The probability of guessing the correct answer to a certain test question is x/12 If the probability of not guessing the correct answer to this question is is equal to2/3 then x=?

Let L: R2 to R2 be the linear transformation such that L (1, 1) = (1, -2), L (-1, 1) = (2, 3). Then L (-1, 5) is equal to:

The number of local extreme values of f(x, y)=y^2−x^2, is :

Number of elements in power set of empty set :

Suppose X = {a, b, c, d} and R is a relation on X. If R = { (a,a), (b,b), (d,d), (a,b), (b,a), (b,d), (d,b) } then :

The remainder when 2^{50} is divided by 7 is :

The number of solutions of 3x = 5(mod7) is/are :

What is the smallest positive integer in the set { 12x + 30 + 3000z | x, y, z∈Z}?

Which of the following is a subspace of the vector space R³?

The equation of tangent at the point (0, 2) to the circle x² + y²-4x+2y-8=0 is:

Differential equation of the curve y = cx+1/c is:

The maximum number of linearly independent solutions of y'''' = 0, y(0) = 1, is

Avobe question

(HPSC PGT 2023) If all the natural number between 1 and 20 are multiplied by 4 then what is the variance of the resulting series ?

Which of the following is correct?

If one cubic cm of water weighs one gm and one cubic cm cube of wood weighs 0.42 gm, then what is the difference in weight of 1 cubic meter of water and 1 cubic meter of wood?

A tank can be filled by Tap-A in 30 minutes and by Tap-B in 45 minutes. Both the taps are kept open for 6 minutes and then Tap-B is turned off. In how many minutes more does the tank get filled?

Let T: R4 to IR be a linear transformation defined by T([X1, X2, X3, X4]) = x1 + x2 + X3+X4 Then one of the basis for ker(T) is