Mathematics Important Questions for Class 12 Board 2023

Here are some good maths important questions for Class 12 Board 2023.

Question (1)

The x-coordinate of a point on the line joining the points P(2, 2, 1) and Q(5, 1, – 2) is 4. Find its z-coordinate

Question (2)

Write the principle value of  tan^-1(1) +cos^-1(-1/2)

Question (3)
A fair coin is tossed 8 times, find the probability of
(i) exactly 5 heads
(ii) at least six heads
(iii) at most six heads

Question (4)
Three cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards

Question (5)

There are three coins. One coin is two headed coin.Second coin is biased one which comes up tail 25% times and third coin is unbiased one.One of the three coin is chosen at random and tossed and head comes. what is the probability that it was the two-headed coin?

Question (6)

Determine the values of ‘a’ and ‘b’ such that the following function is continuous
at x = 0

Question (7)

Determine the value of ‘k’ for which the following function is continuous
at x = 3 :

Question (8)

Find the value of k for which the function

is continuous at x=?/4

Question (9)

if x^y + y^x= a^b find dy/dx

Question (10)

Find the intervals in which the function f given by
f(x) = sin x + cos x, 0 ? x ? 2?
is strictly increasing or strictly decreasing.

Question (11)

Question (12)

Find the intervals in which the function given by

f(x) = 2x³ – 3x² – 36x + 7 is

(a) Strictly increasing

(b) Strictly decreasing

Question (13)

Question (14)

Find the value of the below

Question (15)

If a ,b and c are mutually perpendicular vectors of equal magnitudes, find the angles which the vector 2a +b+ 2c makes with the vectors a ,b and c .

Question (16)
Solve the following linear programming problem graphically:
Minimize: z = 3x + 9y
When: x + 3y ? 60
x + y ? 10
x?   y
x ? 0, y ? 0

Question (17)

There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X

Question (18)

Using Integration, find the area of the following region

{(x, y) : y² ? ax, x² + y² ? 2ax,a > 0}

Question (19)

Find the equation of the plane passing through the point (–1, 3, 2) and perpendicular to
each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0

Question (20)

Let f : R – (-4/3) -> R be function defined as f(x)=4x/3x + 4. Show that f is a one-one
function. Also check whether f is an onto function or not. Hence find f^-1 in
(Range of f) -> R – (-4/3)

Question (21)

$\int { \frac {x^2 -1}{x^4 +1}} dx $

Question (22)

$\int {\left (\sqrt {tanx} + \sqrt {cot x} \right)} dx$