If A is a square matrix of order 3, then |Adj(Adj A2)| =
If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
Let $ X = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \middle| a, b, c, d \in \mathbb{R} \right\} $. If $ f: X \to \mathbb{R} $ is defined by $ f(A) = \det(A) $ for all $ A \in X $, then $ f $ is
If y = \(\frac{3}{4} + \frac{3.5}{4.8}+\frac{5.5.7}{4.8.12}+ \).... to ∞, then
If l,m,n and a,b,c are direction cosines of two lines then
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} sin^2xcos^2x(sinx+cosx)dx=\)
On differentiation if we get f (x,y)dy - g(x,y)dx = 0 from 2x2-3xy+y2+x+2y-8 = 0 then g(2,2)/f(1,1) =
The locus of z such that \(\frac{|z-i|}{|z+i|}\)= 2, where z = x+iy. is
The perimeter of a △ABC is 6 times the arithmetic mean of the values of the sine of its angles. If the side BC is of the unit length, then ∠A =
An amplitude-modulated wave is represented by cm (t) = 10[1+0.6 sin(1250t)] sin(103 t). Then the modulation index is:
Heavy water is used to moderate in nuclear reactor because
There are 10 points in a plane, of which no three points are colinear expect 4. Then the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 colinear points is
Metal detector works on the principle of
lim n→∞ \(\frac{1}{n^3}\) \(\sum_{k=1}^{n} k^{2} =\)
If n is a positive integer and f(n) is the coeffcient of xn in the expansion of (1 + x)(1-x)n, then f(2023) =
A cylindrical vessel, open at the top, contains 15 liters of water. Water drains out through a small opening at the bottom. 5 liters of water comes out in time t1, the next 5 litre in further time t2, and the last 5 litre in further time t3. then:
If a line ax + 2y = k forms a triangle of area 3 sq.units with the coordinate axis and is perpendicular to the line 2x - 3y + 7 = 0, then the product of all the possible values of k is
Consider the following statements about the oxides of halogens A. At room temperature, OF2; is thermally stable B. Order of stability of oxides of halogens is I > Br > Cl C. I2O5 is used in the estimation of CO D. ClO2; is used as a bleaching agent The correct statements are
It is found that a non-zero current is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is:
If cosθ = \(\frac{-3}{5}\)- and π < θ < \(\frac{3π}{2}\), then tan \(\frac{ θ}{2}\) + sin \(\frac{ θ}{2}\)+ 2cos \(\frac{ θ}{2}\) =
The ratio of lone pair of electrons to bond pair of electrons in ozone molecule is:
In △ABC, if a : b : c = 4 : 5 : 6, then the ratio of the circumference to its in radius is
If x+√3y = 3 is the tangent to the ellipse 2x2 + 3y2 = k at a point P then the equation of the normal to this ellipse at P is
The alkali metal with the lowest E M- M+ (V) is X and the alkali metal with highest E M- M+ is Y. Then X and Y are respectively: