A fair coin is tossed 10 times. The probability of obtaining exactly six heads is:

If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(x\)-axis, \(y\)-axis, \(z\)-axis respectively, then the value of \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is equal to:

How many minimum number of times must a man toss a fair coin so that the probability of having at least one head is more than \(90 \%\) ?

Area (in sq. units) of the region bounded by the curves \(y = - 1, y = 2 x = y^3\) and \(x = 0\) is

Match List - I with List - II

List - I	List - II
(A) The degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)=x \sin \left(\frac{d y}{d x}\right)\)	(I) 4
(B) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0\)	(II) 1
(C) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0\)	(III) Not defined
(D) The degree of differential equation \(1+\left(\frac{d y}{d x}\right)^4=7\left(\frac{d^2 y}{d x^2}\right)^3\)	(IV) 3

Choose the correct answer from the options given below:

A person has invested Rs. 20,000 in 2020 for 5 years.
If the CAGR for his investment is 11.84%, the end balance of his investment is [Given \((1.1184)^5=1.7498\) ]

If matrix \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j}=\left\{\begin{array}{l}1, i \neq j \\ 0, i=j\end{array}\right.\) then \(A^3\) is equal to :

Read the following passage carefully.
Restriction enzyme
Restriction enzymes cut the strand of DNA a little away from the center of the palindrome sites, but between the same two bases on the opposite strands. This leaves single stranded portions at the ends. There are overhanging stretches called sticky ends on each strand. These are named so because they form hydrogen bonds with their complementary cut counterparts. This stickiness of the ends facilitates the action of the enzyme DNA ligase. The word palindromes refer to group of letters that forms the same words when read both forward and backward. Restriction endonucleases are used in genetic engineering as molecular scissors.
Overhanging stretches on each strand is called:

Match List-I with List-II

List-I	List-II
(A) The current lags behind the emf by \( \pi/4 \) in phase	(I) A.C. circuit containing only an inductor
(B) The e.m.f. lags behind the current by \( \pi/4 \) in phase	(II) A.C. circuit with resistance and inductances in series
(C) The current lags behind the e.m.f. in phase by \( \pi/2 \)	(III) A.C. circuit containing only as capacitor
(D) The e.m.f. lags behind the current in phase by \( \pi/2 \)	(IV) A.C. circuit with resistance and capacitor in series

Choose the correct answer from the options given below :

When a dielectric slab is introduced in between the plates of a charged capacitor with battery connected across the plates, following are the observations. Choose which observation is incorrect?

Let \(A=\left[\begin{array}{ccc}2 & -3 & 4 \\ 0 & 1 & 5 \\ -4 & 2 & 3\end{array}\right]\), and \(a_{i j}\) be any element of \(A, i, j \in\{1,2,3\}\), then which of the following are TRUE?
(A) Minor of \(a_{23}=16\)
(B) Minor of \(a_{23}=-8\)
(C) Cofactor of \(a_{23}=-16\)
(D) Cofactor of \(a_{23}=8\)
(E) Cofactor of \(a_{13}=4\)
Choose the correct answer from the options given below :

A metal conductor of length 1m rotates in vertical plane about an axis passing through one of its ends at angular velocity 4 rad s-¹. What is the emf developed between the two ends of the conductor, if the horizontal component of the earth's magnetic field is 0.2 G?

In a diffraction experiment, the screen is placed \( D = 2 \text{ m} \) away from a narrow slit. The first minimum observed is at \( x = 5 \text{ mm} \) on either side of the central maximum for wavelength of \( \lambda = 5 \times 10^{-5} \text{ cm} \). The width of the slit a is: