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Maharashtra Board Exam HSC Math Paper Allegedly Leaked; Know What Official Says

Maharashtra board hsc math paper leak: the mathematics exam question paper for class 12 was posted on social media 30 minutes ahead of the examination. .

Image: Maharashtra board exam paper leaked (Shutterstock)

In yet another question paper leak case, the Maharashtra board mathematics exam question paper for class 12 was posted on social media 30 minutes ahead of the examination.

According to officials, Buldhana's Sinkhed Raja town is where the Higher Secondary Certificate (HSC) test question paper was purportedly leaked.

The Maharashtra board administrators acted quickly and requested an investigation into the situation. It has dispatched a team to Buldhana for an initial investigation and intends to lodge a police report in an effort to determine where the photographs came from.

Ajit Pawar and Revenue Minister speaks out

Ajit Pawar, the leader of the opposition, brought up the alleged misconduct at the district's Sindhkhedraja and urged the administration to take action. Congress MLA and former education minister Varsha Gaikwad asked how the question paper could "get out 30 minutes before the start of the exam".

The leak when students were inside classrooms

The three-hour Maharashtra HSC Mathematics Exam was scheduled to take place from 11 am to 2 pm. Due to rules prohibiting entry after 10.30 a.m., the pupils were present within the exam room. Students were there when the pictures were posted on social media.

Notably, Maharashtra Board will be concluding its HSC Exam 2023 till March 20, 2023.

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Maharashtra HSC maths paper leaked? Govt to probe

Maharashtra State HSC Board Question Paper for Class 12th Maths 2019 In PDF

Msbshse hsc board 12th class question paper mathematics english medium 2019 with solutions – free download.

Maharashtra State Board Class 12th maths 2019 question paper with solutions are available on this page, by BYJU’S, in downloadable pdf format and also in the text for the students to prepare well for their exams. The page also consists of Maths Question Paper 2019 Class 12, which acts as an extra resource. Students are able to access all the Maharashtra HSC Board previous year maths question papers here. Students can analyse their confidence and preparation level for the upcoming final exams and also ace it by practising these papers.

Download MSBSHSE HSC 12th Maths Question Paper 2019

Msbshse class 12th maths question paper with solutions 2019.

MSBSHSE Class 12th Maths Question Paper With Solutions 2019 QUESTION PAPER CODE J – 60

maharashtra class 12 exam question paper sol march 2019 01

SECTION – A

Select and write the most appropriate answer from the given alternatives for each question. [6]

Question 1: The principal solution of cot x = -√3 are

(a) 𝛑 / 6, 5𝛑 / 6 (b) 5𝛑 / 6, 7𝛑 / 6

Answer: (c)

cot x = -√3

cot x = – cot (𝛑 / 6)

Question 2: The acute angle between the two planes x + y + 2z = 3 and 3x – 2y + 2z = 7 is _____.

(a) sin -1 (5 / √102) (b) cos -1 (5 / √102)

Answer: (b)

The acute angle between the two planes x + y + 2z = 3 and 3x – 2y + 2z = 7.

cos θ = |n 1 n 2 / n 1 n 2 |

n 1 = i + j + 2k and n 2 = 3i – 2j + 2k

|n 1 | = √1 2 + 1 2 + 2 2 = √6

|n 2 | = √3 2 + (-2) 2 + 2 2 = √17

cos θ = | (i + j + k) . (3i – 2j + 2k) / √6 . √17 |

cos θ = | (1 x 3) + (1 x -2) + (2 x 2) / √102 |

= | 3 – 2 + 4 / √102 |

cos θ = | 5 / √102 |

θ = cos -1 5 / √102

Question 3: The direction ratios of the line which is perpendicular to the lines with direction ratios -1, 2, 2 and 0, 2, 1 are _____.

(a) -2, -1, -2 (b) 2,1, 2 (c) 2, -1, -2 (d) -2, 1, -2

Answer: (d)

i (2 – 4) – j (-1) + k (-2)

= -2i + j – 2k

Question 4: If f(x) = (1 + 2x) 1/x , for x ≠ 0 is continuous at x = 0, then f(0) = _____.

(a) e (b) e 2 (c) 0 (d) 2

f (0) = lim x→0 [(1 + 2x) 1/2x ] 2 = e 2

Question 5: ∫dx / 9x 2 + 1 = _____.

(a) (1 / 3) tan -1 (2x) + c (b) (1 / 3) tan -1 (x) + c

I = ∫dx / 9x 2 + 1

= (1 / 9) ∫dx / x 2 + (1 / 3) 2

= (1 / 3) tan -1 (3x) + c

Question 6: If y = ae 5x + be -5x , then the differential equation is _____.

(a) d 2 y / dx 2 = 25y (b) d 2 y / dx 2 = -25y

Answer: (a)

y = ae 5x + be -5x

dy / dx = 5ae 5x – 5be -5x

d 2 y / dx 2 = 25y

SECTION – B

Question 7: [16]

Write the truth values of the following statement:

(i) 2 is a rational number and √2 is an irrational number.

(ii) 2 + 3 = 5 or √2 + √3 = √5

The given statement is p ^ q.

The truth value of p and q is T.

The truth value of p ^ q is T.

q = √2 + √3 = √5 which is F.

The truth value of the given statement is T v F = T.

Question 8: [a] Find the volume of the parallelepiped if coterminous edges are given by the vectors 2i + 5j – 4k, 5i + 7j + 5k, 4i + 5j – 2k.

