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KEAM
List of top Questions asked in KEAM
If the inequality -13 ≤ x ≤ 5 is expressed in the form |x-a|≤b, then the values of a and b are respectively
KEAM - 2021
KEAM
Mathematics
inequalities
Let
\(\begin{vmatrix} x-1&2&1\\2&x-1&2\\1&x+2&x-1 \end{vmatrix}=ax^3+bx^2+cx+d\)
, where a,b,c and d are constants. Then the value of d is
KEAM - 2021
KEAM
Mathematics
Determinants
The matrix
\(\begin{bmatrix} -2&1&0\\3&4&1\\-4&\lambda&0 \end{bmatrix}\)
is non-singular for
\(\lambda\ne\)
KEAM - 2021
KEAM
Mathematics
Matrices
If
\(AB=\begin{bmatrix} 4&3\\5&4 \end{bmatrix}\)
and
\(A^{-1}=\begin{bmatrix} 3&-2\\-1&1 \end{bmatrix}\)
, then B=
KEAM - 2021
KEAM
Mathematics
Matrices
If
\(\begin{vmatrix} 1&2&1\\0&x&-3\\2&-1&x \end{vmatrix}=0\)
, then the value of x are
KEAM - 2021
KEAM
Mathematics
Determinants
The value of the determinant
\(\begin{vmatrix} 4&4^2&4^3\\3&3^2&3^3\\2&2^2&2^3 \end{vmatrix}\)
is
KEAM - 2021
KEAM
Mathematics
Determinants
Let
\(A+B=\begin{bmatrix} 4&1&4\\1&4&4 \end{bmatrix}\)
and
\(B=\begin{bmatrix} 1&0&-2\\-1&3&0 \end{bmatrix}\)
, then A=
KEAM - 2021
KEAM
Mathematics
Matrices
The term independent of x in the binomial expansion of
\((x+\frac{2}{x^3})^{20}\)
is
KEAM - 2021
KEAM
Mathematics
Binomial theorem
If x
22
is in the (r+1)th term of the binomial expansion of (3x
3
-x
2
)
9
, then the value of r is equal to
KEAM - 2021
KEAM
Mathematics
Binomial theorem
The number of 3-digit numbers that can be formed from the digits 0, 2, 3, 5, 7 is (repetition is allowed)
KEAM - 2021
KEAM
Mathematics
permutations and combinations
A set contains 9 elements. Then the number of subsets of the set which contains at most 4 clements is
KEAM - 2021
KEAM
Mathematics
Sets
The number of ways a committee of 3 women and 5 men can be formed from a panel of 8 men and 5 women is
KEAM - 2021
KEAM
Mathematics
permutations and combinations
A covid-19 vaccination reduces the probability of getting covid-19 infection from 0.4 to 0.1. In a city, 45% people are vaccinated. Then the probability that a non-vaccinated person chosen at random in the city gets covid-19 infection is
KEAM - 2021
KEAM
Mathematics
Probability
The first term of a G.P. is 3 and the common ratio is 2. Then the sum of first eight terms of the G.P. is
KEAM - 2021
KEAM
Mathematics
Geometric Progression
If the 10
th
and 12
th
terms of an A.P. are respectively 15 and 21, then the common difference of the A.P. is
KEAM - 2021
KEAM
Mathematics
Arithmetic Progression
In an A.P. the difference between the last and the first terms is 632 and the common difference is 4. Then the number of terms in the A.P. is
KEAM - 2021
KEAM
Mathematics
Arithmetic Progression
If the first term of a G.P. is 1 and the sum of 3
rd
and 5
th
terms is 90, then the positive common ratio of the G.P. is
KEAM - 2021
KEAM
Mathematics
Geometric Progression
Let t
n
, n = 1,2,3,... be the n
th
term of the A.P. 5, 8, 11,.... Then the value of n for which t
n
= 305 is
KEAM - 2021
KEAM
Mathematics
Arithmetic Progression
If a
1
, a
2
, a
3
,..., an are in A. P. with a
1
= 3, an, = 39 and a
1
+a
2
+...+an = 210, then the value of n is equal to
KEAM - 2021
KEAM
Mathematics
Arithmetic Progression
The value of
\(\displaystyle\sum_{k=5}^{36}\frac{1}{k^2-k}\)
is equal to
KEAM - 2021
KEAM
Mathematics
Sequence and series
The value of
\(\sqrt{(- 25)} + 3\sqrt{(- 4)} + 2\sqrt{(- 9)}\)
is equal to
KEAM - 2021
KEAM
Mathematics
Complex numbers
If the real part of the complex number
\(z=\frac{p+2i}{p-i}\)
,
\(p\isin\R, p\gt0\ is\ \frac{1}{2}\)
, then the value of p is equal to
KEAM - 2021
KEAM
Mathematics
Complex numbers
The area of the triangle on the complex plane formed by the points z, z+iz and iz is 128. Then the value of |z| is
KEAM - 2021
KEAM
Mathematics
Complex numbers
The imaginary part of
\(z=\frac{2+i}{3-i}\)
is
KEAM - 2021
KEAM
Mathematics
Complex numbers
If z=2-i√3, then |z
4
| is equal to
KEAM - 2021
KEAM
Mathematics
Complex numbers
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