CUET (UG) entrance exam Question Bank Solutions for Mathematics

Let `veca` and `vecb` be two unit vectors and θ is the angle between them, Then `veca + vecb` is a unit vector if-

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

If the sum of two-unit vectors is a unit vector, then the magnitude of their difference is

Two equal forces acting at a point with an angle of 60° between them, if the resultant is equal `30sqrt(3)N`, the magnitude of the force will be

The area under a velocity-time curve represents the change in ______?

Angle between two unit-magnitude coplanar vectors P(0.866, 0.500, 0) and Q(0.259, 0.966, 0) will be?

The sum of the series `log_4 2 - log_8 2 + log_16 2 + ...............` to `oo` is

Which of the following statements is false about forces/ couple?

Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is

In a triangle ABC three forces of magnitudes `3vec(AB), 2vec(AC)` and `6vec(CB)` are acting along the sides AB, AC and CB respectively. If the resultant meets AC at D, then the ratio DC : AD will be equal to :

Sum of n terms of series 1.3 + 3.5 + 5.7 + ______ is

Let A_n be the sum of the first n terms of the geometric series `704 + 704/2 + 704/4 + 704/8 + ...` and B_n be the sum of the first n terms of the geometric series `1984 - 1984/2 + 1984/4 + 1984/8 + ...` If A_n = B_n, then the value ofn is (where n ∈ N).

Sum of the first n terms of the series `1/2 + 3/4 + 7/8 + 15/16 +`......... is equal to:

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