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The following Test is based on the syllabus of 60 Days Plan-2023 for UPSC IAS Prelims 2022.
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Consider the following
Types of Clouds | Classification |
1. Nimbostratus | High Clouds |
2. Stratocumulus | Low Clouds |
3. Altocumulus | Middle Clouds |
4. Cirrocumulus | Vertical Clouds |
How many above pairs are correctly matched?
Solution (b)
Types of Clouds | Classification |
1. Cumulus, Cumulonimbus | Vertical Clouds |
2. Stratocumulus, Nimbostratus, Stratus | Low Clouds |
3. Altocumulus, Altostratus | Middle Clouds |
4. Cirrocumulus, Cirrus, Cirrostratus | High Clouds |
Solution (b)
Types of Clouds | Classification |
1. Cumulus, Cumulonimbus | Vertical Clouds |
2. Stratocumulus, Nimbostratus, Stratus | Low Clouds |
3. Altocumulus, Altostratus | Middle Clouds |
4. Cirrocumulus, Cirrus, Cirrostratus | High Clouds |
With reference to Polar Vortex, consider the following statements
How many of the above statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
It is leading to a large-scale ozone depletion over the Polar Regions because it absorbs ozone in a large scale. | It is a low-pressure area surrounding both the poles of the Earth which is found in the upper level in both the North and South poles. It is a persistent, large-scale, low-pressure zone which rotates counter clockwise at the North Pole and clockwise at the South Pole and their rotation is driven by the Coriolis effect. | It is formed mainly in winter and gets weaker in summer. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
It is leading to a large-scale ozone depletion over the Polar Regions because it absorbs ozone in a large scale. | It is a low-pressure area surrounding both the poles of the Earth which is found in the upper level in both the North and South poles. It is a persistent, large-scale, low-pressure zone which rotates counter clockwise at the North Pole and clockwise at the South Pole and their rotation is driven by the Coriolis effect. | It is formed mainly in winter and gets weaker in summer. |
Consider the following statements about the composition of atmosphere
Which of the above statements is/are true?
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
Oxygen constitutes about 21% of the atmosphere which is inhaled by all living organisms. | Nitrogen is an important constituent of all organic compounds.
|
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
Oxygen constitutes about 21% of the atmosphere which is inhaled by all living organisms. | Nitrogen is an important constituent of all organic compounds.
|
Consider the following statements about thunderstorm
How many of the above statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
Thunderstorm is a storm with thunder and lightning along with heavy rain or hail. | They are less frequent on water bodies due to low temperature. | They are violent short duration storms which occur over a small area. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
Thunderstorm is a storm with thunder and lightning along with heavy rain or hail. | They are less frequent on water bodies due to low temperature. | They are violent short duration storms which occur over a small area. |
Consider the following statements
Choose the correct code:
Solution (c)
Statement 1 | Statement 2 |
Correct | Correct |
The Dry Adiabatic Lapse Rate (DALR) is the rate of fall in temperature with altitude for a parcel of dry or unsaturated air rising under adiabatic conditions and is associated with stable conditions (as it has less moisture).
Adiabatic change refers to the change in temperature with pressure. |
The Katabatic Wind is a hot dry wind that blows down a mountain slope which is an example for a falling parcel of air in which the temperature changes happen adiabatically. |
Solution (c)
Statement 1 | Statement 2 |
Correct | Correct |
The Dry Adiabatic Lapse Rate (DALR) is the rate of fall in temperature with altitude for a parcel of dry or unsaturated air rising under adiabatic conditions and is associated with stable conditions (as it has less moisture).
Adiabatic change refers to the change in temperature with pressure. |
The Katabatic Wind is a hot dry wind that blows down a mountain slope which is an example for a falling parcel of air in which the temperature changes happen adiabatically. |
Consider the following statements
Which of the below option best describes the above statements?
Solution (c)
Convectional Rainfall –
Solution (c)
Convectional Rainfall –
Consider the following statements about the conditions required to form a Dew
How many of the above statements are correct?
