HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Area of the region bounded by y = x⁴, x = 1, x = 5 and the X-axis is _______.

Using definite integration, area of the circle x² + y² = 49 is _______.

Fill in the blank :

Area of the region bounded by x² = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.

Fill in the blank :

The area of the region bounded by the curve x² = y, the X-axis and the lines x = 3 and x = 9 is _______.

The area of the region bounded by y² = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

State whether the following is True or False :

The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy` 

State whether the following is True or False :

The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.

State whether the following is True or False :

The area bounded by the curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.

If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.

State whether the following is True or False :

The area of the portion lying above the X-axis is positive.

Solve the following :

Find the area of the region bounded by the curve xy = c², the X-axis, and the lines x = c, x = 2c.

Solve the following :

Find the area of the region bounded by the curve y = x² and the line y = 10.

Find the area of the region bounded by y = x², the X-axis and x = 1, x = 4.

Solve the following:

Find the area of the region bounded by the curve x² = 25y, y = 1, y = 4 and the Y-axis.

Find the accumulated (future) value of annuity of ₹ 800 for 3 years at interest rate 8% compounded annually. [Given (1.08)³ = 1.2597]

A person invested ₹ 5,000 every year in finance company that offered him interest compounded at 10% p.a., what is the amount accumulated after 4 years? [Given (1.1)⁴ = 1.4641]

Find the amount accumulated after 2 years if a sum of ₹ 24,000 is invested every six months at 12% p.a. compounded half yearly. [Given (1.06)⁴ = 1.2625]

Find accumulated value after 1 year of an annuity immediate in which ₹ 10,000 is invested every quarter at 16% p.a. compounded quarterly. [Given (1.04)⁴ = 1.1699]

Find the present value of an annuity immediate of ₹36,000 p.a. for 3 years at 9% p.a. compounded annually. [Given (1.09)⁻³ = 0.7722]

Find the present value of an ordinary annuity of ₹63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given (1.14)⁻⁴ = 0.5921]