List of top Mathematics Questions asked in TS EAMCET

If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of 3 is:
If 4 letters are selected at random from the letters of the word PROBABILITY, compute the probability that at least one letter is repeated in the selection.

Three similar urns \(A,B,C\) contain \(2\) red and \(3\) white balls; \(3\) red and \(2\) white balls; \(1\) red and \(4\) white balls, respectively. If a ball is selected at random from one of the urns is found to be red, then the probability that it is drawn from urn \(C\) is ?

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers on the top faces is ?

If two dice are rolled, determine the probability that the sum of the numbers on the top faces is a multiple of 3, given that their sum is an odd number.
If the probability distribution of a random variable \( X \) is as follows, then the variance of \( X \) is: \[ X = x \quad 2 \quad 3 \quad 5 \quad 9 \] \[ P(X = x) = k \quad 2k \quad 3k^2 \quad k^2 \]

. If a random variable X has the following probability distribution, then the mean of X is:

X = xiP(X = xi)
12k²
2k
3k²

 

The numbers 2, 3, 5, 7, 11, 13 are written on six distinct paper chits. If 3 of them are chosen at random, calculate the probability that the sum of the numbers on the obtained chits is divisible by 3.
If \( X \sim B(6, p) \) is a binomial variate and \[ \frac{P(X=4)}{P(X=2)} = \frac{1}{9}, \] then the value of \( p \) is:
Two cards are drawn at random one after the other with replacement from a pack of playing cards. If \( X \) is the random variable denoting the number of ace cards drawn, then the mean of the probability distribution of \( X \) is:

If three numbers are randomly selected from the set \( \{1,2,3,\dots,50\} \), then the probability that they are in arithmetic progression is: 

The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that the first three tosses resulted in 2 or more heads, is:

A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters in it except two consecutive letters. If 'LI' is left after erasing then the probability that the boy wrote the word PROBABILITY is: \

A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is:
The solution set of the equation \(\cos^2(2x) + \sin^2(3x) = 1\) is \;?
If \( \sin^{-1}(4x) - \cos^{-1}(3x) = \frac{\pi}{6} \), then \( x = \):

Match the functions in List--I with their corresponding properties in List--II:

The maximum value of the function \[ f(x) = 3\sin^{12}x + 4\cos^{16}x \] is ?

If \(A + B + C = 2S\), then \[ \sin(S - A)\,\cos(S - B)\;-\;\sin(S - C)\,\cos S \;=\;? \]
If \( \cos^2 84^\circ + \sin^2 126^\circ - \sin 84^\circ \cos 126^\circ = K \) and \( \cot A + \tan A = 2K \), then the possible values of \( \tan A \) are:
The equation that is satisfied by the general solution of the equation \( 4 - 3 \cos \theta = 5 \sin \theta \cos \theta \) is:
If \(\cos x + \cos y = \tfrac{2}{3}\) and \(\sin x - \sin y = \tfrac{3}{4}\), then \[ \sin(x - y) \;+\; \cos(x - y) \;=\;? \]
If \( \sinh^{-1}(-\sqrt{3}) + \cosh^{-1}(2) = K \), then \( \cosh K = \):
In triangle ABC, if \( a = 4, b = 3, c = 2 \), then \( 2(a - b \cos C)(a - c \sec B) = \):
If \(2\,\tan^{-1}x = 3\,\sin^{-1}x\) and \(x \neq 0\), then \(8x^2 +1 =\;?\)