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WorksheetsMathematics class 12
Total questions: 50
Worksheet time: 25mins
How many three-digit numbers can be formed by using the integers 4, 5, 6, 8 with repetition?
64
27
24
6
Solution of 3x = 1 in ℤ4 is
0
1
2
3
If one of the roots of the equation x2 + ax + b = 0 and x2 + bx + a = 0 is coincident, then the numerical value of (a + b) is
0
-1
2
5
If the system of equations is 3x - 2y = 1 and - x + 4y = 3 then
D ≠ D1
D1 ≠ D2
D = D1 = D2
D ≠ D3
The eccentricity of the ellipse 4x2 + 9y2 = 36 is
1/(2√3)
1/√3
√5/3
√5/6
If a→ and b→ are two vectors then the value of (a→ - b→) × (a→ + b→) is equal to
(Check)
2(a→ × b→)
a2→ - b2→
-2(a→ × b→)
2(a2→ × b2→)
The range of probability of any event A is
0 ≤ P(A) ≤ 1
0 ≤ P(A) < 1
-1 ≤ P(A) ≤ 1
0 < P(A) < 1
∫x cos x2 dx is equal to
-(1/2) sin2 x + c
(1/2) sin2 x + c
-(1/2)sin x2 + c
(1/2) sin x2 + c
The simplex method was developed by
George Dantzig
Pythagoras
Issac Newton
Abel
If two like parallel forces of (P/Q)N and (Q/P)N have a resultant of 2N, then
P = Q
P = -Q
P = 2Q
2P = Q
What is the vertex of the parabola y = x2 - 2x + 1
(-1, 0)
(1, 0)
(0, -1)
(0, 1)
In the expansion of (1+x)50, the sum of the coefficient of odd power of x is
0
249
250
251
If arg z < 0 then arg (-z) - arg (z) is equal to
π
-π
-(π/2)
π/2
If Σn = 55, then Σn2 is equal to
385
506
115
3025
The equation √3 sin x + cos x = 4 has
Only one solution
Two solutions
Infinitely many solutions
No solution
If projections of any line on co-ordinates axes are 3, 4 and 5, then its length is
12
50
5√2
3√2
What would be the range of the square of the correlation coefficient (r2)?
-1 to +1
0 to 1
-∞ to +∞
-1 to 0
If y = 4x - 5 is tangent to the curve y2 = px3 + q at (2, 3), then
p = 2, q = -7
p = -2, q = 7
p = -2, q = -7
p = 2, q = 7
The second order differential equation is
y'2 + x = y2
y' y" + y = sin x
y''' + y" + y = 0
y' = y
In Gauss elimination method, the coefficient of the first variable in first equation must be
zero
non-zero
negative
positive
If a constant force of 'F' N acts on a body of mass 'm' kg for 't' seconds and brings it into motion with an acceleration 'a' m/sec2 and velocity Vm/sec, what will be its impulse?
ma
Fa
Ft
Fv
How many words can be made from the letters of the word INSURANCE, if all videos come together?
18270
17280
12780
None of these
For the set of G = {0, 1, 2, 3, 4} under congruence modulo addition, +⁵, the inverse of 1 is
0
2
3
4
If one root of the equation x2 + px + q = 0 is 2 + √3, then values of p and q are
-4, 1
4, -1
2, √3
-2, -√3
If the equation 2x2 + 5x + k = 0 has the reciprocal roots, what will be the value of k?
-5/2
5/2
-2
2
The system of equations cannot be solved by crammer's rule if
D = 0
D1 = 0
D2 = 0
D3 = 0
The foci of the ellipse 25(x + 1)2 + 9(y + 2)2 = 225 are all
(-1, 2) and (-1, -6)
(-1, 2) and (6, 1)
(-1, 2) and (1, -6)
(-1, -2) and (1, 6)
The unit vector perpendicular to 3i^ + 2j^ -k^ and 12i^ + 5j^ - 5k^ is
(Check)
(5i^ - 3j^ - 9k^)/√115
(5i^ + 3j^ - 9k^)/√115
(-5i^ + 3j^ - 9k^)/√115
(5i^ + 3j^ + 9k^)/√115
A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is
5/108
18/108
30/108
48/108
∫x cos x2dx is equal to
-(1/2)sin2 x + c
1/2 sin2 x + c
-(1/2) sin x2 + c
(1/2) sin x2 + c
In the simplex method, the slack and surplus variables are restricted to be
multiplied
divided
negative
non-negative
If P and Q are two like parallel forces then the resultant is
P + Q
P - Q
P2 + Q2
P2 - Q2
Find the producer surplus of the supply function is y = 2x2 + 4 and the quantity x is 2
32/3
31/3
34/3
35/3
If coefficient of (2r + 3)th and (r - 1)th terms in the expansion of (1 + x)15 are equal then values of r is
5
6
4
3
The argument of complex number -1 + i√3 is
-60°
60°
120°
240°
If x, y, z are in AP and tan-1 x, tan-1 y, tan-1 z are also in AP, then
2x = 3y = 6z
6x = 3y = 2z
6x = 4y = 3z
x = y = z
If tan-1 x + tan-1 y + tan-1 z = π, then x + y + z is equal to
xzy
0
1
2xyz
The length of the perpendicular from the origin to the plane 3x + 4y + 12z = 52 is
3
4
5
None of the above
Karl Pearson's correlation coefficient measures
the strength of relationship between two quantitative variables
the direction of relationship between two quantitative variables
both the strength and the direction of relationship between two quantitative variables
none of the above
The derivative of esinh 2x is
esinh 2x
θcosh 2x
2 cosh 2x esinh 2x
2 esinh 2x
The differential equation of all straight line passing through the point (1, -1) is
y = (x + 1) dy/dx + 1
y = (x + 1) dy/dx - 1
y = (x - 1) dy/dx + 1
y = (x - 1) dy/dx - 1
The system of equations 2x + y = 7 and x + 3y = 11 is
consistent and independent
inconsistent and independent
consistent and dependent
inconsistent and dependent
If the max. range up an inclined plane be one-third of the max. range down the plane then the inclination of the plane is the horizontal is
15°
30°
45°
60°
The number of ways in which a committee of 6 members can be formed from 8 gentleman and 4 ladies so that the committee contains at least 3 ladies is
252
672
444
420
For the set of natural number ℕ under the binary operation multiplication, which one of the following statement is not true?
Closure property is satisfied
Identity element (e) exists and belongs to ℕ
Associative property is satisfied
Inverse of every element also belongs to ℕ
If α, β be the roots is the equation 2x2 + 35x + 2 = 0 then the value of (2α - 35)³ (2β - 35)³ is equal to
1
64
8
None of these
If the system of equations is x + 3y = 4 and x - y = 0 then the value of D =
-4
2
3
0
In the ellipse, mirror acid is 8 and eccentricity is √5/3. Then major axis is
6
12
10
16
Four boys and three girls stand in a queue for an interview, probability that they will be in alternate position is
1/34
1/35
1/17
1/68
In simplex method, the slack and surplus variables are restricted to be
multiplied
divided
negative
non-negative
