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Mathematics · Class 11 Science

West Bengal Wbchse Class 11 Mathematics — Real Previous-Year Papers

with complete answers

Real previous-year board papers, year by year — the official exam pattern, the full question paper, and every question solved the concept-first way. Distinct from the chapter-wise textbook bank.

2018–2018
Years of papers
1
Total Papers
1
Real Board Papers
0
Sample papers
50
Real-paper Q & A
0
Sample-paper Q & A

Real board-paper questions available, by year

50 Q2018complete

West Bengal HS First Year (WBCHSE Class XI) Annual Examination 2018 · Set ANNUAL

Real board examination

This paper has 38 questions on a topic removed in CBSE’s 2023-24 syllabus update (each marked Not in syllabus). It’s kept for historical accuracy — the exam really asked it that year — but isn’t in the current syllabus and doesn’t count toward a concept’s importance. Switch to to focus on what’s still examinable.

About this paper

The real Class-12 board examination held in 2018. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks
—
Questions
—
Duration
—
Sections
—

The marks / questions / duration above are the official exam pattern. We currently have 50 of this paper’s questions, with 50 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

The question paper

The questions we hold for this paper, laid out by section. Solutions are on the Answers tab.

Board Examination

Mathematics

West Bengal HS First Year (WBCHSE Class XI) Annual Examination 2018 · Set ANNUAL

Series/Set: ANNUALRoll No. ________
Time Allowed: —Maximum Marks: —
Section A

Q1.
All possible subsets of set φ is
  • (a) 0
  • (b) 1
  • (c) 2
  • (d) None of these.
⚠ This question is not in the current syllabus
[1]
Q2.
Value of ω^n + ω^2n, where ω = (-1+i√3)/2 and n = 3k+1, is
  • (a) 0
  • (b) -1
  • (c) 1
  • (d) None of these.
⚠ This question is not in the current syllabus
[1]
Q3.
If ⁿCₚ = ⁿCq, then
  • (a) n≠p or p+q=n
  • (b) p=q or p-q=n
  • (c) n=p=q or p+q≠n
  • (d) p=q or p+q=n.
⚠ This question is not in the current syllabus
[1]
Q4.
Value of sin 36° is
  • (a) (1/4)√(10-2√5)
  • (b) (1/4)√(10+2√5)
  • (c) (1/4)√(10+√5)
  • (d) (1/4)√(10-√5).
⚠ This question is not in the current syllabus
[1]
Q5.
The value of lim(x→4) (e^x - e^4)/(x-4) is
  • (a) e^-4
  • (b) e^4
  • (c) 1
  • (d) None of these.
[1]
Q6.
Find the point of z-axis which is equidistant from the points (1, 5, 7) and (5, 1, -4).
  • (a) (0, 0, 3/2)
  • (b) (0, 0, 5)
  • (c) (0, 5, 0)
  • (d) (4, 2, 3).
⚠ This question is not in the current syllabus — Asked in the 2018 WBCHSE Class-XI annual paper; 3D coordinate geometry is not in the current Class-XI syllabus.
[1]
Q7.
The angle made by the straight line x cosα + y sinα = p with the negative direction of x-axis is
  • (a) π/2+α
  • (b) α
  • (c) -α
  • (d) π/2-α.
⚠ This question is not in the current syllabus
[1]
Page 1 of 8
Q8.
If f(x) = |x|, then f'(0) is (a) 0 (b) 1 (c) -1 (d) None of these.
[1]
Q9.
In single throw of two dice, the probability of obtaining 'a total of 8' is (a) 8/36 (b) 3/36 (c) 9/36 (d) 5/36.
[1]
Q10.
If y = 2x + 3, and variance of y is 4, then the standard deviation of x is (a) -1 (b) 4 (c) 1 (d) 2.
⚠ This question is not in the current syllabus
[1]
Section B

Q1.
If A∩B' = φ, then show that A = A∩B, and hence show that A⊆B.
⚠ This question is not in the current syllabus
[2]
Q2.
Find the domain and range of the real function f(x) = 1/(1-x²).
[2]
Q3.
Prove that cos² 48° - sin² 12° = (√5 + 1)/8.
⚠ This question is not in the current syllabus
[2]
Q4.
Show that cot 2x cot x - cot 3x cot 2x - cot 3x cot x = 1.
⚠ This question is not in the current syllabus
[2]
Q5.
Find the value of n, so that (a^(n+1)+b^(n+1))/(aⁿ+bⁿ) may be the geometric mean between a and b.
⚠ This question is not in the current syllabus
[2]
Q6.
Find the value of r, if the coefficients of (2r+4)-th and (r-2)-th terms in the expansion of (1+x)¹8 are equal.
⚠ This question is not in the current syllabus
[2]
Page 2 of 8
Q7.
Find the principal amplitude of (-1-i).
⚠ This question is not in the current syllabus
[2]
Q8.
Find the number of squares in Chessboard.
⚠ This question is not in the current syllabus
[2]
Q9.
Find the focus of the parabola y = x² + x + 1.
⚠ This question is not in the current syllabus
[2]
Q10.
Find the equation of a circle with centre (h, k) and touching both the axes.
⚠ This question is not in the current syllabus
[2]
Q11.
Evaluate: lim(x→π/6) (√3 sin x - cos x)/(x - π/6).
[2]
Q12.
Prove that the derivative of an odd function is an even function.
[2]
Q13.
Find the variance of first n natural numbers.
⚠ This question is not in the current syllabus
[2]
Q14.
If P(A) = 2/3, P(B) = 1/2, P(A∩B) = 1/6, then find the value of P(A∩B') and P(A∪B).
[2]
Q15.
Prove that the major axis of an ellipse is greater than its minor axis.
⚠ This question is not in the current syllabus
[2]
Page 3 of 8
Section C