Solution (b)
The conditions required to form a Dew are –
Note:
Dew – When the moisture is deposited in the form of water droplets on cooler surfaces of solid objects such as stones, grass blades and plant leaves, it is known as dew.
Solution (b)
The conditions required to form a Dew are –
Note:
Dew – When the moisture is deposited in the form of water droplets on cooler surfaces of solid objects such as stones, grass blades and plant leaves, it is known as dew.
Consider the following statements about Jet Stream
Choose the correct code:
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
Jet Stream is a geostrophic wind blowing horizontally through the upper layers of the troposphere, generally from west to east. They are found at an altitude of 20,000 – 50,000 feet. | It is being developed in areas where air masses of differing temperatures meet.
The greater the difference in temperature, faster is the wind velocity inside the jet stream. They extend from 20⁰ latitude to the poles in both hemispheres. |
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
Jet Stream is a geostrophic wind blowing horizontally through the upper layers of the troposphere, generally from west to east. They are found at an altitude of 20,000 – 50,000 feet. | It is being developed in areas where air masses of differing temperatures meet.
The greater the difference in temperature, faster is the wind velocity inside the jet stream. They extend from 20⁰ latitude to the poles in both hemispheres. |
Consider the following statements
Choose the correct code:
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Nor Westers are violent evening thunderstorms in Bengal and Assam.
They are called as Kalbaisakhi – Bengal Bardoli Chheerha – Assam |
Nor westers play a vital role in the cultivation of tea, rice and jute.
|
Note:
The pre-monsoon showers during the end of the summer in Kerala and the coastal areas of Karnataka which helps in the ripening of the mangoes are called as Mango Showers.
The showers which helps in blossoming of coffee flowers in Kerala and nearby areas are called as Blossom Showers.
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Nor Westers are violent evening thunderstorms in Bengal and Assam.
They are called as Kalbaisakhi – Bengal Bardoli Chheerha – Assam |
Nor westers play a vital role in the cultivation of tea, rice and jute.
|
Note:
The pre-monsoon showers during the end of the summer in Kerala and the coastal areas of Karnataka which helps in the ripening of the mangoes are called as Mango Showers.
The showers which helps in blossoming of coffee flowers in Kerala and nearby areas are called as Blossom Showers.
What are the reasons for higher frequency of cyclones in Bay of Bengal when compared to Arabian Sea?
How many of the above statements are correct?
Solution (c)
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Correct |
The warm air currents enhance the surface temperature of Bay of Bengal. | The higher rainfall received in Bay of Bengal. | The constant inflow of fresh warm water from the Ganga and Brahmaputra rivers makes it further impossible to mix with the cooler water below. So, temperatures in Bay of Bengal remain relatively high. |
Solution (c)
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Correct |
The warm air currents enhance the surface temperature of Bay of Bengal. | The higher rainfall received in Bay of Bengal. | The constant inflow of fresh warm water from the Ganga and Brahmaputra rivers makes it further impossible to mix with the cooler water below. So, temperatures in Bay of Bengal remain relatively high. |
Which among the following factors significantly influence the global wind pattern?
How many of the above statements are correct?
Solution (c)
Factors that significantly influence Global wind patterns are:
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Correct |
Rotation of the earth
The rotation of the earth generates a force called the Coriolis force. This Coriolis force exerts an influence of shifting wind pattern orientation towards ‘its right’ in the northern hemisphere and ‘its south’ in the southern hemisphere. |
Atmospheric Pressure Variations
Pressure gradient force is a force that makes a wind travel from High Pressure to Low Pressure. Thus, we notice movements of planetary winds from High-pressure belts to Low-Pressure belts. |
Temperature Variations
Due to the spherical shape of the earth, there is differential heat distribution. Based on the heat, there are pressure differences are created. This influences global wind patterns. |
Solution (c)
Factors that significantly influence Global wind patterns are:
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Correct |
Rotation of the earth
The rotation of the earth generates a force called the Coriolis force. This Coriolis force exerts an influence of shifting wind pattern orientation towards ‘its right’ in the northern hemisphere and ‘its south’ in the southern hemisphere. |
Atmospheric Pressure Variations
Pressure gradient force is a force that makes a wind travel from High Pressure to Low Pressure. Thus, we notice movements of planetary winds from High-pressure belts to Low-Pressure belts. |
Temperature Variations
Due to the spherical shape of the earth, there is differential heat distribution. Based on the heat, there are pressure differences are created. This influences global wind patterns. |
Concerning the origin of Earth’s Atmosphere, consider the following statements:
Which of the above statements is/are incorrect?
