Free Bilingual questions and answers of Quantitative Aptitude
Quantitative Aptitude is an important subject in various government exams, including SSC, Bank, Railway, and UPSC. It is a section that tests the candidate's ability to solve mathematical problems efficiently and accurately. The subject comprises various topics such as arithmetic, algebra, geometry, trigonometry, and data interpretation. Here are some reasons why Quantitative Aptitude is an important subject in government exams:
Importance of Quantitative Aptitude in government exams
- Testing of Mathematical Skills: Quantitative Aptitude section tests the candidate's mathematical skills, which are crucial for various job profiles. Candidates are required to solve mathematical problems accurately and efficiently using their mathematical skills.
- Enhancing Problem-Solving Skills: The subject of Quantitative Aptitude helps in enhancing problem-solving skills. Candidates are required to analyze complex problems and come up with a logical solution using their problem-solving skills.
- Improving Time Management Skills: Quantitative Aptitude section also helps in improving time management skills. Candidates are required to solve mathematical problems within a limited time, which helps in improving their time management skills.
- Testing of Analytical Abilities: The section of Quantitative Aptitude also tests the candidate's analytical abilities, which are essential for data analysis and interpretation. Candidates are required to interpret data and solve problems based on their analytical abilities.
- Enhancing Accuracy: The section of Quantitative Aptitude helps in enhancing accuracy in mathematical calculations. Candidates are required to solve mathematical problems accurately, which helps in improving their overall accuracy.
In conclusion, Quantitative Aptitude is an essential subject in government exams like SSC, Bank, Railway, and UPSC. It tests the candidate's mathematical skills, problem-solving abilities, time management skills, analytical abilities, and accuracy. Candidates must prepare thoroughly for this subject to increase their chances of selection for the job.
- Number Systems
- Simplification and Approximation
- Data Interpretation
- Data Sufficiency
- Number Series
- Ratio and Proportion
- Quadratic Equations
- Averages
- Boats and Streams
- Interest
- Percentage
- Profit and Loss
- Discount
- Mixtures and Alligation
- Permutation and Combination
- Time and Distance
- Time and Work
- Probability
- Partnership
- Pipes and Cistern
- Algebra
- Geometry
- Mensuration
- Trigonometry
- Statistics
Q. In a business A and C invested amounts in the ratio 3:2, whereas A and B invested amounts in the ratio 4:1. If the total profit at the end of a year is Rs 35,650, find the share of A. एक व्यवसाय में A और C ने 3:2 के अनुपात में राशि का निवेश किया, जबकि A और B ने 4:1 के अनुपात में राशि का निवेश किया। यदि एक वर्ष के अंत में कुल लाभ 35,650 रुपये है, तो A का हिस्सा ज्ञात करें।
- (A). Rs 18,600
- (B). Rs 17,400
- (C). Rs 12,800
- (D). Rs 20,000
Q. if $$x+y+z=19$$, $$x^2+y^2+z^2=133$$ and $$xz=y^2$$, then the difference between $$z$$ and $$x$$ is: यदि $$x+y+z=19$$, $$x^2+y^2+z^2=133$$ और $$xz=y^2$$ है, तो $$z$$ और $$x$$ के बीच अंतर है:
- (A). 3
- (B). 4
- (C). 6
- (D). 5
$$(x+y+z)^2$$ = $$x^2+y^2+z^2+2(xy+yz+zx)$$
$$19^2=133+2(xy+yz+y^2)$$
$$2y(x+y+z)=361-133$$
$$2yxx19=228$$
$$y=228/38=6$$
Now,
$$x+z=19-y$$
$$x+z=19-6=13$$
$$x-z=sqrt((x+z)^2-4xz)$$
$$=sqrt(13^2-4y^2)$$
$$=sqrt(169-144)=5$$
Q. In triangle ABC, the points F and E respectively on AB and AC sides are as follows: FE || BC and FE divide the triangle into two parts with equal area. If AD ⊥ BC and AD intersect at FE at point G, then GD: AG =? त्रिभुज ABC में, AB और AC भुजाओं पर क्रमशः बिंदु F और E इस प्रकार हैं: FE || BC और FE त्रिभुज को बराबर क्षेत्रफल वाले दो भागों में विभाजित करते हैं। यदि AD ⊥ BC और AD, FE को बिंदु G पर प्रतिच्छेद करते हैं, तो GD: AG =?
