Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If angle BPC = β , then calculate value of tan β.

What will be the probability that at least one of the event occurs for three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 and P(All the three events occur simultaneously) = 1/16?

Let S = {1, 2, 3, ..... , 9}. For k = 1, 2, ....., 5, let NK be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1 + N2 + N3 + N4 + N5

What will be the beat frequency of the resulting signal in Hz if A stationary source emits sound of frequency f = 492 Hz. The sound is reflected by a large car approaching the source with a speed of 2 m/s. The reflected signal is received by the soruce and superposed with the original (Given that the speed of sound in air is 330 m/s and the car reflects the sound at the frequency it has received)?

Calculate the length of the other edges if Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3?

How many m^2 of cardboard are needed to make the cuboid with dimensions 40 cm 60 cm and 20 cm?

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What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y -2z = 5 and 3x-6y -2z = 7?

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What will be the value of T if A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm,filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 750C. T is given by: (Given : room temperature = 300C, specific heat of copper = 0.1 cal/gm0C)?

What will be the variance of the number of green balls drawn if A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement?

A compound ‘X’ reacts with a compound ‘Y’, to produce a colourless and odourless gas. The gas turns lime water milky. When ‘X’ reacts with methanol in the presences of concentrated H2SO4, a sweet smelling substance is produced. The molecular formula of the compound ‘X’

What is cuboid? What will be the real time examples of the cuboid.

The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 *10^-2m rise of water, h = 1.45 *10^2m Using g = 9.80 m/s2 and the simplified relation T = (rhg*10^)/2 N/ m, the possible error in surface tension is closest to?

What will be the variance of the number of green balls drawn is if A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one by one, with replacement?

What will be maximum area (in sq. m) of the flower-bed if Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector?

A rocket is launched normal to the surface of earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3 *10^5 times heavier than the Earth and is at a distance 2.5 *10^4 times larger than the radius of the Earth. The escape velocity from Earth’s gravitational field is ve = 11.2 km /s The minimum initial (vs) required for the rocket to be able to leave the Sun-earth system is closest to(Ignore the rotation and revolution of the Earth and the presence of any other planet).

An electron in a hydrogen atom undergoes a transition from an orbit with quantum numebr ni to another with quantum number nf. Vi and Vf are respectively the initial and final potential energies of the electon. If vi/ vf =6.25, Then what is smallest possible nf is

The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side ?

If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and midpoint (h, k), then what is(are) possible value(s) of p, h and k ?

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g cm-3, then the number of atoms present in 256 g of the crystal is N × 1024. The value of N?

Why colour of the X2 molecules of group 17 elements changes gradually from yellow to violet down the group?

How many unpaired electrons are present in Co3+ ion?

How many groups are occupied by p-block elements in long form of periodic table?

What is the power of accommodation of the eye?

A myopic person uses specs of power –0.5 D. What is the distance (in meter) of the far point of his eye?

What is Sublimation? Please explain?

Two balls are dropped to the ground from different heights. One ball is dropped 2s after the other but they both strike the ground at the same time. If the first ball takes 5s to reach the ground, then the difference in initial heights is (g = 10 ms–2) 40

16. A train covers a distance of 90km at a uniform speed. Had the speed been 15km/hr more, it would have taken half an hour / hr for the journey. What will be the original Speed of the train.

15. In a two digit number, the sum of the digits is 13. If the number is subtracted from the one obtained by inter changing the result is 45. Find the number.

What will be current through electric iron if an electric iron rated as 800W, 200V operating at the voltage of 100V?

What will be energy of an alfa particle when it is accelerated by a potential difference of 3V?

Number of electrons to be put on a spherical conductor of radius 0.1 m to produce an electric field of 0.036N/C just above its surface is

An Athletic completes one round of a circular track of radius 2.5 m in 12 sec. What will be the magnitude of displacement (in meter) at the end of 54 sec.

## What will be the relative rates of diffusion between CH4 and SO2? (Mol. mass of SO2 = 64 & CH4 = 16)

What will be the relative rates of diffusion between CH4 and SO2? (Mol. mass of SO2 = 64 & CH4 = 16)

Find the volume of a pyramid whose base is a square with side lengths of 10 m and height 9 m.

How many edges faces and vertices are on a cone?

What type of pyramid has four faces?

What is the edge of a cube?

What is a square based pyramid?

How many vertices are in a pyramid?

What is the number of vertices in a pyramid with 10 faces?

What is the rate of acceleration of gravity?

Mr. Sharma and Mr. Arora are family friends and they decided to go for a trip with family . For the trio they reserved their rail tickets . Mr. Arora has not taken a half ticket for his child who is 6 years old where as Mr, Sharma has taken half tickets for his two children who are 6 year and 8.5 year.A railway half ticket costs half of the full fare but the reservation charges are the same as on a FULL TICKET. MR AND MRS ARORA PAID 1700,WHILE MR AND MRS SHARMA PAID 2700. Find the full share of one ticket and reservation charges per ticket.

Can the number n ^6,n being a natural number ,end with the digit 5? Give reasons.

A man has certain note of denomination 20 and 5 which amount to 380 . If the number of notes of each kind are interchanged,they amount to 60 less than before . Find the number of notes of each denomination.

Explain with a suitable diagram

Explain why sodium is more reactive than lithium.