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. | Question | KCET 2024 Maths Answer Key |
|---|---|---|
| 1 | Corner 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 at | Any point on the line segment joining the points (0, 2) and (3, 0) |
| 2 | A the is thrown 10 times. The probability that an odd number will come up at least once is | 1023/1024 |
| 3 | A 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 is | 5/18 |
| 4 | If a random variable X follows the binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3) then p is equal to | 1/10 |
| 5 | If 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 |
| 6 | If 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 |
| 7 | The distance between the two planes 2x + 3y + 4z = 4 and 4x + 6y + z = 12 is | 2/√29 |
| 8 | The sine of the angle between the straight line (x – 2)/3 = (y – 3)/4 = (4 – z)/-5 and the plane 2x – 2y + z = 5 is | 1/5√2 |
| 9 | The equation xy = 0 in three-dimensional space represents | a pair of planes at right angles |
| 10 | The plane containing the point (3, 2, 0) and the line (x – 3)/1 = (y – 6)/5 = (z – 4)/4 is | x – y + z = 1 |
| 11 | Two 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 are | 6, 3 |
| 12 | If [ x ]2 – 5 [ x ] + 6 = 0, where [ x ] denotes the greatest integer function, then | x ∈ [2, 3] |
| 13 | If in two circles, arcs of the same length subtend angles 30° and 78° at the centre, then the ratio of their radii is | 13/5 |
| 14 | If Δ ABC is right-angled at C, then the value of tan A + tan B is | c2/ab |
| 15 | The real value of ‘α’ for which [ (1 – i sinα) / (1 + 2i sinα) ] is purely real is | nπ, n ∈ N |
| 16 | The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm, then | Breadth ≥ 15 cm |
| 17 | The value of 49C3 + 48C3 + 47C3 + 45C3 + 45C4 is | 50C4 |
| 18 | In the expansion (1 + x)n C1/C0 + 2C2/C1 + 3C3/C2 + … + nCn/Cn-1 is equal to | n(n + 1)/2 |
| 19 | If 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 is | 1/(rn + 1) |
| 20 | If A.M. and G.M. of roots of a quadratic equation are 5 and 4 respectively, then the quadratic equation is | x2 – 10x + 16 = 0 |
| 21 | The angle between the line x + y = 3 and the line joining the points (1, 1) and (-3, 4) is | tan-1(1/7) |
| 22 | The equation of parabola whose focus is (6,0) and directrix is x = – 6 is | y2 = 24x |
| 23 | lim (x → π/4) [ (√2 cosx – 1) / (cotx – 1) ] is equal to | 1/2 |
| 24 | The 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. |
| 25 | Let 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 is | S |
| 26 | Let f : R → R be given by f(x) = tan x. Then f-1(1) is | {nπ + π/4; n ∈ Z} |
| 27 | Let f : R → R be defined by f(x) = x2 + 1 Then the pre-images of 17 and -3 respectively are | {4, -4}, Φ |
| 28 | Let (gof) (x) = sin x and (fog) (x) = (sin√x)2. Then | f(x) = sin2x, g(x) = √x |
| 29 | Let 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) is | 6 |
| 30 | If cos-1x + cos-1y + cos-1z = 3, then x (y + z) + y (z + x) + z (x + y) equals to | 6 |
| 31 | If 2sin-1x – 3cos-1x = 4, x ∈ [-1,1] then 2sin-1x + 3cos-1x is equal to | (6π – 4)/5 |
| 32 | If A is a square matrix such that A2 = A, then (I + A)3 is equal to | 7A + I |
| 33 | If A = ( ( 1 1 ), ( 1 1 ) ), then A10 is equal to | 29A |
| 34 | If 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) is | 0 |
| 35 | If 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 to | 11 |
| 36 | If A = | ( x 1 ), ( 1 x ) | and B = | ( x 1 1 ), ( 1 x 1 ), ( 1 1 x ) |, then dB/dx is | 3A |
| 37 | Let f(x) = | ( cosx x 1 ), ( 2sinx x 2x ), ( sinx x x ) |. Then lim (x → 0) f(x)/x2 = | -1 |
| 38 | Which 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. |
| 39 | The function f(x) = |cos x| is | everywhere continuous but not differentiable at odd multiples of π/2 |
| 40 | If y = 2x3x, then dy/dx at x = 1 is | 6 |
| 41 | Let 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) is | 6 |
| 42 | The 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 to | 4/3 |
| 43 | d/dx [ cos2 (cot-1((2 + x)/(2 – x))1/2) ] is | 1/2 |
| 44 | For the function f(x) = x3 – 6x2 + 12x – 3; x = 2 is | not a critical point |
| 45 | The function xx ; x > 0 is strictly increasing at | x > 1/e |
| 46 | The maximum volume of the right circular cone with slant height 6 units is | 16√3 |
| 47 | If f(x) = x ex(1 – x) then f(x) is | increasing on [-1/2, 1] |
| 48 | ∫ [ sinx / (3 + 4cos2x ] dx = ? | -1/2√3 [ tan-1(2cosx/√3) + C |
| 49 | -π∫π ( 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 |
| 52 | 1∫5 ( | x – 3 | + | 1 – x | ) dx = ? | 12 |
| 53 | lim (x → ∞) [ ( n2 / (n2 + 12)) + ( n2 / (n2 + 22)) + ( n2 / (n2 + 32)) + … + ( 1 / 5n) ] = | tan-12 |
| 54 | The area of the region bounded by the line y = 3x and the curve y = x2 in sq. units is | 9/2 |
| 55 | The area of the region bounded by the line y = x and the curve v = x3 is | 0.5 sq. units. |
| 56 | The solution of edy/dx = x + 1, y(0) = 3 is | y + x – 3 = (x +1) log (x + 1) |
| 57 | The 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 is | xy = C |
| 58 | The 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 |
| 59 | The volume of the parallelopiped whose co-terminous edges are j + k, i + k, and i + j is | 2 cu.units |
| 60 | Let a and b be two unit vectors and θ is the angle between them. Then a + b is a unit vector if | 2π/3 |