WBJEE Mathematics Answer Key 2025 Unofficial (OUT) for all Sets

WBJEE Mathematics Answer Key 2025 Unofficial (OUT)

WBJEE Mathematics Answer Key 2025 Unofficial (OUT): Students who took WBJEE Mathematics 2025 exam can find the unofficial answer key for all the sets. The exam was conducted offline, and the answer key has been prepared by subject experts. While all question sets contain the same questions, their order is shuffled, allowing students to verify their answers directly. The Mathematics section of  WBJEE 2025  includes 75 questions. The total marks of the Mathematics section are 100. Candidates can use the reliable unofficial answer key to analyze their performance and calculate expected scores. All questions in the question paper are Multiple-Choice Questions (MCQs), with four options against each question. There will be three categories of questions in each subject.

Also Read | WBJEE Unofficial Answer Key 2025 LIVE Updates

WBJEE Mathematics Answer Key 2025 Unofficial

The unofficial answer key for WBJEE Mathematics 2025 will be provided below in a set-wise PDF format for students to download and verify their answers.

Sr.No. (Not Q.No.)	Question	Answer
1	If f(x)= {x 2 + 3x + a ,x<=1, bx+2, x>1 , x∈R, is everywhere differentiable, then	a=3, b=5
2	Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3 If p(1) = 6 and p(3) = 2 then p'(0) is equal to	3
3	The function f(x)=2x-3x²-12x+4, x∈R has	one local maximum and one local minimum.
4	Let ϕ(x)= f(x)+(2x), x∈ [0, 2a] and f'(x)>0 for all x∈[0, a] Then ϕ(x)	decreasing on [0,a]
5	If g(f(x))= |sinx| and f(g(x))= (sin√x)², then	f(x)= sin 2 x, g(x)=√x
6	The expression 2 4n -15n-1,  where n∈N (the set of natural numbers) is divisible by	225
7	If z are complex numbers such that is 2z1/3z2 is a purely imaginary numbers, then the value of |z1-z2/(z1+z2)|	1
8	The value of intergral	3/2
9	The  line y-√3 x + 3 = 0 cuts the parabola y 2 = x + 2 at the points P and Q. If the coordiantes on point X are (√3, 0) then the value of XP-XQ is	4(2+√3)/3
10	Let f(x)=|1 -2x|, then	f(x) is continuous but not differentiable at x=1/2
11	If 'f' is the inverse function of 'g' and g'(x) = 1/1+x n then the value of f'(x)	1+{f(x)} n
12	If the matrix is orthogonal, then the values of a, b, c are
13		1/5
14	A function f: R→R, satisfies f[(x+y)/3]= [f(x)+f(x)+f(0)]/3 for all x,y ∈R.  If the function 'f' ids differentiable at x=0, then f is	linear
15	Let f be a function which is differentiable for all real x. If f(2)= - 41 and f'(x) >= 6 for all x ∈[2, 4] , then	f(4)>=8
16	If E and F equals are two independent events with P(E)= 0.3 and P(EUF) =0.5, then P(E/F)-P(F/E) equals	1/70
17	The set of points of discontinuity of the function f(x)= x-[x], x∈R is	Z
18	For what value of 'a', the sum of the squares of the roots at the equation x 2 -(a-2)x-a+1=0 will have the least value?	a=1
19		log 2
20	If a, b, c are non-coplanar vectors and A. is a real number then the vectors a+2b+3c,  λb+4c and (2λ-1)  are non-coplanar for	all excpet two values of λ
21	Let ω (≠1) be a cubic root of unity. Then the minimum value of the set  {[a+bω+cω 2 ]} 2 distinct non-zero integers) equals are	3
22		2-√2
23	If the sum of 'n' terms of an A.P. is 3m² + 5n and its mth term is 164, then the value of m is	27
24		9
25	If 9 P 5 +5. 9 P 4 = 10 P r then the value of r is	5
26	If"θ" is the angle between two vectors a and b such that a =7,b =1 and |axb|² =k² -(a-b)² then the values of k and θ are	k=7 and θ is arbitrary
27	Consider three points P(cosα, sinβ), Q(sinα, cosβ) and R (0,0), where 0<α, β<π/4,  then	P, Q, R are non collinear
28	An nxn matrix is formed using 0, 1 and 1 as its elements. The number of such matrices which are skew symmetric is	3 n(n-1)/2
29	Suppose α, β,γ are the roots of the equation x 3 +qx+r=0 (with r≠0) and they are in A.P. Then the rank of the matrix is	2
30	Let f n (x)= tan(x/2)(1 + sec(x))(1 + sec(2x)) ...(1+sec 2 n x) then	f 5 (π/16)=1
31		52 C 4
32	If adj B=A, |P|=|Q|, then adj (Q -1 BP -1 ))=	PAQ
33	Lat a,b and c be vectors of equal magnitude such that the angle between a and b is α, b and c is β and c and a is γ. Then the minimum value of cosα + cosβ+cosγ is	3/2
34	Let f(x) be a second degree polynomial. If f(1)= F(-1) and p, q, are in A.P then f'(p), f'(q), f'(r) are	in A.P.
35	The line parallel to the x-axis passing through the intersection of the lines ax + 2by +3b=0 and bx-2ay-3a where (a, b)≠ (0,0) is	below x-axis at a distance 3/2 from it