Solution (c)
Statement 1 | Statement 2 |
Incorrect | Incorrect |
4.6 billion years ago, the Earth was a barren, rocky, and hot landmass with a thin atmosphere of hydrogen and helium. The amount of water and conducive atmosphere favored the existence of life on this planet. | The Early atmosphere was probably dominated at first by water vapor, which, as the temperature dropped, would rain out and form the oceans. This would have been a deluge of truly global proportions an resulted in further reduction of CO2. |
Solution (c)
Statement 1 | Statement 2 |
Incorrect | Incorrect |
4.6 billion years ago, the Earth was a barren, rocky, and hot landmass with a thin atmosphere of hydrogen and helium. The amount of water and conducive atmosphere favored the existence of life on this planet. | The Early atmosphere was probably dominated at first by water vapor, which, as the temperature dropped, would rain out and form the oceans. This would have been a deluge of truly global proportions an resulted in further reduction of CO2. |
Consider the following statements about layers of Atmosphere.
Which of the above statements is/are correct?
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
The Ionosphere is part of Earth’s upper atmosphere, between 80 and about 600 km where Extreme UltraViolet (EUV) and x-ray solar radiation ionizes the atoms and molecules thus creating a layer of electrons. the ionosphere is important because it reflects and modifies radio waves used for communication and navigation. | Noctilucent clouds are located in the mesosphere. The upper mesosphere is also the region of the ionosphere known as the D layer, which is only present during the day when some ionization occurs with nitric oxide being ionized by Lyman series-alpha hydrogen radiation. The ionization is so weak that when night falls, and the source of ionization is removed, the free electron and ion form back into a neutral molecule |
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
The Ionosphere is part of Earth’s upper atmosphere, between 80 and about 600 km where Extreme UltraViolet (EUV) and x-ray solar radiation ionizes the atoms and molecules thus creating a layer of electrons. the ionosphere is important because it reflects and modifies radio waves used for communication and navigation. | Noctilucent clouds are located in the mesosphere. The upper mesosphere is also the region of the ionosphere known as the D layer, which is only present during the day when some ionization occurs with nitric oxide being ionized by Lyman series-alpha hydrogen radiation. The ionization is so weak that when night falls, and the source of ionization is removed, the free electron and ion form back into a neutral molecule |
Consider the following statements about layers of the atmosphere of the earth.
How many of the above statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Incorrect | Correct | Correct |
The stratosphere has variable temperatures. The temperature tends to increase with the increase in altitude because of the reflection of harmful UV rays. | As there is a Normal Lapse Rate in the Troposphere, this statement is valid | The Normal Lapse Rate in the troposphere states that there is 6 degrees decrease in temperature for every 1 km ascent in altitude. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Incorrect | Correct | Correct |
The stratosphere has variable temperatures. The temperature tends to increase with the increase in altitude because of the reflection of harmful UV rays. | As there is a Normal Lapse Rate in the Troposphere, this statement is valid | The Normal Lapse Rate in the troposphere states that there is 6 degrees decrease in temperature for every 1 km ascent in altitude. |
Consider whether the following statements are correct with respect to thermal inversion?
How many of the above statements are correct?
