List of top Mathematics Questions

The set of all values of a for which the function f(x)=(a²-3a+2)(cos²x/4-sin²x/4)+(a-1)x is decreasing is
If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x\ne0
0, & x=0 endcases then f(x) is
If \( [x] \) denotes the greatest integer less than or equal to \( x \), and \( -1 < x < 0 < y < 1 < z < 2 \), then the value of the determinant

\( \begin{vmatrix} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{vmatrix} \)
is
Let alpha₁,alpha₂ and beta₁,beta₂ be the roots of ax²+bx+c=0 and px²+qx+r=0 respectively. If the system alpha₁ x+alpha₂ y=0, beta₁ y+beta₂ z=0 has a non-trivial solution, then
The number of points at which the function f(x)=(1)/(log|x|) is discontinuous is
If log a,log b,log c are in A.P. and also log a-log 2b,log 2b-log 3c,log 3c-log a are in A.P., then
If the matrix beginpmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endpmatrix is singular, then λ=
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one. Then the common difference of the progression is
If tan(cot x)=cot(tan x), then sin 2x is equal to:
The arithmetic mean of numbers a, b, c, d, e is M. What is the value of (a-M)+(b-M)+(c-M)+(d-M)+(e-M)?
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n respectively are:
The logical expression \( X \), in its simplest form for the truth table \[ \begin{array}{|c|c|c|} \hline A & B & X \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \hline \end{array} \] is
If \( f(a + b - x) = f(x), \) then \( \int_a^b f(x) \, dx \) is
\[ \int x^2 (x^4 + 1)^{3/4} \, dx \text{ is equal to } \]
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is
The domain and range of the function \( f(x) = 2 - |x - 5| \) is
The number of surjective functions from \( A \) to \( B \) where \( A = \{1,2,3,4\} \) and \( B = \{a, b\} \) is
If \( y = 2^x \), then \[ \frac{dy}{dx} \, \text{at} \, x = e \, \text{is} \]
If \( f(x) = (1 + x)^2 \) for \( x>0 \), then \( f(x) \) is
The solution of the equation \[ \sin^2\theta + \cos^2\theta = 1 \] lies in the interval
Number of ways of selecting three squares on a chessboard so that all the three be on a diagonal line of the board or parallel to it is
The foci of the ellipse \( \frac{x^2}{144} + \frac{y^2}{81} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide then value of \( b^2 \) is
The number of common tangents to the circles \( x^2 + y^2 = 16 \) and \( x^2 + y^2 - 6x = 0 \) is
If \( a = 1 \), \( b = 2 \), \( c = 3 \), and \( d = 4 \), then \[ abc = d \]