[b] Find the value of p if the vectors i – 2j + k, 2i – 5j + pk and 5i – 9j + 4k are coplanar.

a = 2i + 5j – 4k

b = 5i + 7j + 5k

c = 4i + 5j – 2k

= |2 (- 14 – 25) – 5 (- 10 – 20) – 4 (25 – 28)|

Since a, b and c are coplanar vectors, their scalar triple product is 0.

a . (b x c) = 0

1 (-20 + 9p) + 2 (8 – 5p) + 1 (-18 + 25) = 0

– 20 + 9p + 16 – 10p – 18 + 25 = 0

– p + 3 = 0

– p = – 3

Question 9: Show that the points A (- 7, 4, -2), B ( – 2, 1, 0) and C (3, – 2, 2) are collinear.

A (- 7, 4, -2), B ( – 2, 1, 0) and C (3, – 2, 2).

If the area of the triangle formed by these points is zero, then, the three points are collinear.

If the value of the determinant of the three vertices is zero, then, the points are collinear.

= – 7 (2 – 0) – 4 ( – 4 – 0) – 2 (4 – 3)

= – 7 (2) – 4 (- 4) – 2 (1)

= – 14 + 16 – 2

The three points A (- 7, 4, -2), B ( – 2, 1, 0) and C (3, – 2, 2) are collinear.

Question 10: Write the equation of the plane 3x + 4y – 2z = 5 in the vector form.

The equation of the given plane is 3x + 4y – 2z = 5.

Let r = xi + yj + zk be any vector in the plane and 3, 4, -2 are direction ratios of n, which is normal to the plane.

n = 3i + 4j – 2k

(xi + yj + zk) . (3i + 4j – 2k) = 5

r . (3i + 4j – 2k) = 5 which is the required form.

Question 11: If y = x x , then find dy / dx.

y = x x —- (1)

Taking log on both the sides,

logy = x log x

On differentiating both sides,

(1 / y) * dy / dx = [x * 1 / x] + log x * 1

dy / dx = y (1 + log x)

= x x (1 + log x)

Question 12: Find the equation of a tangent to the curve y = x 2 + 4x + 1 at point (- 1, – 2).

y = x 2 + 4x + 1

dy / dx = 2x + 4

(dy / dx) at (- 1, – 2) = 2 (-1) + 4 = 2

Slope of the tangent at the point (-1, -2) = 2

Equation of the tangent at the point (-1, -2) is

2x – y = 0

Question 13: Evaluate: ∫e x (1 + x) / cos 2 [xe x ] dx.

Let I = ∫e x (1 + x) / cos 2 [xe x ] dx

Put xe x = t

Differentiate with respect to x

xe x + e x * 1 = dt / dx

e x (x + 1) dx = dt

I = ∫[1 / cos 2 t] dt

= ∫sec 2 t dt

= tan t + c

∫e x (1 + x) / cos 2 [xe x ] = tan (xe x ) + c

Question 14: Evaluate: ∫ 0 𝛑/2 sin 2 x dx.

Let I = ∫ 0 𝛑/2 sin 2 x dx

= ∫ 0 𝛑/2 [1 – cos 2x] / [2] dx

= [(x / 2) – (sin 2x / 4)] 0 𝛑/2

SECTION – C

Question 15: [18]

[a] In △ABC, prove that sin ([B – C] / 2) = ([b – c] / a) cos (A / 2)

[b] Show that sin -1 [5 / 13] + cos -1 [3 / 5] = tan -1 [63 / 16].

= [(k sin B – k sin C)] / [(k sin A)] * cos (A / 2)

= k (sin B – sin C) / k sin A * cos (A / 2)

= 2 [cos [B + C] / 2] [sin [(B – C)] / 2] / 2 sin (A / 2) cos (A / 2) * cos (A / 2)

= 2 cos ([𝛑 / 2] – [A / 2]) sin ([B – C] / 2) / 2 sin (A / 2)

⇒ sin -1 5 / 13 + cos -1 3 / 5

⇒ tan -1 5 / 12 + tan -1 4 / 3

⇒ tan -1 (63 / 13)

Question 16: If A ( $\begin{array}{l}(\bar {a})\end{array} $ ) and ( $\begin{array}{l}(\bar {b})\end{array} $ ) are any two points and R ( $\begin{array}{l}(\bar {r})\end{array} $ ) be a point on the line segment AB dividing it internally in the ratio m:n, then prove that

( $\begin{array}{l}(\bar {r})\end{array} $ ) = m ( $\begin{array}{l}(\bar {b})\end{array} $ ) + n ( $\begin{array}{l}(\bar {a})\end{array} $ ) / m + n.

( $\begin{array}{l}(\bar {a})\end{array} $ ), ( $\begin{array}{l}(\bar {b})\end{array} $ ), ( $\begin{array}{l}(\bar {r})\end{array} $ ) be the position vectors of A, B, R respectively.

( $\begin{array}{l}(\bar {AR})\end{array} $ ) = ( $\begin{array}{l}(\bar {r})\end{array} $ ) – ( $\begin{array}{l}(\bar {a})\end{array} $ ), ( $\begin{array}{l}(\bar {RB})\end{array} $ ) = ( $\begin{array}{l}(\bar {b})\end{array} $ ) – ( $\begin{array}{l}(\bar {r})\end{array} $ )

R is a midpoint of the line segment AB and A-R-B which divides the AB in the ratio m:n.