Solution (d)
Statement 1 | Statement 2 | Statement 3 |
Incorrect | Incorrect | Incorrect |
A frontal inversion occurs when a cold air mass undercuts a warm air mass and lifts it aloft; the front between the two air masses then has warm air above and cold air below. | A subsidence inversion develops when a widespread layer of air descends. The layer is compressed and heated by the resulting increase in atmospheric pressure, and as a result the lapse rate of temperature is reduced. | Surface temperature inversions occur when air temperature increases with height from the ground surface, which is the opposite of what normally happens (i.e., the temperature profile is ‘inverted’). This results in a layer of cool, still air being trapped below warmer air. |
Solution (d)
Statement 1 | Statement 2 | Statement 3 |
Incorrect | Incorrect | Incorrect |
A frontal inversion occurs when a cold air mass undercuts a warm air mass and lifts it aloft; the front between the two air masses then has warm air above and cold air below. | A subsidence inversion develops when a widespread layer of air descends. The layer is compressed and heated by the resulting increase in atmospheric pressure, and as a result the lapse rate of temperature is reduced. | Surface temperature inversions occur when air temperature increases with height from the ground surface, which is the opposite of what normally happens (i.e., the temperature profile is ‘inverted’). This results in a layer of cool, still air being trapped below warmer air. |
Consider the following statements about the presence/absence of phenomenon of temperature inversion in different layers of the atmosphere.
Layers of Atmosphere – Temperature Inversion
How many pairs is/are correctly matched?
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Incorrect | Incorrect | Incorrect | Incorrect |
The troposphere is the first layer where the Normal lapse rate is followed and temperature inversion is absent | The stratosphere is the second layer of the earth and temperature inversion is observed here because of UV radiations reflected from the ozone layer | The mesosphere is the third layer of the atmosphere where temperature decreases as the altitude increases. | The ionosphere is the fourth layer of the atmosphere where the temperature inversion phenomenon is observed because of the rarefaction of ions |
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Incorrect | Incorrect | Incorrect | Incorrect |
The troposphere is the first layer where the Normal lapse rate is followed and temperature inversion is absent | The stratosphere is the second layer of the earth and temperature inversion is observed here because of UV radiations reflected from the ozone layer | The mesosphere is the third layer of the atmosphere where temperature decreases as the altitude increases. | The ionosphere is the fourth layer of the atmosphere where the temperature inversion phenomenon is observed because of the rarefaction of ions |
Consider the following statements with respect to the Western Cyclonic Disturbances.
Which of the statements given above is/are correct?
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
The Western cyclonic disturbances are weather phenomena of the winter months brought in by the Westerly flow from the Mediterranean region. | They usually influence the weather of the North and North-Western regions of India.
Western Disturbances are low pressure systems, embedded in Western winds (Westerlies) that flow from the West to the East. |
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
The Western cyclonic disturbances are weather phenomena of the winter months brought in by the Westerly flow from the Mediterranean region. | They usually influence the weather of the North and North-Western regions of India.
Western Disturbances are low pressure systems, embedded in Western winds (Westerlies) that flow from the West to the East. |
Consider the following statements regarding extra-tropical cyclones:
How many of the above given statements are correct?
Solution (b)
The low-pressure storm systems developing in the mid and high latitudes (35° latitude and 65° latitude in both hemispheres), beyond the tropics, are called the middle latitude or extratropical cyclones, or frontal cyclones. The passage of the front causes abrupt changes in the weather conditions over the area in the middle and high latitudes. Extratropical cyclones form along the polar front. Initially, the front is stationary. In the northern hemisphere, warm air blows from the south and cold air from the north of the front. When the pressure drops along the front, the warm air moves northwards and the cold air moves towards the south setting in motion an anticlockwise cyclonic circulation. The cyclonic circulation leads to a well-developed extratropical cyclone, with a warm front and a cold front.
