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Explore Class 12 Mathematics past and model questions by chapter, year, marks and question type.
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Consider a⃗ × b⃗ = c⃗ × d⃗ and a⃗ × c⃗ = b⃗ × d⃗. Which one of the following is parallel to (b⃗ - c⃗)?
a-b
a-c
a-d
c-d
Which of the following is the integral value of ∫ dx/(x² − 1)
2 log((x + 1)/(x − 1)) + C
2 log((x − 1)/(x + 1)) + C
log((x − 1)/(x + 1)) + C
1/2 log((x + 1)/(x − 1)) + C
Two simultaneous linear equations are given as 2x + y = 5 and x + 4y = 6.
What is the equation obtained after eliminating x?
7y = 5
7y = 6
7y = 7
7y = 12
What is the amount of gravity exerted by the earth on the mass of 100 kg?
g is acceleration due to gravity.
100 Newtons
100g Newtons
g/100 Newtons
100/g Newtons
Using L'Hospital's rule, evaluate:
lim (x → ∞) [ ln(2x² + 5) / ln(3x³ − 4) ]
X and Y are two like parallel forces acting at A and B respectively.
Show that if they interchange positions, the point of application of the resultant is displaced a distance
(X − Y) / (X + Y) × AB, where X > Y.
If
x = y/1! + y²/2! + (y³/3!) + …,
show that
y = x − x²/2 + x³/3 − …
Write any one application of the above statement?
The height (x) in cm and weight (y) in kg are given for 5 persons in a community.
X | 160 | 162 | 165 | 161 | 162 |
|---|---|---|---|---|---|
Y | 63 | 62 | 64 | 60 | 61 |
Find the correlation coefficient between X and Y and regression coefficient Y on X.
Using the vector method, find the area of the triangle with vertices A(1, 4, 6), B(−2, 5, 1) and C(1, −1, 1).
Given n⁴ < 10ⁿ for a fixed positive integer n ≥ 2, prove that (n + 1)⁴ < 10ⁿ⁺¹ using the principle of mathematical induction.
Write any one property of binomial coefficients.
What should be the advertisement expenditure if the departmental store wants to attain a sales target of Rs. 200 lakhs?
Integrate 1/(x^4 − 1) dx using the concept of partial fraction. Also, give an example of proper rational
fraction and improper rational fraction.
State Rolle’s Theorem.
f′(x) and g′(x) are derivatives of the functions f(x) and g(x). What is the expression equal to
lim (x→a) f(x)/g(x) according to L’Hospital’s rule for form ∞/∞?
The set of points whose sum of distances from two fixed points is constant represents:
Circle
Parabola
Hyperbola
Ellipse
Write any one difference between like parallel forces and unlike parallel forces. A heavy uniform beam whose mass is 60 kg is suspended in a horizontal position by two vertical strings each of which can sustain a tension of 52.5 kg wt. How far from the centre of the beam must a body of mass 30 kg be placed so that one of the strings may just break?
If 2cosθ + 1 = 0, then the general value of θ is:
If 2cosθ + 1 = 0, then the general value of θ is:
nπ + 2π/3, n ∈ ℤ
2nπ ± 2π/3, n ∈ ℤ
2nπ + π/3, n ∈ ℤ