A piece of paper in the shape of a sector of a circle (see figure 1) is rolled up to form a right circular cone (see figure 2). The value of the angle is
The number of pairs of real (x, y) such that x = x2 + y2 and y = 2xy is
In a right triangle ABC, the incircle touches the hypotenuse AC at D. If AD = 10 and DC = 3, the inradius of ABC is
A man covered a certain distance by train at the rate of 25 kmph and walked back at the rate of 4 kmph. The whole journey took 5 hours 48 minutes. What is the total distance covered by him?
If a + b + c = 6 and , then find
A woman has 10 keys out of which only one opens a lock. She tries the keys one after the other (keeping aside the failed ones) till she succeeds in opening the lock. What is the chance that it is the seventh key that works?
The area of a circle is 154 cm2. If the radius gets doubled, what will be the new area?
The lengths of the sides of a right-angled triangle are in the ratio 3 : 4. The area of the triangle is 726 square units. The length of the hypotenuse (in proper units) is
The number of positive integers n in the set {1, 2, 3, ..., 100}, for which the number is an integer, is
A cow is tied to a corner (vertex) of a regular hexagonal fenced area of side a metres by a rope of length 5a/2 metres in a grass field. The cow cannot graze inside the fenced area. What is the maximum possible area of the grass field to which the cow has access to graze?
'A' can construct a wall in 30 days, whereas 'B' can construct or destroy the same wall in the same time i.e. destroy time is equal to construct time. If 'A' constructs and 'B' destroys, it takes 60 days to construct the wall. How many days will it take to construct the wall, if both 'A' and 'B' work towards constructing the wall?
In a triangle, three lines are drawn so that each line connects the mid-point on one side with any point on an adjacent side. What is the greatest number of over-lapping regions in the triangle that can be formed by the sides and the three lines?
Rohan sleeps at 10 pm and wakes up at 7 am. He bathes from 7 am to 8 am. He plays from 8 am to 10 am and again from 5 pm to 8 pm. He takes his dinner from 8 pm to 9 pm and watches TV from 9 pm to 10 pm and he studies the rest of the time. Which of the following represents his study time in fractions?
A rectangle is divided into 16 sub-rectangles as shown in the figure. The number in each sub-rectangle represents the area of that sub-rectangle. What is the area of the rectangle KLMN?
If the sides of a triangle are 13 units, 14 units, and 15 units, then the radius of its in-circle is
Two immiscible liquids, A and B are kept in a U-tube. If the density of liquid A is smaller than the density of liquid B, then the equilibrium situation is
We are able to squeeze snow and make balls out of it because of
Consider the circuit below. The bulb will light up if
A soldier with a machine gun, falling from an airplane gets detached from his parachute. He is able to resist the downward acceleration if he shoots 40 bullets a second at the speed of 500 m/s. If the weight of a bullet is 49 gm, what is the weight of the man with the gun? Ignore resistance due to air and assume the acceleration due to gravity g = 9.8 ms-2.
A bus and a car start from rest and run along a straight road with uniform acceleration of 2 m/s2 and 3 m/s2 respectively, with the car behind the bus at a distance of 1 m. How long will it take for both the bus and car travel side by side?
Twelve positive charges of magnitude q are placed on a circle of radius R in a manner that they are equally spaced. A charge +Q is placed at the centre. If one of the charges q is removed, then the force on Q is
An electric heater consists of a nichrome coil and runs under 220 V, consuming 1 kW power. Part of its coil burns out and it is reconnected after cutting off the burnt portion. The power it will consume now is
A ray of light passes through an equilateral prism such that an angle of incidence is equal to the angle of emergence, and the latter is equal to th the angle of prism. The angle of deviation is
What is the resistance between point A and C?
When a fuse is rated 8 A, it means it
A symmetric double convex lens is cut into two equal parts by a plane perpendicular to the principal axis. If the power of original lens is 4D, the power of a cut lens will be
A juggler tosses a ball up in the air with initial speed 'u'. At the instant it reaches its maximum height H, he tosses up a second ball with the same initial speed. The two balls will meet at
On a horizontal frictionless frozen lake, a girl (36 kg) and a box (9 kg) are connected to each other by means of a rope. Initially they are 20 m apart. The girl exerts a horizontal force on the box, pulling it towards her. How far has the girl travelled when she touches the box?
The principle used for the transmission of light signals through the optical fibre is
A convex lens is used to form an image of an object on a screen. If the upper half of the lens is blackened so that it becomes opaque, then
The molecular formula of marsh gas is ________.
The correct order of increasing basic nature for bases NH3, CH3NH2, (CH3)2 NH is
The type of hybridisation in CH2 = CH2 is
Which of the following will have the highest second ionisation energy from the ground state of electronic configuration of various electrons?
Two isotonic nuclides X and Y have mass numbers 35 and 37 respectively. If the atomic number of X is 17, the atomic number of Y will be _______.