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
Since fronts can be formed on both land and sea, extratropical cyclones can also be formed on land and sea as their occurrence requires the formation of fronts. | Under the influence of westerlies, the extratropical cyclones move in the west-to-east direction. | The pattern of wind direction in extratropical cyclones is anticlockwise in the northern hemisphere and clockwise in the southern hemisphere. |
Solution (b)
The low-pressure storm systems developing in the mid and high latitudes (35° latitude and 65° latitude in both hemispheres), beyond the tropics, are called the middle latitude or extratropical cyclones, or frontal cyclones. The passage of the front causes abrupt changes in the weather conditions over the area in the middle and high latitudes. Extratropical cyclones form along the polar front. Initially, the front is stationary. In the northern hemisphere, warm air blows from the south and cold air from the north of the front. When the pressure drops along the front, the warm air moves northwards and the cold air moves towards the south setting in motion an anticlockwise cyclonic circulation. The cyclonic circulation leads to a well-developed extratropical cyclone, with a warm front and a cold front.
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
Since fronts can be formed on both land and sea, extratropical cyclones can also be formed on land and sea as their occurrence requires the formation of fronts. | Under the influence of westerlies, the extratropical cyclones move in the west-to-east direction. | The pattern of wind direction in extratropical cyclones is anticlockwise in the northern hemisphere and clockwise in the southern hemisphere. |
Which of the following statements is/ are correct about ‘humidity’?
How many of the above given statements are correct?
Solution (a)
Statement 1 | Statement 2 | Statement 3 |
Incorrect | Correct | Incorrect |
The actual amount of water vapour present in the atmosphere is known as absolute humidity. It is the weight of water vapour per unit volume of air and is expressed in terms of grams per cubic meter. | The ability of
the air to hold water vapour depends entirely on its temperature. As warm air can hold more water vapour than cool air, the relative humidity decreases with increased temperatures. |
The percentage of moisture present in the atmosphere as compared to its full capacity at a given temperature is known as the relative humidity. With the change of air temperature, the capacity to retain moisture increases or decreases, and the relative humidity is also affected. It is greater over the oceans and least over the continents. |
Solution (a)
Statement 1 | Statement 2 | Statement 3 |
Incorrect | Correct | Incorrect |
The actual amount of water vapour present in the atmosphere is known as absolute humidity. It is the weight of water vapour per unit volume of air and is expressed in terms of grams per cubic meter. | The ability of
the air to hold water vapour depends entirely on its temperature. As warm air can hold more water vapour than cool air, the relative humidity decreases with increased temperatures. |
The percentage of moisture present in the atmosphere as compared to its full capacity at a given temperature is known as the relative humidity. With the change of air temperature, the capacity to retain moisture increases or decreases, and the relative humidity is also affected. It is greater over the oceans and least over the continents. |
What is the chief reason for tropical cyclones not developing close to the equator?
How many of the above given statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Incorrect | Correct | Incorrect |
The Coriolis force is zero at the equator (no cyclones at equator because of zero Coriolis Force) but it increases with latitude. Thus, weak Coriolis force not favoring circular motion is correct. | High temperature near the equator is a favourable factor for development of cyclone. It is only because of weak Coriolis force that cyclone does not develop. | Wind velocity in the doldrums belt near equator is very low. For a cyclone to be formed it requires High wind velocity and wind sheer. Thus it is a correct statement. | High humidity is a favourable condition for the formation of a cyclone and not a hindrance. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Incorrect | Correct | Incorrect |
The Coriolis force is zero at the equator (no cyclones at equator because of zero Coriolis Force) but it increases with latitude. Thus, weak Coriolis force not favoring circular motion is correct. | High temperature near the equator is a favourable factor for development of cyclone. It is only because of weak Coriolis force that cyclone does not develop. | Wind velocity in the doldrums belt near equator is very low. For a cyclone to be formed it requires High wind velocity and wind sheer. Thus it is a correct statement. | High humidity is a favourable condition for the formation of a cyclone and not a hindrance. |
Which of the following are the committees related to prison reforms in India?
Choose the correct code:
Solution (d)
Hence option d is correct.
Solution (d)
Hence option d is correct.
Consider the following statements:
How many of the above statements are correct?
Solution (b)
Note: The Toto is a primitive and isolated tribal group residing only in a small enclave called Totopara in the Jalpaiguri of West Bengal, India. The Totos are considered Mongoloid people and are generally endogamous and marry within their tribe.
