Mathematics · Class 12 Science

Nagaland Nbse Class 12 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.

2016–2025
Years of papers: 10
Total Papers: 10
Real Board Papers: 0
Sample papers: 340
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

31 Q2025complete

31 Q2024complete

34 Q2023complete

34 Q2022complete

35 Q2021complete

35 Q2020complete

35 Q2019complete

35 Q2018complete

35 Q2017complete

35 Q2016complete

Nagaland Board of School Education 2025 · Set ANNUAL

Real board examination

About this paper

The real Class-12 board examination held in 2025. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks: 80
Questions: 31
Duration: 180 min
Sections: 4

The marks / questions / duration above are the official exam pattern. We currently have 31 of this paper’s questions (100% of the full paper), with 31 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

Section	Type	Questions	Marks each	Total
ASection A	compulsory	10	1	10
BSection B	compulsory	9	2	18
CSection C	compulsory	8	4	32
DSection D	compulsory	4	5	20
Total		31		80

The question paper

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

Board Examination

Mathematics

Nagaland Board of School Education 2025 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 31 questions divided into 4 sections — A, B, C, D.
Section A comprises 10 questions of 1 mark each (compulsory).
Section B comprises 9 questions of 2 marks each (compulsory).
Section C comprises 8 questions of 4 marks each (compulsory).
Section D comprises 4 questions of 5 marks each (compulsory).

Above is the official exam pattern. The questions printed below are those we currently hold for this paper.

Section A

compulsory · 1 mark each · 10 of 10 shown

Q1.

Let

f:\mathbf{Z}\to\mathbf{Z}

define as

f(x)=x^{2}

. Then

f

(a) injective
(b) surjective
(c) bijective
(d) neither injective nor surjective

[1]

Q2.

The principal value of

\cos^{-1}\left(\dfrac{-1}{\sqrt 2}\right)

(a) $\dfrac{\pi}{4}$
(b) $\dfrac{-\pi}{4}$
(c) $\dfrac{3\pi}{4}$
(d) $\dfrac{-3\pi}{4}$

[1]

Q3.

A=\begin{bmatrix}3 & x-1\\ 2x+3 & x+2\end{bmatrix}

is a symmetric matrix, then

(a) $x=-4$
(b) $x=4$
(c) $x=-3$
(d) $x=3$

[1]

Q4.

y=\log(\cos x)

, then the value of

\dfrac{dy}{dx}

(a) $\dfrac{1}{\cos x}$
(b) $-\tan x$
(c) $-\cot x$
(d) $\dfrac{-\sin x}{x}$

[1]

Q5.

The function

f(x)=\sin x

is increasing in the interval

(a) $\left(0,\dfrac{\pi}{2}\right)$
(b) $\left(\dfrac{\pi}{2},\pi\right)$
(c) $(0,\pi)$
(d) $(0,2\pi)$

[1]

Q6.

The value of

\displaystyle\int \dfrac{e^{2x}-1}{e^{2x}+1}\,dx

(a) $\log(e^{2x}+1)+c$
(b) $\log(e^{2x}-1)+c$
(c) $\log(e^{x}+e^{-x})+c$
(d) $\log(e^{x}-e^{-x})+c$

[1]

Page 1 of 6

Q7.

∫₀π/4 sin 2xdx is equal to (a) 0 (b) 1 (c) 2 (d) (1)/(2)

[1]

Q8.

The order of the differential equation ((ds)/(dt))⁴+3sdfracd²sdt²=0 is (a) 4 (b) 2 (c) 1 (d) not defined

[1]

Q9.

The unit vector in the direction of the vector vec a=hat i+hat j+2hat k is (a) (1)/(2)hat i+(1)/(2)hat j+hat k (b) (1)/(√ 3)hat i+(1)/(√ 3)hat j+(2)/(√ 3)hat k (c) (1)/(√ 5)hat i+(1)/(√ 5)hat j+(2)/(√ 5)hat k (d) (1)/(√ 6)hat i+(1)/(√ 6)hat j+(2)/(√ 6)hat k

[1]

Q10.

If P(A)=(1)/(2), P(B)=0, then P(A/B) is (a) 0 (b) (1)/(2) (c) 1 (d) not defined

[1]

Section B

compulsory · 2 marks each · 9 of 9 shown

Q1.

Find the value of tan⁻¹(1)+cos⁻¹(-(1)/(2))+sin⁻¹(-(1)/(2)).

[2]

Q2.

