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Sum of two numbers is 40 and their difference is 4. Find the ratio of the two numbers. [Answer Limit: 20 words, Marks: 02] [UKPSC-2016]
Who was the real founder of the Slave dynasty? [Answer Limit: 20 words] [UKPSC 2023]
The real founder of the Slave Dynasty was Qutb al-Din Aibak, who established the dynasty and the Delhi Sultanate.
The real founder of the Slave Dynasty was Qutb al-Din Aibak, who established the dynasty and the Delhi Sultanate.
See lessदो संख्याओं का योग 40 एवं उनमें अन्तर 4 है। दोनों संख्याओं का अनुपात ज्ञात कीजिये | [उत्तर सीमा 20 शब्द, अंक: 02] [UKPSC-2016]
मान लेते हैं दो संख्याएँ xx x और yy y हैं। दिया गया है: x+y=40x + y = 40 x+y=40 x−y=4x - y = 4 x−y=4 इन दोनों समीकरणों को हल करते हैं: जोड़ने पर: 2x=442x = 44 2x=44 x=22x = 22 x=22 घटाने पर: 2y=362y = 36 2y=36 y=18y = 18 y=18 अतः, दोनों संख्याओं का अनुपात है: xy=2218=119\fracRead more
मान लेते हैं दो संख्याएँ
x और
y हैं।
दिया गया है:
x+y=40
x−y=4
इन दोनों समीकरणों को हल करते हैं:
2x=44
x=22
2y=36
y=18
अतः, दोनों संख्याओं का अनुपात है:
yx=1822=911
इसलिए, अनुपात
11:9 है।
See lessIf the co-ordinates of the centroid of a triangle are (3, 2) and co-ordinates of the two vertices are (1, 1) and (2, 5), then find the co-ordinates of the third vertex. [Answer Limit: 20 words, Marks: 02] [UKPSC-2016]
To find the coordinates of the third vertex of a triangle when the coordinates of the centroid and two vertices are known, we can use the properties of the centroid. The centroid of a triangle is the point where the medians intersect, and it divides each median into a ratio of 2:1. The coordinates oRead more
To find the coordinates of the third vertex of a triangle when the coordinates of the centroid and two vertices are known, we can use the properties of the centroid. The centroid of a triangle is the point where the medians intersect, and it divides each median into a ratio of 2:1. The coordinates of the centroid ( G ) of a triangle with vertices ( A(x_1, y_1) ), ( B(x_2, y_2) ), and ( C(x_3, y_3) ) are given by the formula:
[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) ]
Given that the coordinates of the centroid ( G ) are ( (3, 2) ) and the coordinates of two vertices ( A ) and ( B ) are ( (1, 1) ) and ( (2, 5) ) respectively, we can set up the following equations:
[ 3 = \frac{1 + 2 + x_3}{3} ] [ 2 = \frac{1 + 5 + y_3}{3} ]
First, solve for ( x_3 ):
[ 3 = \frac{1 + 2 + x_3}{3} ] [ 9 = 1 + 2 + x_3 ] [ 9 = 3 + x_3 ] [ x_3 = 6 ]
Next, solve for ( y_3 ):
[ 2 = \frac{1 + 5 + y_3}{3} ] [ 6 = 1 + 5 + y_3 ] [ 6 = 6 + y_3 ] [ y_3 = 0 ]
Thus, the coordinates of the third vertex ( C ) are ( (6, 0) ). This solution demonstrates how the centroid formula can be used to find the missing vertex of a triangle when the coordinates of the other two vertices and the centroid are known. The method involves setting up and solving linear equations based on the given coordinates and the properties of the centroid.
