CUET (UG) entrance exam Question Bank Solutions for Mathematics

Let `veca, vecb, vecc` be three vectors of magnitudes 3, 4 and 5 respectively. If each one is petpendicular to the sum of the other two vectors, then `|veca + vecb + vecc|` =

If `x (dy)/(dx) = y(log y - log x + 1)`, then the solution of the dx equation is

The value (s) of m does the system of equations 3x + my = m and 2x – 5y = 20 has a solution satisfying the conditions x > 0, y > 0.

The system of simultaneous linear equations kx + 2y – z = 1,  (k – 1)y – 2z = 2 and (k + 2)z = 3 have a unique solution if k equals:

If c < 1 and the system of equations x + y – 1 = 0, 2x – y – c = 0 and – bx+ 3by – c = 0 is consistent, then the possible real values of b are

If a, b, c are non-zeros, then the system of equations (α + a)x + αy + αz = 0, αx + (α + b)y + αz = 0, αx+ αy + (α + c)z = 0 has a non-trivial solution if

In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.

For what value of p, is the system of equations:

p³x + (p + 1)³y = (p + 2)³

px + (p + 1)y = p + 2

x + y = 1

consistent?

What is the nature of the given system of equations

`{:(x + 2y = 2),(2x + 3y = 3):}`

Choose the correct option:

If a, b, c are in A.P. then the determinant `[(x + 2, x + 3, x + 2a),(x + 3, x + 4, x + 2b),(x + 4, x + 5, x + 2c)]` is

If `|(x + 1, x + 2, x + a),(x + 2, x + 3, x + b),(x + 3, x + 4, x + c)|` = 0, then a, b, care in

If `|(x + a, beta, y),(a, x + beta, y),(a, beta, x + y)|` = 0, then 'x' is equal to

The number of real value of 'x satisfying `|(x, 3x + 2, 2x - 1),(2x - 1, 4x, 3x + 1),(7x - 2, 17x + 6, 12x - 1)|` = 0 is

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

The value of `hati(hatj + hatk)hatj * (hati + hatk) + hatk - (hati + hatj)` is-

If `θ` be the angle between any two vectors `veca` and `vecb`, then `|veca * vecb| = |veca xx vecb|`, when `θ` is equal to

The value of `lim_(x -> 0) [(d/(dx) int_0^(x^2) sec^2 xdx),(d/(dx) (x sin x))]` is equal to

If f" = C, C ≠ 0, where C is a constant, then the value of `lim_(x -> 0) (f(x) - 2f (2x) + 3f (3x))/x^2` is

Left `f(x) = {{:(1",", "if x is rational number"),(0",", "if x is irrational number"):}`. The value `fof (sqrt(3))` is

The limit of the function defined by `f(x) = {{:(|x|/x",", if x ≠ 0),(0",", "otherwisw"):}`