Class 12 · Mathematics
Translate the problem into a system of equations.
Short answer
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160 questions
Class 12 · Mathematics
In subparts (i) to (xi) choose the correct options and in subparts (xii) to (xv), answer the questions as instructed.
Assertion: The equality tan(cot -1 x) = cot(tan-1 x), is true for all x ∈ R
π
Reason: The identity tan-1 x + cot -1 x = 2 , is true for all x ∈ R
Which of the following is correct?1 markMCQ
Class 12 · Mathematics
5] In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed.
If a⃗ and b⃗ are unit vectors enclosing an angle θ and |a⃗ + b⃗| < 1, then find the values
between which θ lies.
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ISC (CLASS XII) SPECIMEN QUESTION PAPER 2026Short answer
Class 12 · Mathematics
Based on your calculations, decide: Should the teachers coordinate better? Or is the
current plan acceptable?
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ISC (CLASS XII) SPECIMEN QUESTION PAPER 2026Short answer
Class 12 · Mathematics
Find the probability for each possible number of surprise tests.
Short answer
Class 12 · Mathematics
A linear programming problem is given by Z = px + qy where p, q > 0 subject to
the constraints:
x + y ≤ 60, 5x + y ≤ 100, x ≥ 0 and y ≥ 0
(a) Solve graphically to find the corner points of the feasible region.
(b) If Z = px + qy is maximum at (0,60) and (10, 50), find the relation of
p and q. Also mention the number of optimal solution(s) in this case.
ORShort answer
Class 12 · Mathematics
Hence, find the cost of one paper bag, one scrap book and one pastel sheet.
Short answer
Class 12 · Mathematics
2] (i) A building is to be constructed in the form of a triangular pyramid ABCD as shown in the figure. Let the angular points be A (0, 1, 2), B (3, 0, 1), C (4, 3, 6) and D (2, 3, 2) and let G be the point of intersection of the medians of ∆BCD. Using the above information, answer the following (a) What will be the length of vector ⃗⃗⃗⃗⃗⃗ AG ? (b) Find the area of ∆ABC. OR
What are the values of x for which the angle between the vectors?
2x 2 î + 3xĵ + k̂ and î - 2ĵ + x 2 k̂ is obtuse?Short answer
Class 12 · Mathematics
5] In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed.
The total revenue received from the sale of x unit of a product is given by
R(x) = 3x 2 + 36x + 5. Find the marginal revenue when x = 5.Short answer
Class 12 · Mathematics
5] In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed.
Which condition is true if Average Cost (AC) is constant at all levels of output?MCQ
Class 12 · Mathematics
Solve the following differential equation:
dy
(1 + x 2 ) + 2xy = 4x 2
dxShort answer
Class 12 · Mathematics
Use the probabilities to build a distribution table.
Short answer
Class 12 · Mathematics
Solve the following differential equation:
dy y
x dx = y - x tan ( x )
ORShort answer
Class 12 · Mathematics
Solve the system of equation by using matrix method.
Short answer
Class 12 · Mathematics
x 2 +x+1
Evaluate: ∫ (x+2 )(x 2 +1) dx
ORNumerical
Class 12 · Mathematics
In subparts (i) to (xi) choose the correct options and in subparts (xii) to (xv), answer the questions as instructed.
If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.1 markShort answer
Class 12 · Mathematics
5] In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed.
Consider the following statements and choose the correct option:
Statement 1: If a⃗ and b⃗⃗ represents two adjacent sides of a parallelogram then the
diagonals are represented by a⃗ + b⃗ and a⃗ - b⃗ .
Statement 2: If a⃗ and b⃗ represents two diagonals of a parallelogram then the adjacent
sides are represented by 2(a⃗ + b⃗ ) and 2(a⃗ - b⃗).
Which of the following is correct?MCQ
Class 12 · Mathematics
In subparts (i) to (xi) choose the correct options and in subparts (xii) to (xv), answer the questions as instructed.
Statement 1: If a relation R on a set A satisfies R = R -1, then R is symmetric.
Statement 2: For a relation R to be symmetric, it is necessary that R = R -1
Which one of the following is correct?1 markMCQ
Class 12 · Mathematics
In subparts (i) to (xi) choose the correct options and in subparts (xii) to (xv), answer the questions as instructed.
The given function f: R → R is many to one function. Give reason.1 markShort answer
Class 12 · Mathematics
Three friends go to a restaurant to have pizza. They decide who will pay for the pizza
by tossing a coin. It is decided that each one of them will toss a coin and if one person
gets a different result (heads or tails) than the other two, that person would pay. If all
three get the same result (all heads or all tails), they will toss again until they get a
different result.
(a) What is the probability that all three friends will get the same result (all heads
or all tails) in one round of tossing?
(b) What is the probability that they will get a different result in one round of
tossing?
(c) What is the probability that they will need exactly four rounds of tossing to
determine who would pay?
ORShort answer