CUET (UG) entrance exam Question Bank Solutions for Mathematics

A block rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take g = 10 m/s²)

What is the angle between two vectors `veca` and `vecb` with magnitudes `sqrt(3)` and 2 respectively, such that `veca * vecb = sqrt(6)`

What is the angle between the vectors `hati - 2hatj + 3hatk` and `3hati - 2hatj + hatk`

What is the projection of vector `hati - hatj` on the vector `hati + hatj`.

If `veca` is a non zero vector of magnitude `a` and `lambda` `veca` non-zero scolor, then `lambda` is a unit vector of.

A can finish a piece of work in 24 days. B is 20% more efficient than A. C is 25% more efficient than B. In how many days Band C together can finish the same piece of work?

Which one of the following statements is correct for a moving body?

S and S are the focii of the ellipse `x^2/a^2 + y^2/b^2 - 1` whose one of the ends of the minor axis is the point B If ∠SBS' = 90°, then the eccentricity of the ellipse is

A stone is dropped from the top of a cliff 40 m high and at the same instant another stone is shot vertically up from the foot of the cliff with a velocity 20 m per sec. Both stones meet each other after

A metro train starts from rest and in 5 s achieves 108 km/h. After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 395 m, find total time of travelling.

The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs ₹ 48 per hour at 16 miles per hour. The most economical speed if the fixed charges i.e. salaries etc. amount to ₹ 300 per hour is

`phi` is the angle of the incline when a block of mass m just starts slipping down. The distance covered by the block if thrown up the incline with an initial speed u₀ is

The coordinates of the point on the parabola y² = 8x which is at minimum distance from the circle x² + (y + 6)² = 1 are

`int_1^sqrt(3) (dx)/(1 + x^2)` equals

`int_6^(2/3) (dx)/(4 + 9x^2)` equals

A bullet of mass m and velocity a is fired into a large block of wood of mass M The final velocity of the system is

Let `vecalpha = hati + 2hatj - hatk, vecbeta = 2hati - hatj + 3hatk, vecγ = 2hati + hatj + 6hatk`. If `vecalpha` and `vecbeta` are both perpendicular to a vector `vecδ` and `vecδ. vecγ` = 10, then the magnitude of `vecδ` is

The n^th term of the series 2 + 4 + 7 + 11 + ..... is

The sum of the infinite series `x + (1 + 2)/(2!) x^2 + (1 + 2 + 3)/(3!) x^3 +` .... equals

A body of 6 kg rests in limiting equilibrium on an inclined plane whose slope is 30°. If the plane is raised to a slope of 60°, then the force along the plane to support the body is