WBJEE Mathematics Sample Paper I
80 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests | WBJEE Mathematics Sample Paper I
| 1 Crore+ students have signed up on EduRev. Have you? |
The eccentricity of the hyperbola 4x2 – 9y2 = 36 is
The length of the latus rectum of the ellipse 16x2+ 25y2 = 400 is
Length of latus rectum =
The vertex of the parabola y2+ 6x – 2y + 13 = 0 is
(y -1)2 - 6x - 12
Vertex → (2, 1)
(y -1)2 - 6x - 12
Vertex → (2, 1)
The coordinates of a moving point p are (2t2+ 4, 4t + 6). Then its locus will be a
The equation 8x2+ 12y2 – 4x + 4y – 1 = 0 represents
If the straight line y = mx lies outside of the circle x2+ y2 – 20y + 90 = 0, then the value of m will satisfy
The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is
Centre lies on y-axis locus x = 0
The coordinates of the two points lying on x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are
The intercept on the line y = x by the circle x2+ y2 – 2x = 0 is AB. Equation of the circle with AB as diameter is
If the coordinates of one end of a diameter of the circle x2+y2+4x–8y+5=0, is (2,1), the coordinates of the other end is
Centre circle (–2, 4)
If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y is
If 
and θ lies in the second quadrant, then cosθ is equal to
θ in 2nd quad Cosθ < 0
The solutions set of inequation cos–1x < sin–1x is
cos–1x < sin–1x is
√5<3 No solution
and 
then α + β is
If sinθ and cosθ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation
If A and B are two matrices such that A+B and AB are both defined, then
Addition is defined if order of A is equal to order of B
A B
nxm nxm is defined if m = n
⇒ A, B are square matrices of same order
is a symmetric matrix, then the value of x isA = AT
= Real
The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ) y + a sin θ = 0 is
y = a sin θ
x = a cos θ.
sin θ + cos θ = 0
⇒ tan θ = – 1 
The period of the function f(x) = cos 4x + tan 3x is
If y = 2x3 – 2x2 + 3x – 5, then for x = 2 and ∆ x = 0.1 value of ∆ y is
The approximate value of 
correct to 4 decimal places is
y = 2 + 1/80
dx is
Rolle’s theorem is
The general solution of the differential equation 
auxilary equation m2 + 8m + 16 = 0 ⇒ m = – 4
Solution 
The degree and order of the differential equation 
are respectively
The function f (x) is
The function f(x) = ax + b is strictly increasing for all real x if
f′ (x) = a
f′(x) > 0 ⇒ a > 0
The general solution of the differential equation 
C2 → C2 – C3
C3 → C3 + C2
C3 → C3 + ωC1
C2 → C2 – C1
4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is
A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is
If A and B are coefficients of xn in the expansions of (1+ x)2n and (1+x)2n – 1 respectively, then A/B is equal to
A = 2nCn.
B = 2n – 1Cn
If n > 1 is an integer and x ≠0, then (1 + x)n – nx – 1is divisible by
The number of diagonals in a polygon is 20. The number of sides of the polygon is
nC2 –n = 20
n = 8
Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0
If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, then 
If α and β are the roots of the equation x2 + x + 1 = 0, then the equation whose roots are α19 and β7 is
α and β are the roots of x2 + x + 1 = 0
α = ω β = ω2
α19= ω β7= ω2
x2 – (α19 + β7)x + α19β7= 0
Thou,
x2 – (ω + ω2 ) x + ω . ω2 = 0
x2 + x + 1 = 0
For the real parameter t, the locus of the complex number 
in the complex plane is
Given
Let z = x + iy
x = 1 – t2
y2 = 1 + t2
Thus, x + y2 = 2
y2 = 2 – x
y2 = – (x – 2)
Thus parabola
If ω ≠ 1 is a cube root of unity, then the sum of the series S = 1 + 2ω + 3ω² + .......... + 3nω3n – 1 is
If log3x + log3y = 2 + log32 and log3 (x + y) = 2, then
: log3x + log3y = 2 + log32
⇒ x.y = 18
log (x + y) = 2 ⇒ x + y = 9
we will get x = 3 and y = 6
log4928 = log724 × 7
log a . (2log a – log b)(3log a – 2 log b)
= T2 – T1 = log a – log b
= T3 – T2 = log a – log b
If in a triangle ABC, sin A, sin B, sin C are in A.P., then
: c1 → c1 + c2 + c3
Let f(x) = x3 e–3x, x > 0. Then the maximum value of f(x) is
f(x) = x3 .e–3x
= f′(x) = 3x2 e–3x + x3 e–3x (–3)
= x23e–3x[1 – x] = 0, x = 1
Maximum at x = 1
f(1) = e–3
The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec2 . The time taken by the particle to move the second metre is
Integrating Factor (I.F.) of the defferential equation
The differential equation of y = aebx (a & b are parameters) is
y = a.ebx ............ (i)
y1 = abebx
y1 = by ........................... (ii)
y2 = by1 ......................... (iii)
Dividing (ii) & (iii) 
= 2x f(x)
Let f(x) = tan–1x. Then f′(x) + f′′(x) is = 0, when x is equal to
f(x) = tan–1x
= π
Put A = 0.
If f(x) is continuous at x = 2, the value of λ will be
If f(x + 2y, x – 2y) = xy, then f(x, y) is equal to
The locus of the middle points of all chords of the parabola y2 = 4ax passing through the vertex is
2h = x, 2k = y
y2 = 4ax
k2 = 2ah
y2 = 2ax
|
4 videos|10 docs|54 tests
|
|
Use Code STAYHOME200 and get INR 200 additional OFF
|
Use Coupon Code |
|
4 videos|10 docs|54 tests
|
Download free EduRev App
Related content with WBJEE Mathematics Sample Paper I
|
|
|
|
Related tests with WBJEE Mathematics Sample Paper I
|
|
|
|
|
|
© EduRev
|
Follow Us
|