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling price are ₹80, ₹60 and ₹40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

[2]

Q3.

Examine the continuity of the function f, defined by f(x)= x+1, if x≥ 1x²+1, if x<1 at x=1.

[2]

Q4.

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

[2]

Page 2 of 6

Q5.

Evaluate ∫ sin⁻¹(dfrac2x1+x²)dx.

[2]

Q6.

Find the general solution of the differential equation (dy)/(dx)=√4-y², (-2<y<2).

[2]

Q7.

Find the area of a parallelogram whose adjacent sides are given by the vectors vec a=3hat i+hat j+4hat k and vec b=hat i-hat j+hat k.

[2]

Q8.

If vec a=2hat i+2hat j+3hat k, vec b=-hat i+2hat j+hat k and vec c=3hat i+hat j are such that vec a+λ vec b is perpendicular to vec c, then find the value of λ.

[2]

Q9.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that i) first ball is black and second ball is red. ii) one of them is black and other is red.

[2]

Section C

compulsory · 4 marks each · 8 of 8 shown

Q1.

A confectionery shop is a place where sweets and chocolates are sold. The table below gives information on four varieties of chocolates sold there. | Chocolate name | Cost price (₹) | |---|---| | Dairy milk (D) | 5 | | 5-Star (S) | 10 | | Crunch (C) | 20 | | Kit-kat (K) | 50 | Let A=\D,S,C,K\ be the set containing the chocolates and B=\5,10,20,50\ be the set containing their costs. A relation R is defined on set A as, R=\(x,y): cost of x ≤ cost of y\. Read the information given above and answer the following: (i) Express the relation R in roster form. (ii) Is R reflexive relation? Justify. (iii) Is R symmetric relation? Justify. (iv) Is R transitive relation? Justify.

[4]

Page 3 of 6

Q2.

If A= 3 1\-1 2 , show that A²-5A+7I=0. Using this equation find A⁻¹. **OR** Express the matrix A= 3 3 -1\-2 -2 1\-4 -5 2 as the sum of a symmetric and a skew symmetric matrix.

[4]

Q3.

Differentiate xsin x+(sin x)cos x with respect to x.

[4]

Q4.

Integrate dfrac3x+5x³-x²-x+1 **OR** Evaluate ∫₀π/4 log(1+tan x)dx.

[4]

Q5.

Find the general solution of the differential equation (x+y)(dy)/(dx)=1. **OR** Show that the given differential equation is homogeneous and solve it: (x²-y²)dx + 2xydy = 0.

[4]

Q6.

Find the angle between the pair of lines (x-2)/(2)=(y-1)/(5)=(z+3)/(-3) and (x+2)/(-1)=(y-4)/(8)=(z-5)/(4).

[4]

Q7.

Solve the Linear Programming problem graphically: Minimise Z=3x+5y subject to constraints x+3y≥ 3, x+y≥ 2; x,y≥ 0.

[4]

Page 4 of 6

Q8.

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholar attain A grade in their annual Examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hosteller? **OR** In answering a question on a multiple choice test, a student either knows the answer or guesses. Let (3)/(4) be the probability that he knows the answer and (1)/(4) be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability (1)/(4). What is the probability that the student knows the answer given that he answered it correctly?

[4]

Section D

compulsory · 5 marks each · 4 of 4 shown

Q1.

The sum of three number is 6. If we multiply third number by 3 and add second number to it, we get 11. By adding first and third number, we get double of the second number. Represent it algebraically and find the numbers using matrix method. **OR** If A= 1 3 3\1 4 3\1 3 4 , then verify that AadjA = |A|I. Also find A⁻¹.

[5]

Q2.

Prove that the volume of the largest cone that can be inscribe in a sphere of radius R is (8)/(27) of the volume of the sphere. **OR** Show that the right circular cone of least curved surface and given volume has an altitude equal to √(2) times the radius of the base.

[5]

Q3.

Using integration prove that the area of circle with centre at the origin and radius 'a' is π a². **OR** Find the area of the region bounded by the ellipse 9x²+16y²=144.

[5]

Page 5 of 6

Q4.

Find the shortest distance between the lines vec r=hat i+hat j+λ(2hat i-hat j+hat k) and vec r=2hat i+hat j-hat k+μ(3hat i-5hat j+2hat k). **OR** Find the shortest distance between the lines (x+3)/(-4)=(y-6)/(3)=(z)/(2) and (x+2)/(-4)=(y)/(1)=(z-7)/(1).

[5]

Page 6 of 6