If \(a_1, a_2 ; a_3, \ldots, a_{10}\) is a geometric progression and \(\frac{a_3}{a_1}=25\), then \(\frac{a_9}{a_5}\) equals

\( \int_{0}^{\frac{\pi}{2}} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x \) is equal to

If A and B are invertible square matrices of order n, then which of the following is not correct?

If the area of the parallelogram with \(\mathbf{a}\) and \(\mathbf{b}\) as two adjacent sides is 15 sq units, then the area of the parallelogram having \(3 \mathbf{a}+2 \mathbf{b}\) and \(\mathbf{a}+3 \mathbf{b}\) as two adjacent sides in sq units is

If the parabola \(y=\alpha x^{2}-6 x+\beta\) passes through the point \((0,2)\) and has its tangent at \(x=\frac{3}{2}\) parallel to \(X\)-axis, then

Recent studies suggest that \(12\%\) of the world population is left handed. Depending on parents' hand usage, the chances of having left handed children are as follows:
A: Both parents are left handed, chances of having left handed children \(= 24\%\)
B: Both parents are right handed, chances of having left handed children \(= 9\%\)
C: Father left handed and mother right handed, chances of having left handed children \(= 17\%\)
D: Father right handed and mother left handed, chances of having left handed children \(= 22\%\)
Given \(P(A) = P(B) = P(C) = P(D) = 1/4\) and L denotes child is left handed. What is the probability that \(P(A \mid L)\)?

The coordinates of the foot of the perpendicular drawn from the point \((3,4)\) on the line \(2 x+y-7=0\) is

For a reaction, the value of rate constant at \(300 \mathrm{~K}\) is \(6.0 \times 10^5 \mathrm{~s}^{-1}\). The value of Arrhenius factor \(A\) at infinitely high temperature is

An animal which has both exoskeletal endoskeletal structure is

An organic compound \(X\) is oxidised by using acidified \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\). The product obtained reacts with phenyl hydrazine but does not answer silver mirror test. The possible structure of \(X\) is

In a potentiometer experiment, the balancing point with a cell is at a length \( 240 \mathrm{~cm} \). On
shunting the cell with a resistance of \( 2 \Omega \), the balancing length becomes \( 120 \mathrm{~cm} \). The internal
resistance of the cell is

\(9.65 \mathrm{C}\) of electric current is passed through fused anhydrous magnesium chloride. The magnesium metal thus, obtained is completely converted into a Grignard reagent. The number of moles of the Grignard reagent obtained is

For the arrangement of capacitors as shown in the circuit, the effective capacitance between the points \( A \) and \( B \) is (capacitance of each capacitor is \( 4 \mu \mathrm{F} \) )