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چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔
ہائیڈروکلورک ایسڈ کا پی ایچ _____ ہے؟
Equal to 7
Less than 7
Greater than 7
All of these
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Explanation
Hydrochloric acid (HCl) is a strong acid that completely dissociates in water, releasing H⁺ ions.
The pH scale ranges from 0 to 14 , where pH < 7 indicates acidity.
Since HCl increases H⁺ concentration, its pH is always less than 7 .
3
4
5
None of these
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Explanation
Let's determine the number of significant figures in the number 2.3040 .
Rules for Significant Figures :
All non-zero digits are significant. Zeros between non-zero digits are significant. Leading zeros (zeros before the first non-zero digit) are not significant. Trailing zeros (zeros after the last non-zero digit) are significant if there is a decimal point. Now, analyze 2.3040:
The digits 2, 3, and 4 are non-zero and significant. The zero 0 between 3 and 4 is a trapped zero, so it is significant. The last zero 0 is a trailing zero and there is a decimal point, so it is significant. So, the significant digits are: 2, 3, 0, 4, 0 → that's 5 significant figures .
آلے کے غلط کام کرنے سے پیدا ہونے والی خرابی ______ ہے؟
Determinant Error
Systematic Error
Indeterminant
Both A and B
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Explanation
Systematic errors are caused by faulty or improper functioning of instruments, or by a flaw in the experimental design.
These errors are consistent and repeatable, and can be identified and corrected.
متواتر جدول میں سونے کی علامت کیا ہے؟
Au
Ag
S
None of these
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Explanation
Au comes from the Latin word aurum , meaning "gold" (from "glowing dawn") Atomic number: 79 Belongs to group 11 Category: transition metal Additional information:
Atomic mass: 196.97 u Melting point: 1,064°C Boiling point: 2,856°C Density : 19.3 g/cm³ (very heavy)
-1
0
1
None of these
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Explanation
Let's evaluate the cross product step by step:
Given: i × ( j × k ) i × ( j × k )
Recall the vector triple product identity:
a × ( b × c ) = ( a ⋅ c ) b − ( a ⋅ b ) c a × ( b × c ) = ( a ⋅ c ) b − ( a ⋅ b ) c
Apply this with a = i a = i b = j b = j c = k c = k
i × ( j × k ) = ( i ⋅ k ) j − ( i ⋅ j ) k i × ( j × k ) = ( i ⋅ k ) j − ( i ⋅ j ) k
Now, compute the dot products:
So,
i × ( j × k ) = ( 0 ) j − ( 0 ) k = 0 i × ( j × k ) = ( 0 ) j − ( 0 ) k = 0
2
4
6
None of these
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Explanation
To find the slope of the tangent to the curve y = x 2 y = x 2 ( 2 , 4 ) ( 2 , 4 ) y y x x
Differentiate y = x 2 y = x 2
d y d x = 2 x d x d y = 2 x Evaluate the derivative at x = 2 x = 2
d y d x ∣ x = 2 = 2 × 2 = 4 d x d y x = 2 = 2 × 2 = 4 Therefore, the slope of the tangent at ( 2 , 4 ) ( 2 , 4 ) is 4 4 .
9
6
2
None of these
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Explanation
Let's evaluate the limit:
lim x → 3 x 2 − 9 x − 3 x → 3 lim x − 3 x 2 − 9
Step 1: Direct substitution gives 0 0 0 0
Notice that x 2 − 9 = ( x − 3 ) ( x + 3 ) x 2 − 9 = ( x − 3 ) ( x + 3 )
x 2 − 9 x − 3 = ( x − 3 ) ( x + 3 ) x − 3 = x + 3 (for x ≠ 3 ) x − 3 x 2 − 9 = x − 3 ( x − 3 ) ( x + 3 ) = x + 3 (for x = 3 )
Step 2: Now take the limit:
lim x → 3 ( x + 3 ) = 3 + 3 = 6 x → 3 lim ( x + 3 ) = 3 + 3 = 6
2/3
-3/2
-2/3
None of these
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Explanation
Let's evaluate the definite integral:
∫ 0 1 ( 5 t 2 − 2 t ) d t ∫ 0 1 ( 5 t 2 − 2 t ) d t
Step 1: Find the antiderivative (indefinite integral):
∫ ( 5 t 2 − 2 t ) d t = 5 ⋅ t 3 3 − 2 ⋅ t 2 2 + C = 5 3 t 3 − t 2 + C ∫ ( 5 t 2 − 2 t ) d t = 5 ⋅ 3 t 3 − 2 ⋅ 2 t 2 + C = 3 5 t 3 − t 2 + C
Step 2: Evaluate from 0 to 1:
[ 5 3 t 3 − t 2 ] 0 1 = ( 5 3 ( 1 ) 3 − ( 1 ) 2 ) − ( 5 3 ( 0 ) 3 − ( 0 ) 2 ) = ( 5 3 − 1 ) − ( 0 ) = 5 3 − 3 3 = 2 3 [ 3 5 t 3 − t 2 ] 0 1 = ( 3 5 ( 1 ) 3 − ( 1 ) 2 ) − ( 3 5 ( 0 ) 3 − ( 0 ) 2 ) = ( 3 5 − 1 ) − ( 0 ) = 3 5 − 3 3 = 3 2
So, the value is 2 3 3 2 .
Bijective
Injective
Surjective
None of these
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Explanation
The range of the function is equal to its codomain.
In this case, since the codomain is the set A, the condition "range = A" means the function is surjective .
5
7
3
None of these
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Explanation
Let's evaluate f ( 2 ) f ( 2 ) f ( x ) = x 3 − x 2 + x + 1 f ( x ) = x 3 − x 2 + x + 1
Substitute x = 2 x = 2
f ( 2 ) = ( 2 ) 3 − ( 2 ) 2 + ( 2 ) + 1 f ( 2 ) = ( 2 ) 3 − ( 2 ) 2 + ( 2 ) + 1
Calculate step by step:
2 3 = 8 2 3 = 8
2 2 = 4 2 2 = 4
So, 8 − 4 = 4 8 − 4 = 4
Then, 4 + 2 = 6 4 + 2 = 6
Finally, 6 + 1 = 7 6 + 1 = 7
Therefore, f ( 2 ) = 7 f ( 2 ) = 7 .
