List of top Mathematics Questions asked in COMEDK UGET

The value of \( \frac{1}{2\sin 10^\circ} - 2\sin 70^\circ \) is

If two vertices of a triangle are \( (3,-2) \) and \( (-2,3) \) and its orthocentre is \( (-6,1) \). Then the difference between ordinate and abscissa of the third vertex of the triangle is

If \( n(A) = 3 \) and \( n(B) = 7 \) and \( A \subseteq B \) then the number of elements in \( A \cap B \) is equal to

If \( y = \sin^{-1}\left(\frac{1}{\sqrt{x+1}}\right) \) then \( \frac{dy}{dx} = \)

The area bounded by the parabola \( y^2 = 36x \) and its latus rectum is

Area of the region bounded by the curve \( y = \sin\left(\frac{x}{2}\right) \) between \( -4\pi \) and \( 0 \) is

If \( \sin A + \sin B = \frac{21}{65} \), \( \cos A + \cos B = \frac{27}{65} \), then \( \sin(A+B) \) is

\( \int \log x^2 \, dx = \)

Distance of the point \( (-2,3) \) from the line \( 12x - 5y - 2 = 0 \) is \( \frac{41}{k} \). Then the value of \( k \) is

If \( A = \begin{pmatrix} 0 & 1 & -2 -1 & 0 & 3 2 & -3 & 0 \end{pmatrix} \), then \( A^{-1} \)

Codes used in vehicle identification consists of two distinct English alphabets followed by two distinct digits from 1 to 9. How many of them end with an even number.

If \( A = \begin{pmatrix} 1 & -2 4 & 5 \end{pmatrix} \); \( f(t) = t^2 - 3t + 7 \) then \( f(A) + \begin{pmatrix 3 & 6 -12 & -9 \end{pmatrix} = \)}

Let \(A\) and \(B\) be two events such that one of the two events must occur. Given that the chance of occurrence of \(A\) is \( \frac{2}{3} \) the chance of occurrence of \(B\), then odds in favour of \(B\) is

If \(y=\sqrt{\frac{x}{a}}+\sqrt{\frac{a}{x}}\), then \(2xy\frac{dy}{dx}\) is equal to

Equation of a circle whose area is 154 sq units and having \(2x-3y+12=0\) and \(x+4y-5=0\) as diameters is

For two matrices \(A\) and \(B\), given that \( A^{-1} = \frac{1}{8}B \) then inverse of \( (8A) \) is

\( \int \tan^2\left(5-\frac{x}{2}\right) dx = \)

\( \int \frac{1}{\sqrt{9+8x-x^2}}\,dx = \varphi(x) + c \), then \( \varphi(x) = \)

A person writes four letters and addresses four envelopes. If the letters are placed in the envelopes at random, then the probability that not all letters are placed in the right envelope is

The general solution of the differential equation \( (x-y)dy=(x+y)dx \) is

Let \( M \) be the set of all \( 2 \times 2 \) matrices with entries from the set \( R \) of real numbers. Then the function \( f : M \to R \) defined by \( f(A) = |A| \) for every \( A \in M \) is

If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( a \neq 0 \) and \( \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}) \), \( |\vec{a}| = |\vec{c}| = 1 \), \( |\vec{b}| = 4 \) and \( |\vec{b} \times \vec{c}| = \sqrt{15} \), if \( \vec{b} - 2\vec{c} = \lambda \vec{a} \) then \( \lambda^2 \) equals:

A line \(L_1\) passes through the points \( (h,k), (1,2) \) and \( (-3,4) \). The points \( (4,3) \) and \( (h,k) \) lie on the line \(L_2\). Given \(L_1 \perp L_2\), then \( (k-h) \) equals to

P is a point on the line joining the points \( (3,5,-1) \) and \( (6,3,-2) \). If \( y \)-coordinate of point P is 2, then \( x \)-coordinate will be

The sum of three numbers is 6. Twice the third number, when added to the first number gives 7. On adding the sum of the second and third numbers to thrice the first number, we get 12. The above situation can be represented in matrix form as \( AX = B \). Then \( | \text{adj } A | \) is equal to