Solution (b)
Note: The Toto is a primitive and isolated tribal group residing only in a small enclave called Totopara in the Jalpaiguri of West Bengal, India. The Totos are considered Mongoloid people and are generally endogamous and marry within their tribe.
Consider the following statements about the Insolvency and Bankruptcy Board of India (IBBI)
Choose the correct code:
Solution (a)
Solution (a)
Consider the following statements:
How many of the above statements are correct?
Solution (b)
Solution (b)
Consider the following statements about Kawar Lake
How many of the above statements are correct?
Solution (c)
Note: Karnataka is the only state in India which does not have a Ramsar Site. Tamil Nadu has the most number of Ramsar Sites.
Solution (c)
Note: Karnataka is the only state in India which does not have a Ramsar Site. Tamil Nadu has the most number of Ramsar Sites.
Consider the following statements about the findings of the Global Hunger Index 2023
How many of the above statements are correct?
Solution (c)
Solution (c)
Consider the following statements about the Colombo Security Conclave (CSC)
How many of the above statements are correct?
Solution (c)
Solution (c)
Consider the following statements about the applications of attophysics
How many of the above statements are correct?
Solution (c)
An attosecond is an astonishingly short unit of time, equivalent to one quintillionth of a second, or 10 to the power of 18 seconds. These pulses are used to unravel dynamical processes in matter with unprecedented time resolution .
Attosecond science is a branch of physics that deals with light-matter interaction phenomena, the production of extremely short light pulses, and using them to study superfast processes.
The applications of attophysics:
Solution (c)
An attosecond is an astonishingly short unit of time, equivalent to one quintillionth of a second, or 10 to the power of 18 seconds. These pulses are used to unravel dynamical processes in matter with unprecedented time resolution .
Attosecond science is a branch of physics that deals with light-matter interaction phenomena, the production of extremely short light pulses, and using them to study superfast processes.
The applications of attophysics:
Consider the following statements:
Choose the correct code:
Solution (a)
Solution (a)
Al-Hilal was an Urdu language newspaper founded by
Solution (d)
Al-Hilal was an Urdu-language newspaper founded by Maulana Abul Kalam Azad. It was used as a tool for opposing the British Raj in India. It also supported the Indian freedom movement’s cause and encouraged Indian Muslims to join the movement. It had been shut down under the 1914 Press Act. “Al-Hilal” (The Crescent) was published in Calcutta, started a new chapter in Urdu journalism, and appealed to Muslims in the city immediately. Hence option d is correct.
Solution (d)
Al-Hilal was an Urdu-language newspaper founded by Maulana Abul Kalam Azad. It was used as a tool for opposing the British Raj in India. It also supported the Indian freedom movement’s cause and encouraged Indian Muslims to join the movement. It had been shut down under the 1914 Press Act. “Al-Hilal” (The Crescent) was published in Calcutta, started a new chapter in Urdu journalism, and appealed to Muslims in the city immediately. Hence option d is correct.
If the number 97215*6 is completely divisible by 11, then the smallest whole number in place of * will be?
Solution (a)
Divisibility of 11:
(sum of digits in odd places) – (sum of digits in even places) = 0 or multiple of 11, then the number is divisible by. [usually looked from right to left]
22 – (8+*) = 0 or multiple of 11
14 – * = 0 or multiple of 11
Here multiple of ’11’ is the best option which is ’11’ itself 14 – * = 11
Hence * = 3
Hence ‘3’ is the smallest number that should replace * so that the number 97215*6 is divisible by 11.
Solution (a)
Divisibility of 11:
(sum of digits in odd places) – (sum of digits in even places) = 0 or multiple of 11, then the number is divisible by. [usually looked from right to left]
22 – (8+*) = 0 or multiple of 11
14 – * = 0 or multiple of 11
Here multiple of ’11’ is the best option which is ’11’ itself 14 – * = 11
Hence * = 3
Hence ‘3’ is the smallest number that should replace * so that the number 97215*6 is divisible by 11.
In UPSC Mains 2018 examination, 52% students failed in compulsory Hindi paper and 42% in compulsory English. If 17% failed in both the subjects, what percentage of students passed in both the subjects?