Q1.
Find the eccentricity of a hyperbola whose conjugate axis and latus rectum are equal.
⚠ This question is not in the current syllabus
[3]
Section D

Q1.
Let A = x∈N : x²-5x+6=0, B = x∈W : 0≤x<2 and C = x∈N : x<3, then verify that A×(B∪C) = (A×B)∪(A×C).
[4]
Q2.
Prove that in any ΔABC, (b-c)cot(A/2) + (c-a)cot(B/2) + (a-b)cot(C/2) = 0.
⚠ This question is not in the current syllabus
[4]
Q3.
Solve: sec x - tan x = √3.
⚠ This question is not in the current syllabus
[4]
Q4.
If p-th, q-th and r-th terms of an AP as well as those of a GP are a, b, c respectively, then prove that a^(b-c) . b^(c-a) . c^(a-b) = 1.
⚠ This question is not in the current syllabus
[4]
Page 4 of 8
Q5.
Using the principle of mathematical induction, prove that xⁿ - yⁿ is divisible by (x-y) for all n∈N.
⚠ This question is not in the current syllabus
[4]
Q6.
If z = x + iy and w = (1-iz)/(1+iz) such that |w| = 1, then show that z is purely real.
⚠ This question is not in the current syllabus
[4]
Q7.
Find the rank of the word 'MOTHER' in dictionary format.
⚠ This question is not in the current syllabus
[4]
Q8.
If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x)²n are in A.P., show that 2n²-9n+7 = 0.
⚠ This question is not in the current syllabus
[4]
Q9.
(2a, 0) and (0, a) are the extremities of the base of an isosceles triangle, and the equation of one of the equal sides is x = 2a. Find the equations of other two sides and the area of triangle.
⚠ This question is not in the current syllabus
[4]
Q10.
A variable straight line passes through the point of intersection of straight lines x/a+y/b=1 and x/b+y/a=1 and intersects the axes at P and Q. Find the locus of mid-point of PQ.
⚠ This question is not in the current syllabus
[4]
Page 5 of 8
Q11.
The abscissae of the two points A and B are the roots of the equation x²+2ax-b²=0 and their ordinates are the roots of the equation x²+2px-q²=0. Find the equation and the radius of the circle with AB as diameter.
⚠ This question is not in the current syllabus
[4]
Q12.
If 2f(x)+f(-x) = 1+x, find f'(10), where f'(x) denotes derivative of f(x).
[4]
Q13.
Evaluate lim(x→π/4) (4√2-(cos x+sin x)⁵)/(1-sin 2x).
[4]
Q14.
a) Write the negation of each of the following statements: p: For every real number x, x²>x; q: For every real number x, either x>1 or x<1. b) "Mathematics is fun" - check whether this sentence is a statement.
⚠ This question is not in the current syllabus — Asked in the 2018 WBCHSE Class-XI annual paper; Mathematical Reasoning is not in the current WBCHSE syllabus.
[4]
Q15.
Consider the statement p: If x is a real number such that x³+4x=0, then x=0, prove that p is a true statement, using a) method of contradiction and b) method of contrapositive.
⚠ This question is not in the current syllabus — Asked in the 2018 WBCHSE Class-XI annual paper; Mathematical Reasoning is not in the current WBCHSE syllabus.
[4]
Q16.
A bag contains 5 white and 4 black balls. If 3 balls are drawn at random, find the probability that at least two of them are white.
[4]
Page 6 of 8
Q17.
The arithmetic mean and standard deviation of 7 observations are respectively 8 and 4. If five of the observations are 2, 4, 10, 12 and 14, then find the values of the remaining two.
⚠ This question is not in the current syllabus
[4]
Section E

Q1.
Prove that if x = a(cosθ+sinθ sin2θ) and y = a(sinθ+cosθ sin2θ), then (x+y)^(2/3)+(x-y)^(2/3) = 2a^(2/3).
⚠ This question is not in the current syllabus
[5]
Q2.
Show that 3[sin⁴(3π/2-α)+sin⁴(3π+α)] - 2[sin⁶(π/2+α)+sin⁶(5π-α)] = 1.
⚠ This question is not in the current syllabus
[5]
Q3.
Draw the graph of the solution set of the inequations 2x+y≥2, x-y≤1, x+2y≤8, x≥0 and y≥0, also shade the solution region. (Graph paper not necessary)
[5]
Q4.
Find the number of permutations and the number of combinations in the letters of the word 'EXPRESSION' taken four at a time.
⚠ This question is not in the current syllabus
[5]
Page 7 of 8
Q5.
Find the sum of the integers between 90 and 890 which are perfect squares.
⚠ This question is not in the current syllabus
[5]
Q6.
If z1 and z2 be two non-zero complex numbers such that |z1+z2| = |z1|+|z2|, then prove that arg z1 - arg z2 = 0.
⚠ This question is not in the current syllabus
[5]
Q7.
The directrix of a parabola is x+y+4=0 and vertex is at (-1,-1). Find the position of the focus and the equation of parabola.
⚠ This question is not in the current syllabus
[5]
Page 8 of 8