CUET (UG) entrance exam Question Bank Solutions for Mathematics

Let `[x^y]` denotes the greatest integer of x^r and |x| denotes the modulus of x. Then `lim_(x -> 0) (sum_(r = 1)^(100) [x^r])/(1 + |x|)`

If n is a positive integer, then `int_0^(2pi) (sin^(2n) x)/(sin^(2n) x + cos^(2n) x)  dx` is equal to

The point P(2, 4) is first reflected on the line y = x and then the image point Q is again reflected on the line y = – x to get the image point Q'. Then the circumcentre of the ΔPQO' is

lf the straight lines `ax + by + p` = 0 and `x cos alpha + y sin alpha = p` are inclined at an angle π/4 and concurrent with the straight line `x sin alpha - y cos alpha` = 0, then the value of `a^2 + b^2` is

There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?

If `y = log_2 log_2(x)` then `(dy)/(dx)` =

If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is

The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be

A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is

`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to

If sin y = x sin (a + y), then value of dy/dx is

`d/(dx)(tan^-1  (sqrt(1 + x^2) - 1)/x)` is equal to:

The differential equation (1 + y²)x dx – (1 + x²)y dy = 0 represents a family of:

A type of problems which seek to maximise (or, minimise) profit (or cost) form a general class of problems called.

A type of problems which seek to maximise (or, minimise) profit (or cost) form a general class of problems called.

If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:

If 19^th term of a non-zero arithmetic progression (AP) is zero, then its (49^th term) : (29^th term) is

Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?

The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form as

`root(3)(4663) + 349` = ? ÷ 21.003