AR / RB = m:n

MSBSHSE Class 12 Maths 2019 Question Paper Solutions Q16

n( $\begin{array}{l}(\bar {AR})\end{array} $ ) = m( $\begin{array}{l}(\bar {RB})\end{array} $ )

n( $\begin{array}{l}(\bar {r})\end{array} $ ) – ( $\begin{array}{l}(\bar {a})\end{array} $ ) = m( $\begin{array}{l}(\bar {b})\end{array} $ ) – ( $\begin{array}{l}(\bar {r})\end{array} $ )

( $\begin{array}{l}(\bar {r})\end{array} $ ) = m ( $\begin{array}{l}(\bar {b})\end{array} $ ) + n ( $\begin{array}{l}(\bar {a})\end{array} $ ) / m + n

Question 17: The equation of a line is 2x – 2 = 3y + 1 = 6z – 2, find its direction ratios and also find the vector equation of the line.

The cartesian equation of the line is 2x – 2 = 3y + 1 = 6z – 2.

2 (x – 1) = 3 (y + 1 / 3) = 6 (z – 1 / 3)

Dividing by 6 on both sides

(x – 1) / 3 = y + (1 / 3) / 2 = z – (1 / 3) / 1

The direction ratios of the line are 3, 2, 1.

The line passes through the point (1, (-1 / 3), (1 / 3)).

Let A = (1, (-1 / 3), (1 / 3))

The line passes through the point having the position vector.

a = 1i – (1 / 3)j + (1 / 3)k

b = 3i + 2j + k

The line is parallel to the vector b.

The vector equation of the line is

( $\begin{array}{l}(\bar {r})\end{array} $ ) = ( $\begin{array}{l}(\bar {a})\end{array} $ ) + ƛ ( $\begin{array}{l}(\bar {b})\end{array} $ )

Question 18: Discuss the continuity of the function

f (x) = [log (2 + x) – log (2 – x) / tan x], for x ≠ 0

= 1 , for x = 0

at the point x = 0.

Here f (0) = 1 —- (i)

L = lim x→0 f (x)

= lim x→0 f (x) = lim x→0 log (2 + x) – log (2 – x) / tan x

= lim x→0 log ([(1 + x / 2) / (1 – x / 2)] / x) / (tan x) / x

= lim x→0 log [(1 + x / 2) – log (1 – x / 2) / x] / lim x→0 (tan x / x)

= 1 —- (ii)

From (i) and (ii), lim x→0 f (x) = f (0).

The given function is continuous at x = 0.

Question 19: [a] The probability distribution of a random variable X, the number of defect per 10 meters of fabric is given by

Find the variance of X.

[b] For the following probability density function of X, find

[i] P (X < 1)

[ii] P (|X| < 1)

if f (x) = x 2 / 18, -3 < x < 3

= 0, otherwise

E (X) = μ = ∑p i x i = 0.82

Var (X) = ∑p i x i 2 – μ 2

= 1.54 – (0.82) 2

Var (X) = 0.8676

= ∫ -3 1 (x 2 / 18) dx

= (1 / 18) * (x 3 / 3) -3 1

= ∫ -1 1 (x 2 / 18) dx

= (1 / 18) * (x 3 / 3) -1 1

Question 20: Given X ~ B (n, p). If E (X) = 6, Var (X) = 4.2, then find n and p.

X ~ B (n, p); E (X) = 6, Var (X) = 4.2

Var (X) = npq

Var (X) / E (X) = npq / np = q = 4.2 / 6 = 0.7

p = 1 – q = 1 – 0.7 = 0.3

n = 6 / p = 6 / 0.3 = 20

Question 21: Find the symbolic form of the given switching circuit. Construct its switching table and interpret its result.

MSBSHSE Class 12 Maths 2019 Question Paper Solutions Q21

Let p,q denote the statements that the switches S 1 , S 2 are closed respectively.

Let ~p, ~ q denote the statements that switch S 1 and S 2 are closed respectively. The symbolic form of the given switching circuit is (p v q) and (~p and ~q).

The switching table for the given switching circuit is as follows:

MSBSHSE Class 12 Maths 2019 Question Paper Solutions Q21 Answer

In the last column of the switching table, each entry is zero, i.e. it is a contradiction. Hence, no current will flow in the circuit irrespective of the positions of the switches.

Question 22: If three numbers are added, their sum is 2. If two times the second number is subtracted from the sum of first and third numbers we get 8 and if three times the first number is added to the sum of second and third numbers we get 4. Find the numbers using matrices.

Let the three numbers be x, y and z.

x + y + z = 2 —- (1)

(x + z) – 2y = 8

x – 2y + z = 8 —- (2)

3x + y + z = 4 —- (3)

The matrix form of these equations are

On applying the row operations,

-3y = 6 —- (2)

– 2y – 2z = -2 —- (3)

The required numbers are 1, -2, 3.

Question 23: [a] In triangle ABC, with usual notations prove that b 2 = c 2 + a 2 – 2a cos B.

[b] In triangle ABC, with usual notations prove that (a – b) 2 cos 2 (C / 2) + (a + b) 2 sin 2 (C / 2) = c 2 .

