + x – 3 = (x +1) log (x + 1)
57The family of curves whose x and y intercepts of a tangent at any point are respectively double the x and y coordinates of that point isxy = C
58The vectors AB = 3 i + 4 k and AC = 5 i – 2 j + 4 k are the sides of a triangle ABC. The length of the median through A is√18
59The volume of the parallelopiped whose co-terminous edges are j + k, i + k, and i + j is2 cu.units
60Let a and b be two unit vectors and θ is the angle between them. Then a + b is a unit vector if2π/3

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