- (A). $$(sqrt2+1):1$$
- (B). $$(sqrt2-1):1$$
- (C). $$2sqrt2:1$$
- (D). $$sqrt2:1$$
Since, EF||BC
AF/FB=AG/GD=AE/EC
AF/AB=AG/AD=AE/AC
Also, triangle ABC ~ triangle AFE
(Area(triangle ABC))/(Area(triangle AFE))=(AD)^2/(AG)^2
(AD)^2/(AG)^2=2xx(Area(triangle AFE))/(Area(triangle AFE))
AD/AG=(sqrt2)/1
AD/AG-1=(sqrt2)/1-1
DG/AG=(sqrt2-1)/1
Hence, DG:AG = (sqrt2-1):1
Q. A solid cube with a volume of 13824cm3 is cut into eight cubes of the same volume. The ratio of the surface area of the original cube and the total sum of the surface area of three smaller cubes will be: 13824cm3 आयतन वाले एक ठोस घन को समान आयतन वाले आठ घनों में काटा जाता है | मूल घन के पृष्ठीय क्षेत्रफल तथा तीन छोटे घनों के पृष्ठीय क्षेत्रफल के कुल योग का अनुपात होगा:
- (A). 2 : 3
- (B). 2 : 1
- (C). 4 : 3
- (D). 8 : 3
Edge of the original cube = 138241/3 = 24
Surface area of the original cube = 6(24)2 = 6 * 576 = 3456cm2
Now the larger cube is cut into 8 smaller cubes means,
It will be bisected along with its height, breadth, and length.
so, the edge of the smaller cubes will be half of the larger cube.
Now, Volume of one smaller cube = 123 = 1728
Since the larger cube is divided into 8 equal parts so the volume of each part = 13824/8 = 1728
now, the edge of one smaller cube = 17281/3 = 12cm
Total surface area of three smaller cubes
= 3 * 6 * 122
= 18 * 144
= 2592
Required ratio = 3456 : 2592 = 4 : 3
मूल घन का किनारा = 138241/3 = 24
मूल घन के पृष्ठीय क्षेत्रफल = 6(24)2 = 6 * 576 = 3456cm2
अब बड़े घन को 8 छोटे घनों में काटा जाता है अर्थात,
इसकी ऊंचाई, चौड़ाई और लंबाई के साथ इसे दो भागों में विभाजित किया जाएगा।
अतः छोटे घनों का किनारा बड़े घन का आधा होगा।
अब, एक छोटे घन का आयतन = 123 = 1728
चूंकि बड़े घन को 8 बराबर भागों में बांटा गया है, इसलिए प्रत्येक भाग का आयतन = 13824/8 = 1728
अब, एक छोटे घन का किनारा = 17281/3 = 12cm
तीन छोटे घनों का कुल पृष्ठीय क्षेत्रफल
= 3 * 6 * 122
= 18 * 144
= 2592
आवश्यक अनुपात = 3456 : 2592 = 4 : 3
Q. $$(2+tan^2theta+cot^2theta)/(sectheta cosectheta)$$is equal to: $$(2+tan^2theta+cot^2theta)/(sectheta cosectheta)$$ के बराबर है:
- (A). $$sectheta cosectheta$$
- (B). $$cottheta$$
- (C). $$tantheta$$
- (D). $$costhetasintheta$$
$$(2+tan^2theta+cot^2theta)/(sectheta cosectheta)$$
$$=(1+tan^2theta+1+cot^2theta)/(sectheta cosectheta)$$
$$=(sec^2theta+cosec^2theta)/(sectheta cosectheta)$$
$$=sectheta sintheta+cosectheta costheta$$
$$=(sintheta)/(costheta)+(costheta)/(sintheta)$$
$$=((sintheta)+(costheta))/(sintheta costheta)$$
$$=1/(sintheta costheta)$$
$$=sectheta cosectheta$$