MSBSHSE Class 12 Maths 2019 Question Paper Solutions Q23a

Using the cartesian co-ordinate system in the above figure,

we get B ≣ (0,0) ; A ≣ (c cos B , c cos B) and C ≣ (a,0)

Now consider l (CA) = b

b 2 = (a – c cos B) 2 + (0 – c sin B) 2

By distance formula,

b 2 = a 2 – 2 ac cos B + c 2 cos 2 B + c 2 sin 2 B

b 2 = a 2 – 2 ac cos B + c 2 (sin 2 B + cos 2 B)

b 2 = a 2 + c 2 – 2 ac cos B

= (a – b) 2 cos 2 C / 2 + (a + b) 2 sin 2 C / 2

= (a 2 + b 2 – 2ab) cos 2 C / 2 + (a 2 + b 2 + 2ab) . sin C / 2

= (a 2 + b 2 ) cos C / 2 – 2ab cos 2 C / 2 + (a 2 + b 2 ) . sin 2 C / 2 + 2ab sin 2 C / 2

= (a 2 + b 2 ) (cos 2 C / 2 + sin 2 C / 2) – 2ab (cos 2 C / 2 – sin 2 C / 2)

= (a 2 + b 2 ) – 2ab cos C {By cosine Rule}

Question 24: Find ‘p’ and ‘q’ if the equation, px 2 – 8xy + 3y 2 + 14x + 2y + q = 0 represents a pair of perpendicular lines.

Given general equation is px 2 – 8xy + 3y 2 + 14x + 2y + q = 0.

a = p , h = -4 , b = 3 , g = 7, f = 1 , c = q

Since the equation represents perpendicular lines;

Since the equation represents a pair of lines.

-3 (3q – 1) + 4 (- 4q – 7) + 7 (- 4 – 21) = 0

-9q + 3 – 16q – 28 – 175 = 0

-25q – 200 = 0

p = -3 , q = -8

Question 25: Maximise: z = 3x + 5y subject to

x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.

MSBSHSE Class 12 Maths 2019 Question Paper Solutions Q25

Z is maximum at the point (4, 5).

Question 26: If x = f(t) and y = g(t) are differentiable functions of t, then prove that y is a differentiable function of x and

dy / dx = (dy / dt) / (dx / dt), where dx / dt ≠ 0.

Hence, find dy / dt if x = acos 2 t and y = asin 2 t.

Let δx and δy be the increments in x andy y, respectively, corresponding to the increment δt in t.

Since x and y are differentiable functions of t,

dx / dt = lim (δt→0) (δx) / (δx) and dy / dt = lim (δt→0) (δy) / (δt)…(1)

Also, as (δt→0), (δx→0) … (2)

Now , (δy) / (δx) = (δy) / (δt) / (δx) / (δt) …. (δt ≠ 0)

Taking limits as (δt→0),

lim (δt→0) (δy) / (δx) = lim (δt→0) (δy) / (δt) / (δx) / (δt) as (δt ≠ 0)

lim (δt→0) (δy) / (δx) = lim (δt→0) (δy) / (δt) / (δx) / (δt)

lim (δx→0) (δy) / (δx) = (lim (δt→0) (δy) / (δt) / (lim (δx→0) (δx) / (δt)

∵ The limits in RHS exist.

lim (δx→0) (δy) / (δx) exists and is equal to dy / dx.

dy / dx = (dy / dt) / (dx / dt) if dx / dt ≠ 0

x = a cos 2 t

dx / dt = 2acost (-sint)

y = a sin 2 t

dy / dt = 2 a sint cos t

dy / dx = (dy / dt) / (dx / dt)

= 2a sint cost / -2a cost sint

Question 27: [a] f (x) = (x – 1) (x – 2) (x – 3), x ⥺ [0, 4], find ‘c’ if LMVT can be applied.

[b] A rod of 108 meters long is bent to form a rectangle. Find its dimensions if the area is maximum.

f (x) = x 3 – 6x 2 + 11x – 6

As f (x) is a polynomial in x,

(i) f (x) is continuous on [0, 4].

(ii) f (x) is differentiable on (0, 4).

Thus, all the conditions of LMVT are satisfied.

To verify LMVT we have to find c & c ⥺ (0, 4), such that

f’ (c) = f (4) – f (0) / 4 – 0 ……..(1)

f (4) = (4 – 1) (4 – 2) (4 – 3) = 6

f (0) = (0 – 1) (0 – 2) (0 – 3) = -6 and

f ‘ (x) = 3x 2 – 12x + 11

f ‘ (c) = 3x 2 – 12x + 11

f (4) – f (0) / 4 – 0 = 3c 2 – 12c + 11

(6 – (-6)) / 4 = 3c 2 – 12c + 11

3 = 3c 2 – 12c + 11

3c 2 – 12c + 8 =0

c = 12 ± √(144 – 96)) / 6

c = 12 ± √48) / 6

c = 2 ± [2 / 3] √3

c = 2 ± 2 / √3

Both the value of c lie between 0 and 4.

y = 54 – x

Now, area of rectangle = xy = x (54 – x)

f (x) = 54x – x 2

f ‘ (x) = 54 – 2x

f ” (x) = -2

For extreme values f ‘( x) = 0

54 – 2x = 0

f ” (27) = -2 < 0

Area is maximum when x =27 , y = 27

The dimensions of rectangle are 27m * 27m.

It is a square.

Question 28: Prove that: ∫dx / √x 2 + a 2 = log |x + √x 2 + a 2 | + c.

