Practice NAT Mathematics questions with answers and explanations.
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For ax² + bx + c = 0, the sum of roots is -b/a.
Here, -(-9)/1 = 9.
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For ax² + bx + c = 0, the product of roots is c/a.
Here, 20/1 = 20.
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Substitute x = -4 into the expression.
Then y = 3(-4) - 2 = -14.
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Slope-intercept form is y = mx + c.
With m = 2 and c = 3, the equation is y = 2x + 3.
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A point with x = 0 gives the y-intercept 4.
Using y = mx + c with m = -1 gives y = -x + 4.
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The sum of the roots is 6.
Their average is 6/2 = 3.
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The total population is 100,000.
The largest town has 45,000, so the fraction is 45/100 = 9/20.
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For two positive integers a and b, gcd(a,b) × lcm(a,b) = ab.
This identity links common factors and common multiples.
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Rent and food use 55%, leaving 45%.
Forty-five percent of Rs. 60,000 is Rs. 27,000.
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If n ≡ 4 mod 7, then 2n ≡ 8 mod 7.
The remainder of 8 divided by 7 is 1.
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Compare Tuesday sales with Monday: 210/150 × 100.
This equals 140%.
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Add 5 to both sides to get 3x > 15.
Dividing by 3 gives x > 5.