36	A function/is defined by f(x)= 2+(x-1) 2/3 on [0, 2]. Which of the following statements is incorrect?	Reoole's theorem is applicable on  [0,2]
37	The number of reflexive relations on a set A of n elements is equal to n	2 n(n-1)
38	Let f(t) be continuous on [0.5], and differentiable in (0, 5). If f(0)= 0 and |f'(x)|<1/5 for all x in (0, 5) then Vex in [0,5]	|f(x)|<=1
39		tan 10-10
40	If cos- 1 α+cos -1 β+cos -1 γ=3π, then α(3+γ)+β(y + α) + γ(α + β) is equal to	6
41	If α=3i-k, |β |= sqrt(5) and α.β= 3, then the area of the parallelogram for which α and β are adjacent tides is	√41
42	If x = - 1 and x = 2 are extreme points of f(x) = α log|x| + βx 2 + x, (x ≠0) then	α=2, β=-1/2
43		2
44	If a, b, c are positive real numbers each distinct from unity, then the value of derterminant	0
45	The straight line (x-3)/2= (y-2)/1 =(z- 1)/0 is	parallel to z-axis
46	The sum of the first four terms of an arithmetic progression is 56. The sum of the last four terms is 112. If its first term is 11, then the number of terms is	11
47		0
48	If the sum of the squares of the roots of the equation  x 2 -(a-2)x(a+1)=0 is less for an appropriate value of the variable parameter a & then that value of 'a' will be	1
49	If (1+x-2x 2 ) 6 = 1 + ax + a 2 x² +.....a 12 x 12 then the value of a 2 +a 4 +a 6 ....._a 12 is	31
50	Let a,b,e be unit vectors Suppose a.b-a.c=0,  and the angle between b and c is π/6. Then a is	bxc
51	The probability that a non loop year selected at random will have 53 Sundays or 53 Saturdays is	2/7
52	If |z1|=|z2|=|z3| and Z1+Z2+Z3=0, then the area of the tringle whose vertices are Z1.Z2.Z3 is	3√3/4
53	Suppose A and B are respectively maximum and minimum values of f(θ). Then (A, B0 is equal to Then (Alb	(2, 0)
54
55	Let f(x)= max(x+x-[x]}, where [x] stands for the greatest integer not greater than x. Then ∫ 3 -3 f(x) dx has the value	21/2
56	If a, b, c are in A.P. and if the equations (b-c)x²+(c-a)x+(a-b)=0 and 2(c+a)x²+(b+c)x=0 have a common root, then	a 2 , c 2 , b 2 are in A.P.
57	Let x-y= 0 and a + y = 1 be two perpendicular diameters of a circle of radus R. The circle will pass through the origin if R is equal to	1/√2
58	Let f(x)= |x-α|+ |x-ẞl, where a, ẞ are the roots of the equation x³-3x+2=0. Then the number of points in (α,ẞ] at which f is not differentiable is	0
59	The maximum number of common normals of y 2 = 4ax and x 2 = 4by is equal to	5
60	The number of common tangents x 2 +y 2 -4x+6y-12= 0, x 2 +y 2 -6x+18y+26= 0, is	3
61	The number of solutions of sin -1 x+ sin -1 ( 1-x) =cos -1 x is	2
62	Let u+v+w=3, u, v, ∈ R and f(x) = ux²+vx+w be such that f(x + y) = f(x)+f(x)+xy, ∀ x, y,z ∈ R. Then f(1) is equal to	3
63		0
64	If cos (θ+Φ)=3/5, sin (θ+Φ)= 5/13, 0<θ<π/4,  then cot (2θ) has the value	16/63
65	If f(x) and g(x) are two polynomials such that Φ(x)= f(x 3 )+xg(x 3 ) is  divisible by x² + x + 1, then	Φ(x) is divisible by (x-1)
66	The equation sin 4 x-(p+2) sin²x-(p+3)=0 has a solution, the p must lie in the interval	[-3, -2]
67	If 0 <= a, b<= 3 and the equation x 2 + 4 + 3cos(ax + b) = 2x has real solutions, then the value of (a + b) is	π
68	Let f(x)=x 3 ,x€[-1,1]. Then which of the following are correct?	'f' has the maximum at x=1
69	Three numbers are chosen at random without replacement from (1, 2,3.....10). The probability that the minimum of the chosen numbers is 3 or their maximum is 7, is	11/40
70	The population p(t) at time of a certain mouse species follows the differential equation, dp(t)/dt= 0.5 p(t)-450. If p(0)=850, then the time at which the population becomes zero is	2 log 18
71	If P is a non-singular matrix of order 5x5 and the sum of the elements of each sum of the elements of each row is 1, then the sum of the elements of each row in P -1 is	1
72	The solution set of the equation (x∈(0, π/2))*(tan(tanπx) = cot (π cot x) is	Φ
73		π/4
74	The value ∫ 100 -100 (x+x 3 +x 5 )/(1+x 2+ x 4 +x 6 ) dx is	0
75		f+g is continuous at the x=2/3 but/and gare discontinuous at x =2/3

Also Read | WBJEE Result Expected Release Date 2025

In the Mathematics section, each question in Category 1 carries 1 mark. A total of 50 questions are asked, and for each incorrect option, 0.25 marks are deducted. In Category 2 total of 15 questions are asked, each carrying 2 marks. For each incorrect attempt, 0.5 marks are deducted. Each question in Category 3 carries 2 marks, with a total of 10 questions. There is no negative marking in this category.

WBJEE Subject-wise Answer Key 2025 Unofficial |

WBJEE 2025 Expected Rank |

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