Let I = ∫ 1 / √x 2 + a 2 dx

Put x = a tan 𝛉

tan 𝛉 = x / a

dx = a sec 2 𝛉 d𝛉

I = ∫ 1/ √(a 2 tan 2 𝛉 + a 2 ) asec 2 𝛉 d 𝛉

= ∫ (a . sec 2 𝛉) / (a √(1 + tan 2 𝛉)) d𝛉

= ∫ (sec 2 𝛉) / (sec 𝛉) d𝛉

= ∫ sec 𝛉 . d 𝛉

= log |sec 𝛉 + tan 𝛉| + c 1

= log |x / a + √(sec 2 𝛉)| + c 1

= log |x / a + √ 1 + tan 2 𝛉 | + c 1

= log |x / a + √(1 + x 2 / a 2 )| + c 1

= log |x / a + √(a 2 + x 2 ) / a| + c 1

= log |x + √(x 2 + a 2 )| – log a + c 1

∫dx / √x 2 + a 2 = log |x + √x 2 + a 2 | + c, where c = – log a +c

Question 29: Show that: ∫ 0 𝛑/4 log (1 + tan x) dx = 𝛑 / 8 log 2.

MSBSHSE Class 12 Maths 2019 Question Paper Solutions Q29

Question 30: [a] Solve the differential equation (dy / dx) + y sec x = tan x.

[b] Solve the differential equation (x + y) dy / dx = 1.

IF = e ∫sec xdx = e log(sec x + tan x) = secx + tanx

y * IF = ∫Q * IF

y (sec + tan x) = ∫(sec x + tan x) tan x.dx

= ∫sec x tan x + ∫ tan 2 x dx

= secx + ∫(sec 2 x – 1) dx

y(sec x + tan x) = sec x + tan x – x + c

dy / dx = 1 / x + y

dx / dy = x + y

dx / dy + (-1) x = y

Comparing with dx / dy + P * x = Q,

P = -1, Q = y

= e ∫-1ydy = e -y

The general solution is

x (IF) = ∫Q * IF dy + c

xe -y = y ∫e -y dy + c

xe -y = -ye -y – e -y + C

(x + y + 1) = ce y

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Maharashtra Board (MSBSHSE) Question Paper for Class 12 Maths 2019

Maharashtra Board HSC Maths Class 12 Question Paper 2019 with Solutions - Free PDF Download

At Vedantu, we believe that the more you practice, the better you perform in the exams. That’s why we have provided Maharashtra Board (MSBSHSE) Maths Class 12 Previous Year papers 2019 PDF here so that you become thorough with the question paper pattern. Practising Maharashtra Board HSC Class 12 Maths previous year question papers has many advantages. One of the most important factors these papers address is the management of time. We have seen that many students would have studied hard and learned the concepts well, but still, struggle to finish answering the paper.

Download PDF of Maharashtra Board (MSBSHSE) Question Paper for Class 12 Maths 2019

Maharashtra board hsc maths class 12 question paper, benefits of these previous year papers .

Read along to know how these previous years solved question papers can help you in your preparation for the examinations:

One Would Know What to Expect from the Exam

These MSBSHSE practice papers will give a fair idea about actual examination questions. Practising these would adapt one to the pattern in which the exam is set. There are high chances of either repetition of the previous year questions or a simple modification of the same questions. Therefore, sufficient practice of these papers ensures good quality of preparation.

Bridge the Gap

These previous years Maharashtra board papers bridge the gap between preparation for the exam and attempt in exam. These practice papers acquaint the students well with examination patterns and questions. These also provide an idea about important topics that carry more weightage of marks. Utilising these practise papers in your preparation period is suggested to improve your performance in the exam.

Time Management

The biggest advantage of having practised ample Maharashtra board’s previous year papers is one gets a clear idea about their speed of attempting the exam. The speed of writing answers keeps getting better during the practice of these papers. This saves one some crucial minutes for revision of the answer sheet during the exam. Time management is a key factor that determines how well the strategy of attempting the exam will be executed. This skill of time management during stressful conditions (such as examination days) is honed with practice.

Solving Maths 2019 previous question papers for Class 12 familiarizes the student with the format of the paper beforehand. Students who struggle to finish on time are advised to start solving these papers at the earliest so that they don’t lag. Our highly qualified teachers have curated these Maharashtra Board Maths Class 12 past years question papers and have developed a set of sample papers in PDF format that are available for free download.

Keep the MSBSHSE previous year papers handy during preparation. Good luck with your examination practice.

FAQs on Maharashtra Board (MSBSHSE) Question Paper for Class 12 Maths 2019

1. Are these 2019 examination papers free to download?

Yes. These sample papers can be downloaded for free from the Vedantu website . Once downloaded you would be able to access these offline as well and study anytime throughout the day. These papers do not just have questions but solutions to every question that was asked in the examination. The biggest advantage of downloading the papers is that they are organised and digital. Thus, the hassle of maintaining multiple notes and registers is reduced. These papers are stored in an efficient way.

2. What are the benefits of studying these papers?

These papers have answers with detailed solutions to every question of the examination. These solutions are genuine and provided by credible subject matter experts. These papers will help you study and practise the solutions directly and offline. The answers provided are precise. Practising these papers will strengthen your concepts as the experts have answered in a self-explanatory manner. These will also help you perform better by improving your time-management skills as practise of these papers hone the time management skill of the students.

3. When is the right time to practise these papers?

One must keep ample time for practising from these papers. These practices should not be rushed through during the tail end of the preparation period. The best time to begin studying from the papers would be after the Maharashtra board’s syllabus for Maths is complete once during the academic year. Only after completion of syllabus once, can one start the practise of previous year papers. This first attempt of solving/studying from the previous year’s papers would give a better idea of your understanding and preparedness for the exam. In case of any major flaws, one would have enough time to practise again and rectify the mistakes.

