'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is

If \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right]\), then \(A^{-1}\) is equal to :

For the matrix \(A=\left[\begin{array}{ccc}2 & -1 & -1 \\ 0 & 2 & 3 \\ 1 & -2 & 1\end{array}\right]\), which of the following statements are correct?
(A) The order of the matrix is 3 × 3
(B) |A| = 21
(C) |adj A| = 225
(D) A is skew symmetric matrix
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The volume of a cube is increasing at a rate of 9 cubic centimeter per second. Then rate of change of surface area when the length of an edge is 10 centimeter is:

Let \(\vec{a}=\hat{i}+4 \hat{j}, \vec{b}=4 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-2 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d}=16\), then \(|\vec{d}|\) is equal to:

If the matrix \(\left[\begin{array}{ccc}0 & 1 & 4 x \\ -1 & 0 & -5 \\ 2 & 5 & y\end{array}\right]\) is skew-symmetric, then :

Find the maximum value of the function sin x(1 + cos x) is:

When we consider a balanced chemical equation of an elementary reaction which statement is applicable on it?
(A) Molecularity can never be zero
(B) Order is less than molecularity
(C) Order is equal to molecularity
(D) Order is greater than the molecularity
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Answer the question on the basis of passage given below :
One of the notable features of the transition element is the great variety of oxidation states it may show in its compounds. The elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at the extreme ends is either due to losing or sharing of few electrons (Sc, Ti) or too many d electrons of higher valence. Early in the first series scandium (II) is virtually unknown and titanium (IV) which is more stable than Ti (III) or Ti (II). On the other end, the only oxidation state of zinc is \(+ 2\).
For balancing the given reaction, value of \(x\) will be.
\(4 FeCr_2 O_4+Na_2 CO_3+7 O_2 \longrightarrow x Na_2 CrO_4+2 Fe_2 O_3+8 CO_2\)

\(\int \frac{x+\sqrt{x}}{2 \sqrt{x}} d x=\)

The capacitance of a capacitor becomes \( \frac{9}{7} \) times of its original value when a dielectric slab of thickness \( t = \frac{d}{4} \) is inserted between the plates, where d is the separation between the plates. The dielectric constant of the slab is

A system has two charges, \( q_A = 5 \times 10^{-7} \, \text{C} \) and \( q_B = -5 \times 10^{-7} \, \text{C} \), located at points \( A : (0, 0, -10 \, \text{cm}) \) and \( B : (0, 0, +10 \, \text{cm}) \), respectively. Which of the following are true?
(A) The electric field of dipole at point (0, 0, -15 cm) is \( 1.73 \times 10^6 \, \text{NC}^{-1} \)
(B) Electric field intensity is zero at origin (0, 0, 0)
(C) dipole moment \( (p) = 5 \times 10^{-8} \, \text{C-m} \)
(D) direction of the dipole moment is along the negative z- axis
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Match List-I with List-II

List-I (Differential equation)	List-II (Order and Degree)
(A) \(\frac{d^3 y}{d x^3}+y^2+e^{d y / d x}=0\)	(I) order \(=3\), degree \(=1\)
(B) \(\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\frac{d y}{d x}+1=0\)	(II) order \(=3\), degree not defined
(C) \(2 x^2 \frac{d^2 y}{d x^2}-3\left(\frac{d y}{d x}\right)^2+y=0\)	(III) order \(=2\), degree \(=3\)
(D) \(\frac{d^3 y}{d x^3}+2\left(\frac{d y}{d x}\right)^2+\frac{d y}{d x}=0\)	(IV) order \(=2\), degree \(=1\)

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