CUET (UG) entrance exam Question Bank Solutions

What is the sum of the first 50 terms of the series (1 × 3) + (3 × 5) + (5 × 7) + ...?

The sum of the series 3.6 + 4.7 + 5.8 + ....... upto (n – 2) terms

Find the intercepts cut off by the plane `2x + y - z` = 5

Find the equation of the plane with intercept 3 on the y-axis and parallel to zox plane.

Find the equation of the plane passing through the line of intersection of the planes `vecr * (hati + hatj + hatk)` = 1 and `vecr * (2hati + 3hatj - hatk) + 4` = 0 and parallel to x-axis

Find the distance of the point (–1, –5, –10) from the point of intersection of the line `vecr = 2hati - hatj - 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr * (hati - hatj + hatk)` = 5

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane `vecr * (hati + 2hatj + 5hatk) + 9` = 0

Find the equation of the plane passing through (a, b, c) and parallel to the plane `vecr  * (hati + hatj + hatk)` = 2

`int (dx)/(e^x + e^(-x))` is equal to ______.

If `f(a + b - x) = f(x)`, then `int_0^b x f(x)  dx` is equal to

The value of `int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2))  dx` is

What is the Cartesian product of A= {l, 2} and B= {a, b}?

If z + z^–1 = 1, then z¹⁰⁰ + z^–100 is equal to

If A, B are Symmetric matrices of same order, then AB – BA is a

If A, B are Symmetric matrices of same order, then AB – BA is a

A matrix in which the number of rows are equal to the number of columns is said to be a

If the total energy of a particle executing SHM is E, then the potential energy V and the kinetic energy K of the particle in terms of E when its displacement is half of its amplitude will be ______.

A spring balance has a scale that reads 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this spring, when displaced and released, oscillates with a period of 0.60 s. What is the weight of the body?

When a beam of 10.6 eV photons of intensity 2.0 W/m² falls on a platinum surface of area 1.0 × 10^-4 m², only 53% of the incident photons eject photoelectrons. The number of photoelectrons emitted per second is ______.

A cylinder of radius R, length Land density p floats upright in a fluid of density p₀. The cylinder is given a gentle downward push as a result of which there is a vertical displacement of size x; it is then released; the time period of resulting (undampe (D) oscillations is ______.