4. Are these papers useful for Maharashtra board students?

Certainly, yes. These previous year 2019 papers are of Maharashtra board’s 2019 examination. These papers have detailed and well explained solutions to all the questions of the exam of 2019. These answering styles and solutions are following the Maharashtra board’s guidelines. The solutions provided by expert teachers are aligned with every guideline and scoring criteria provided by the Maharashtra board. Thus, these answers are as per the standards of Maharashtra board and specific to it. These are customized as per the MSBSHSE board requirements.

5. What do students gain from these previous year paper solutions ?

It is very well known that Mathematics is a typical subject and has the full potential of getting students confused in the exams. Hence, practice of previous year papers gives students an overview of the exam. Students during the preparation phase learn how to answer and what to omit from answers. The solutions provided give students tips and tricks about the strategy to attempt the exam. These also serve as mock tests. Students tend to practise the same concept in a versatile manner and as a result these solutions are imbibed by the mind and come handy at the time of exam.

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HSC Past Maths Exam Paper General Maths 2021

HSC Past Exam Paper : 2021 Higher School Certificate (HSC) maths paper is a great revision resource for students sitting for General Mathematics Examination, GM Paper 1 and Paper 2 .

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Grade 12 Exam Topics: The exam topics are a good revision guide when revising for the final national examination. We lay out the topics in order. Check out this page for the list of Grade 12 Core Topics . Use it as a revision guide when you are studying.

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Maharashtra HSC (Class 12th) 2023 Exam Pattern & Marking Scheme - Check Details Here

Maharashtra HSC Exam Pattern 2022-23 has been released for all the subjects based on the latest syllabus of Class 12 Maharashtra Board for Science, Commerce & Arts. Students can access Maharashtra HSC blueprint 2023 on the Board's official webpage.

Maharashtra HSC Exams 2022 Paper Pattern & Marking Scheme

Maharashtra HSC Exam Pattern 2023 - Highilghts

Maharashtra hsc exam pattern 2022-23, maharashtra hsc board exam 2023 - revised pattern, maharashtra hsc (class 12) marking scheme 2022-23.

Maharashtra HSC (Class 12) Paper Pattern & Marking Scheme 2023 …

Maharashtra HSC Exam 2023: Preparation Tips

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MSBSHSE has published the Maharashtra HSC Exam Pattern 2022-23 for all the subjects based on the updated Maharashtra HSC Syllabus 2022-23. Unlike the previous session, the Board will conduct only one exam this year. The exam pattern of pre-covid era has been implemented again. The Maharashtra HSC exam 2023 will be conducted in offline mode this year, where students will have to answer questions that are very short, short, long, and essay-style. Students must note that in order to clear the Class 12 exam, they will have to score 35 per cent marks in each subject. The questions in the exams will be asked from the Maharashtra HSC Syllabus 2023. Students are advised to go through the Maharashtra 12th exam pattern while they are preparing for the exam as it will help them know about the typology of the questions and work on their time management skills. Maharashtra 12th admit card was released on January 27, 2023. Maharashtra State Board of Secondary revised the Maharashtra HSC timetable 2023 on December 30, 2022. Maharashtra Class 12th exam dates for General and vocational courses are available in separate files on official website of Board. Theory exams for Class 12 Maharashtra board 2023 will be held from February 21 to March 21, 2023 in pen and paper mode . The theory exams will be conducted in two shifts, morning shift (11 AM – 2 PM), and evening shift (3 PM – 6 PM). The Practical exams for HSC Boards have been commenced from February 1, and will continue till February 20, 2023. Maharashtra HSC Result 2023 will be announced in May 2023, tentatively. Read the complete article to know more about the exam pattern, marking scheme, and preparation tips of the Maharashtra Board HSC Exam 2023.

Refer to the table below about the important highlights of Maharashtra Board exam 2023:

Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHE) will conduct HSC Board Exams from February 21 to March 21, 2023 . In class 12, students have to appear for five subjects including English which is a compulsory language paper. Apart from the other three compulsory subjects, students can choose any language paper as their fifth subject.

Also Read: Maharashtra B.Tech Admissions - All You Need to Know!

The Board has revised the Maharashtra HSC Exam Pattern 2022-23. The following is a list of changes made to the Maharashtra Board HSC exam pattern.

1. A 25% increase in objective questions: The board agreed to include 25% objective type questions in the HSC examination question paper as part of the updated evaluation process. These questions will be in the form of Multiple Choice Questions (MCQs).

2 . Reduction in total marks for final assessment: Another significant modification made by the Maharashtra Board is the reduction in total marks for final assessment. The total marks for MH Class 12 2022 students will be 600 instead of 650 starting in the academic year 2022-23.

3. All topics have an internal assessment or practical component: The school board has implemented a 20-mark internal assessment or practical exam for all subjects in class 12. The theoretical paper will now be worth 80 marks, with 20 marks set aside for internal review.

These 20 marks will be bifurcated in the following way-

In all of Class 10th's topics, the same criterion will be applied.

You may also find helpful: How to Prepare - Maharashtra Board and MHT CET 2022 Simultaneously?

Given in the table below is the subject wise Maharashtra HSC (Class 12) Marking Scheme 2023:

Maharashtra HSC (Class 12) Paper Pattern & Marking Scheme 2023 PDF

Students appearing for Maharashtra Board HSC exam 2023, are advised to go through the following preparation tips to perform well in their exams.

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Lovely Professional University or LPU’s B.Tech in Computer Science and Engineering (CSE) programme is one of the best industry-relevant courses offered here. The CSE programme is always in huge demand as students tend to secure placements in some of the top companies and organisations in India and abroad. The B.Tech CSE course is a four-year-long undergraduate programme divided into eight semesters. The LPU BTech fees are around Rs 9.60 lakh. Admission to this course is based on the LPUNEST exam. Candidates with a JEE Main score will be exempted from taking the LPUNEST exam and will be considered …

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What are the UG courses offered by Mumbai University?

