WBJEE Maths Answer Key 2025 (Available): Unofficial Key PDF

Questions

Answers

Q1) if f(x)={x2+3x+a, bx+2, x<=1, x>1, x e R, is everywhere differentiable then

A)a=3, b=5

Q2) Let p(x) be a real polynomial of the least degree that 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

C) 3

Q 3) The function f(x)= 2x3-3x2-12x+4, x eR has

C) one local maximum and one local minimum

Q4) Let x=f(x)+ f(2a-x), x[0,2a] and f(x)>0 for all x9[0,a]. Then (x) is

A)Decreasing on [0,a]

Q5) if g(f(x))= sin x and f(g(x))= (sin √x)2, then 

1. f(x)= sin2 x, g (x)=√x

Q6) The expression 24n-15n-1, where n N is divisible by 24n-15n-

1. 225

Q7) If z1, z2 are complex numbers such that 2z1/3z2 is a purely imaginary number, then the value of |z1-z2/z1+z2| is

Q8) The value of the integral ∫3√x/√9-x + x√x  dx 

A) 3/2

Q9) The line y-√3x+3=0 cuts the parabola y2=x+2 at the points P and Q. If the point X is (√3,0), then the value of XP XQ is

A) 4(2+√3/3

Q10) Let f(x)=|1-2x|, then

A) f(x) is continuous but not differentiable at x=1/2

Q11) if f is the inverse function of g and g(x)=1/1+xn, then value of f(x) is

A) 1+{f(x)}n

Q12) Let f be a function that is differentiable for all real x. If f(2) = -4 and f(x)>=6 for all x equivalent[2,4], then

C) f(4)>=8

Q13) If E and F are two independent events with P(E)= 0.3 and P(E u F0 = 0.5, then P(E/F)-P(F/E)

C)1/70

Q14) the set of points of discontinuity of the function f(x) = x-[x], x equivalent R is

D) Z

Q15) For what value of “a”, the sum of squares of the roots of the equation x2-(a-2)x-a+1=0 will have the least value

D) 1

Q16) ∫11 x3+|x|+1/x2+2|x|+1 dx is equal to

A) 2 log 2

Q17) If sum of n terms of an AP is 3n2+5n and its mth term is 164, then the value of m is

B) 27

Q18)  If 9P5+5, 9P4=10Pr, then the value of r is

C) 5

Q19) An n×n matrix is formed using 0,1, and -1 as its elements. The number of such matrices that are skew-symmetric is

D) 3n(n-1)/2

Q20) Let f(x) be a second-degree polynomial. If f(1) and p. Q, r are in AP then f(P) f(q), f(r) are

A) In AP

Q21) A function f is defined by f(x)=2+(x-1)2/3 on|0,2|. Find correct statement.

A), B), and C)

Q22) The straight line x-3/3=y-2/1=z-1/0 is

D) perpendicular to the z axis

Q23) If the sum of squares of the roots of the equation x2-(a-2)x-(a+1)=0 is least for an appropriate value of the variable parameter the value of a is

C) 1

Q24) Let x-y=0 and x+y=1 be two perpendicular diameters of a circle of radius R. The circle will pass through the origin if R is equal to

1/√2