See lessयदि एक त्रिभुज के केंद्रक के निर्देशांक (3, 2) और दो शीर्षों के निर्देशांक (1, 1) और (2, 4) हों, तो तीसरे शीर्ष के निर्देशांक ज्ञात कीजिये | [उत्तर सीमा 20 शब्द, अंक: 02] [UKPSC-2016]
यदि त्रिभुज के केंद्रक के निर्देशांक (3,2)(3, 2) (3,2) हैं और दो शीर्ष (1,1)(1, 1) (1,1) और (2,4)(2, 4) (2,4) हैं, तो तीसरे शीर्ष के निर्देशांक (x,y)(x, y) (x,y) को निम्नलिखित समीकरण से ज्ञात किया जा सकता है: (1+2+x3,1+4+y3)=(3,2)\left( \frac{1 + 2 + x}{3}, \frac{1 + 4 + y}{3} \right) = (3, 2) (31+2Read more
यदि त्रिभुज के केंद्रक के निर्देशांक
(3,2) हैं और दो शीर्ष
(1,1) और
(2,4) हैं, तो तीसरे शीर्ष के निर्देशांक
(x,y) को निम्नलिखित समीकरण से ज्ञात किया जा सकता है:
(31+2+x,31+4+y)=(3,2)
इससे हमें दो समीकरण मिलते हैं:
33+x=3
3+x=9
x=6
35+y=2
5+y=6
y=1
अतः तीसरे शीर्ष के निर्देशांक
(6,1) हैं।
See lessIf A is the solution set of 9x+27×2, where x is a natural number, then find A. [Answer Limit: 20 words, Marks: 02] [UKPSC-2016]
यदि 9x + 2>7×2, जहाँ x एक प्राकृतिक संख्या है, के हल का समुच्च A हो तो A ज्ञात कीजिये | [उत्तर सीमा 20 शब्द, अंक: 02] [UKPSC-2016]
दी गई असमानता को हल करते हैं: 9x+2>149x + 2 > 14 9x+2>14 9x>129x > 12 9x>12 x>129x > \frac{12}{9} x>912 x>43x > \frac{4}{3} x>34 चूंकि xx x एक प्राकृतिक संख्या है, x=2,3,4,…x = 2, 3, 4, \ldots x=2,3,4,… अतः A={2,3,4,…}A = \{2, 3, 4, \ldots\} A={2,3,4,…}
दी गई असमानता को हल करते हैं:
9x+2>14
9x>12
x>912
x>34
चूंकि
x एक प्राकृतिक संख्या है,
x=2,3,4,…
अतः
A={2,3,4,…}
See lessThe number 0.01, is what percent of the number 0.1? [Answer Limit: 20 words, Marks: 02] [UKPSC-2016]
Percentage=(0.01/0.1)*100 0.1*100=10 So, 0.01 is 10% of 0.1
संख्या 0.01, संख्या 0.1 की कितनी प्रतिशत है? [उत्तर सीमा 20 शब्द, अंक: 02] [UKPSC-2016]
If FINANCE = 39, MARKETING = 52, then PRODUCTION = ? [Answer Limit: 20 words, Marks: 02] [UKPSC-2016]
Finance has 7 word F-6 I-9 N-14 A-1 N-14 C-3 E-5 SUM OF LETTER= 6+9+14+1+14+3+5 MARKETING HAS 9 WORD M -13 A-1 R-18 K-11 E-5 T-20 I-9 N-14 G-7 SUM OF LETTER=13+1+18+11+5+20+14+7=98 DIVIDE 39 BY 7 39/7 =5.57 (APPROX 6) Divide 53 by 9 52/9=5.78(approx 6) Production has 10 letter 10*6=60 Value of produRead more
Finance has 7 word
F-6
I-9
N-14
A-1
N-14
C-3
E-5
SUM OF LETTER= 6+9+14+1+14+3+5
MARKETING HAS 9 WORD
M -13
A-1
R-18
K-11
E-5
T-20
I-9
N-14
G-7
SUM OF LETTER=13+1+18+11+5+20+14+7=98
DIVIDE 39 BY 7
39/7 =5.57 (APPROX 6)
Divide 53 by 9
52/9=5.78(approx 6)
Production has 10 letter
10*6=60
Value of production is 60
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