Mumbai University offers UG courses with different specializations in arts, science and commerce. BSc. courses include specializations like CS, IT, Bio-Tech, Home Science, Maritime Sciences, Forensic Science, Avionics, etc., while arts programmes include Bachelor of Arts (B.A), Bachelor’s of Mass Media (B.M.M.), Bachelor in Heritage Management (B.H.M.), Bachelor of Social Work (B.S.W.), Bachelor’s Degree in Library & Information Science (B.L.I.Sc., B.A. Programme in Film, Television and New Media Production. In commerce stream, Mumbai University offers courses like Bachelor of Commerce (B. Com.), Bachelor of Management Studies (B.M.S.), Bachelor of Commerce (Accounting & Finance), Bachelor of Commerce (Banking & Insurance), Bachelor …

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Matrix Blog

Hsc solutions, 2022 hsc maths advanced exam paper solutions.

Congratulations Year 12 on making it this far into your HSC exam season! You've found the 2022 Maths Advanced HSC Solutions put together by the Matrix Maths Team. Read on to see how you went!

In this article, we reveal 2022 HSC Maths Adv Exam Paper Solutions, complete with full explanations written by the Matrix Maths Team.

Have you seen the 2022 HSC Mathematics Advanced exam paper yet? For reference, you can find it, here .

Doing past papers? Find all the solutions to the 2018 – 2022 HSC Maths Adv Exams, here .

Multiple Choice Questions

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Question 11, question 12, question 13, question 14.

Question 15

Question 24

Question 25, question 26, question 27.

Question 28

Question 29, question 30, question 31, question 32, written by matrix maths team.

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Now HSC Maths paper leaked in Buldhana 30 minutes before scheduled time

In yet another case of ‘paper leak’, the mathematics paper of the ongoing class 12 higher secondary certificate (hsc) exams purportedly went viral on social media around 30 minutes ahead of the scheduled time.

PUNE: In yet another case of ‘paper leak’, the Mathematics paper of the ongoing Class 12 Higher Secondary Certificate (HSC) exams purportedly went viral on social media around 30 minutes ahead of the scheduled time. While the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE) is conducting a detailed inquiry into the incident which allegedly occurred at one of the exam centres in Sindkhed Raja city in Buldhana district at around 10.30 am on Friday.

A complaint has been lodged at Sakhar Kherda police station in Sindkhed Raja about the alleged paper leak. (REPRESENTATIVE PIC)

A complaint has been lodged at Sakhar Kherda police station in Sindkhed Raja about the alleged paper leak. Even in Pune, the state board has ordered that a case be filed in this regard. While there is no information yet on the exact examination centre in Sindkhed Raja from where the paper leak occurred, the police are investigating the matter.

Sharad Gosawi, chairman, state board, said, “We have received information about the paper tampering case of the Class 12 exam at Sindkhed Raja in Buldhana district. The concerned officials have been asked to submit a complete report to the board. While appropriate legal action will be taken against those found guilty in the paper leak case.”

Questions are now being raised as to how the Mathematics paper went viral on social media despite mobile phones being banned at exam centres. Opposition leader Ajit Pawar too raised the issue of the paper leak in the legislative assembly on Friday.

Earlier, there were reports of teachers of the Mahalingeshwar Secondary and Higher Secondary School leaking the English question paper and providing copies to the students. While the state board along with the district authorities is running a ‘copy-free’ campaign to make HSC and SSC exams copy-free, cases of cheating are being regularly reported from various exam centres across the state. Doubts are now being raised as to how this kind of cheating is taking place despite the increase in vigilance at exam centres and question papers being carried to exam centres under full security among other preventive measures.

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HSC Maths Paper 'leak': Five people from Buldhana arrested

The police, in a statement, said that they are probing if there are other people involved in the malpractice..

Mumbai: The Buldhana Police on Saturday arrested five people, including two teachers at a private school, for allegedly leaking parts of the Maths paper of the ongoing class 12 board exam 30 minutes before the test on Friday.

Three of the accused hail from Bhandari village the district's Sindkhed Raja Taluka, while the teachers live are residents of Shendurjan village in Sindkhed Raja and Kingaon Jattu village in the nearby Lonar taluka. The police, in a statement, said that they are probing if there are other people involved in the malpractice.

A first information report (FIR) was registered under sections 5 and 6 of the Maharashtra Prevention of Malpractices at University, Board and Other Specified Examinations Act, 1982 on Saturday following a complaint of paper leak by Rangnath Gawde, Block Education Officer, Panchayat Samiti, Sindkhed Raja. The Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE) is also investigating the matter.

However, the board has said that there won't be any re-test of Maths paper as it didn't find the purported leak to be widespread. It also said that the students had entered their exam centres for the 11 am Higher Secondary School Certificate (HSC) paper before the images were out on social media at 10:30 am.

The alleged incident has occurred despite the stringent measures put in place by the state government to curb cheating and other malpractices during the first comprehensive board exams after Covid-19 pandemic that started on February 2. While last year, the candidates took the test at their own schools, this time they were allotted different exam centres, as is the norm.

Last week, The Pune Zilla Parishad flying squad detected a case of mass copying at Jawahar Vidyalaya and junior college in Kedgaon, Daund. an FIR was against nine teachers at a Pune school who allegedly aided and abetted mass cheating in the physics exam.