Which of the following is a polar compound?
What will be the number of molecules present in 16 g of O2?
The helical structure of proteins is stabilized by
A solution is highly acidic in nature and a small quantity of a weakly basic solution is added to it. What will be the chemical nature of the resulting solution?
In the reaction PCl5 (g) PCl3 (g) + Cl2 (g), the equilibrium concentrations of PCl5 and PCl3 are 0.4 and 0.2 mole/litre, respectively. If the value of KC is 0.5, then what is the concentration of Cl2 in mole/litre?
In which of the following compounds does nitrogen have an oxidation state of − 1?
Non-metals are poor conductors of electricity because of the absence of
Which of the following compounds is not a hydrocarbon?
Which of the following word equations is incorrect?
The correct increasing order of energies of atomic orbitals is
Vitamin excreted by urine in higher vertebrates is
Which of the following is related to the central nervous system?
Identify the group among the following, which contains all the viral diseases.
If tall height (TT) is a dominant trait and short height is a recessive trait (tt) in the garden pea, then which of the following statements is true?
Fucus, an alga has which of the following types of life cycle?
Bidder's canal is found in
Klinefelter's syndrome in humans is an archetype of chromosomal aneuploidy. It is diagnosed by
At what stage of the cell cycle are histone proteins synthesized in a eukaryotic cell?
Which of the following cell types is considered as cell fragment and not a complete cell?
The fusion of sperm and egg initially results in formation of
In meiosis, germ cells will undergo two successive divisions in which
The enzymes which differ slightly in structure, but can catalyze the same type of reaction, are known as
Where do endocrine glands release their secretions?
Which of the following is the feature of skeletal muscle fibres?
Sacculated, fusiform or cylindrical forms are the main forms of which of the following diseases?
Solve the following system of inequalities:(A) 3x - 4 < 8x + 6(B) 2x - 1 > 5x - 4 (C) 11x - 9 15x + 3
Two vertices of a triangle are (– 2, 3) and (5, – 1). Its orthocentre lies at the origin and centroid lies on the line x + y = 7. Then the third vertex lies at
In the figure below, ΔAOB is an equilateral triangle. What is CAB?
A rectangle having dimensions x y has a unit square placed in the bottom right corner. Diagonal of length d, joining the bottom left corner with the top right corner of the rectangle, passes through the vertex of the square. If the area of the rectangle is an integer, then which one of the following is a possible value of d2 + 1?
In a triangle ABC, AB = AC = 37. Let D be a point on BC such that BD = 7, AD = 33. The length of CD is
The same force acts on two bodies of different masses 3 kg and 5 kg initially at rest. The ratio of times required to acquire the same final velocity is
According to the quantum theory, a photon of electromagnetic radiation of frequency has energy E = h, where 'h' is known as Planck`s constant. According to the theory of relativity, a particle of mass 'm' has equivalent energy E = mc2, where 'c' is the speed of light. Thus, a photon can be treated as a particle having effective mass m = . If a flash of light is sent horizontally in the earth's gravitational field, then photons while travelling a horizontal distance 'd' would fall through a distance given by
The current I in the given circuit is
The magnifying power of objective of a compound microscope is 5. If the magnifying power of microscope is 30, then the magnifying power of eyepiece will be
Two identical spheres carrying charges - 9 µC and 5 µC, respectively are kept in contact and then separated from each other. Choose the correct option which completes the following sentence. In each sphere,
Directions: The following question has four choices out of which ONLY ONE is correct.The reduction electrode potential (E) of 0.1 M solution of M+ ions (EoRP = – 2.36V) is
Directions: The following question has four choices out of which ONLY ONE is correct.Compound 'A' has molecular formula C5H10Cl2. It, on hydrolysis, gives C5H10O, which reacts with NH2OH to form iodoform, but does not give Fehling test. 'A' is
How many stereoisomers is shown by a glucose molecule having 4-asymmetric carbonation?
An organic compound containing carbon, hydrogen and oxygen contains 52.20% carbon and 13.04% hydrogen. Vapour density of the compound is 23 g/m3. Its molecular formula will be
For the reaction: H2(g) + I2(g) ⇌ 2HI(g), the equilibrium constants expressed in terms of concentration Kc and partial pressure Kp are related as
Portuguese man o' war or physalia is a
In a cross between red-eyed female dragonfly and a white-eyed male dragonfly what percent of the male progenies will have white eyes? (White eyes are X-linked recessive)
Mechanical support, enzyme circulation and protein synthesis are the main functions of
According to widely accepted "fluid mosaic model" cell membranes are semi–fluid, where lipids and integral proteins can diffuse randomly. In recent years, this model has been modified in several respects. In this regard, which of the following statements is incorrect?
Organisation of stem apex into corpus and tunica is determined mainly by
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