Solution (c)
Total percent of failed students = 52+42-17=77
Formula: n(A∪B) = n(A) + n(B) – n(A∩B)
Therefore, percentage of passed students = 100-77=23%.
Solution (c)
Total percent of failed students = 52+42-17=77
Formula: n(A∪B) = n(A) + n(B) – n(A∩B)
Therefore, percentage of passed students = 100-77=23%.
A purse contains 225 currency notes consisting of 5-rupee, 10- rupee and 50-rupee currencies in the ratio 3 : 7 : 5 respectively. Out of this, Rs. 25 is spent and the left out money is exchanged for 500- rupee currency notes then the number of 500-rupee currency notes is
Solution (c)
Value of Rs. 5 note = 3/15 × 225 × 5 = Rs. 225
Value of Rs. 10 note = 7/15 × 225 × 10 = Rs. 1050
Value of Rs. 50 note = 5/15 × 225 × 50 = Rs. 3750
Total money = Rs. 5025 Money remaining = Rs. 5025 – 25 = Rs. 5000
No. of Rs. 500 notes = Rs.5000 /Rs.500 = 10
Solution (c)
Value of Rs. 5 note = 3/15 × 225 × 5 = Rs. 225
Value of Rs. 10 note = 7/15 × 225 × 10 = Rs. 1050
Value of Rs. 50 note = 5/15 × 225 × 50 = Rs. 3750
Total money = Rs. 5025 Money remaining = Rs. 5025 – 25 = Rs. 5000
No. of Rs. 500 notes = Rs.5000 /Rs.500 = 10
554, 444, 757, 577 etc. are examples of number with repeated digits. How many such whole numbers from 1 to 201 are there which have repeated digits?
Solution (c)
From 1 to 201 we have Single digits 1 to 9 – No such repeated digit number
Therefore,required Number = 0
Double digit is 10 to 99 ->Number of numbers with repeated digits 11, 22, 33, 44, 55, 66, 77, 88, 99
Therefore, Required Number = 9
Triple digit i.e. 100 to 200 Number of numbers with repeated digits are: 100, 101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 133, 141, 144, 151, 155, 161, 166, 171, 177, 181, 188, 191, 199, 200.
Therefore, Required Number = 29.
Hence, total number = 9 + 29 =38
Solution (c)
From 1 to 201 we have Single digits 1 to 9 – No such repeated digit number
Therefore,required Number = 0
Double digit is 10 to 99 ->Number of numbers with repeated digits 11, 22, 33, 44, 55, 66, 77, 88, 99
Therefore, Required Number = 9
Triple digit i.e. 100 to 200 Number of numbers with repeated digits are: 100, 101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 133, 141, 144, 151, 155, 161, 166, 171, 177, 181, 188, 191, 199, 200.
Therefore, Required Number = 29.
Hence, total number = 9 + 29 =38
Appointments are to be made to the Higher Judiciary in India, one to the office of Chief Justice of India and two to the Judges of the Supreme Courts. Among the six candidates selected by the Collegium of Judges, only two are approved as eligible by the Government of India for the office of Chief Justice of India while all are eligible for appointment as the Judges of the Supreme Court of India. The number of possible combination of appointees is?
Solution (b)
Out of the appointments of the 2 Judges of the Supreme Court, one can be appointed in 2C1 = 2 ways.
Out of the remaining 5 Judges identified by the Collegium, 2 Judges to the Supreme Court can be appointed in 5C2 ways = (5 x 4)/2 = 10 ways Hence, number of possible combination of appointees = 2 x 10 = 20 ways.
Solution (b)
Out of the appointments of the 2 Judges of the Supreme Court, one can be appointed in 2C1 = 2 ways.
Out of the remaining 5 Judges identified by the Collegium, 2 Judges to the Supreme Court can be appointed in 5C2 ways = (5 x 4)/2 = 10 ways Hence, number of possible combination of appointees = 2 x 10 = 20 ways.
All the Best
IASbaba