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बातम्या / मुंबई

HSC Exam : बारावीच्या गणिताच्या पेपरफुटीची मुंबई कनेक्शन; विद्यार्थ्याच्या मोबाईलमध्ये पेपर, तीन विद्यार्थ्यांसह अज्ञात व्यक्तिविरोधात गुन्हा

Hsc maths paper leak : मुंबईतील विद्यार्थ्याच्या मोबाईलमध्ये गणित पेपरचा काही भाग आढळला आहे. या प्रकरणी तीन विद्यार्थ्यांसह अज्ञात व्यक्तीविरोधात गुन्हा दाखल करण्यात आला आहे. .

By: डॉ. संजय महाजन | Updated at : 05 Mar 2023 10:49 AM (IST)

Edited By: स्नेहल पावनाक

HSC Exam 2023 Maths paper leak case Mumbai connection maths paper found in student s mobile case filed against with three students HSC Exam : बारावीच्या गणिताच्या पेपरफुटीची मुंबई कनेक्शन; विद्यार्थ्याच्या मोबाईलमध्ये पेपर, तीन विद्यार्थ्यांसह अज्ञात व्यक्तिविरोधात गुन्हा

HSC Maths Paper Leak Case

HSC Exam 2023 Maths Paper Leak : बारावीच्या (HSC Board) गणिताच्या पेपरफुटी (Maths Paper Leak) प्रकरणाचा संबंध मुंबईतील विद्यार्थ्यांशीही असल्याचं समोर आलं आहे. मुंबईतील विद्यार्थ्याच्या मोबाईलमध्ये गणित पेपरचा काही भाग आढळला आहे. डॉ. अँथोनी डिसिल्वा हायस्कूलमधील विज्ञान शाखेतील (Science Stream) परीक्षार्थीच्या मोबाईलमध्ये दहा वाजून 17 मिनिटांनी गणिताचा पेपर सापडला. या प्रकरणी तीन विद्यार्थ्यांसह अज्ञात व्यक्तीविरोधात गुन्हा दाखल करण्यात आला असून तपास क्राईम ब्रांचकडे वर्ग करण्यात आला आहे.

बारावीच्या गणिताच्या पेपरफुटीची मुंबई कनेक्शन

बारावीच्या गणिताचा पेपरफुटी प्रकरणाचं मुंबई कनेक्शन समोर आलं आहे. बारावीच्या गणिताच्या पेपरफुटी प्रकरणाचा संबंध मुंबईतील विद्यार्थ्यांशीही असल्याचं उघड झालं आहे. मुंबईतील विद्यार्थ्याच्या मोबाईलमध्ये गणित पेपरचा काही भाग आढळला आहे. या प्रकरणी तीन विद्यार्थ्यांसह अज्ञात व्यक्तीविरोधात गुन्हा दाखल करण्यात आला असून तपास क्राईम ब्रांचकडे वर्ग करण्यात आला आहे. बुलढाण्यातील कथित पेपरफुटी प्रकरणी पेपर फुटला नसल्याचा बोर्डाने केला होता.

बुलढाण्यात फुटला गणिताचा पेपर

बारावी बोर्डाचा आज गणित विषयाच्या प्रश्नपत्रिकेतील दोन पानं सिंदखेड राजा तालुक्यातील एका परीक्षा केंद्रावरून व्हायरल झाली होती. याबाबतची बातमी आज सर्व वृत्तवाहिन्यावरून प्रसिध्द झाली. दरम्या, या विषयाची प्रश्नपत्रिका विद्यार्थ्यापर्यंत पोहोचल्याचे राज्यात कोठेही आढळून आलेलं नव्हतं नाही. यामुळे इयत्ता 12 वी च्या गणित विषयाची परीक्षा पुन्हा घेतली जाणार नसल्याचे राज्य मंडळाच्या सचिव अनुराधा ओक यांनी स्पष्ट केलं होतं. मात्र मुंबईतील विद्यार्थ्याच्या मोबाईलमध्ये गणिताच्या पेपरची काही पानं आढळल्याने या प्रकरणाला वेगळं वळण लागलं आहे.

मुंबईतील विद्यार्थ्याच्या मोबाईलमध्ये पेपर

तीन विद्यार्थ्यांसह अज्ञात व्यक्तिविरोधात गुन्हा.

दरम्यान, या प्रकरणी शिवाजी पार्क पोलिसांनी तीन परीक्षार्थींसह एका अज्ञाताविरोधात केला गुन्हा दाखल केला आहे. या प्रकरणाचं गांभीर्य लक्षात घेता याचा तपास गुन्हे शाखेकडे देण्यात आला आहे. बुलढाण्यात परीक्षा सुरू झाल्यानंतर अर्ध्या तासातच फुटल्याचं समोर आलं होतं. गणिताचा पेपर सोशल मीडियावर व्हायरल झाल्याने एकच खळबळ उडाली होती. दरम्यान, बुलढाण्यात गणिताचा पेपर फुटला नाही, असं बोर्डाकडून स्पष्टीकरण देण्यात आलं होतं. मात्र आता याप्रकरणी तपासाला नवं वळ लागलं असून बोर्डावर प्रश्न उपस्थित होत आहेत.

महत्त्वाच्या इतर बातम्या :

HSC Paper Leak: बुलढाण्यात बारावीचा गणिताचा पेपर फुटल्याची चर्चा, परीक्षा सुरु झाल्यानंतर अर्ध्या तासात पेपर सोशल मीडियावर व्हायरल

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