Practice questions
17 published questions with worked solutions.
- In a group of 3 girls and 4 boys, there are two boys B_1 and B_2. The number of ways, in which these girls and boys can stand in...
- Let , , and be the coefficients of x^7, x^5, x^3 and x respectively in the expansion of (x + x^3 - 1 )^5 + (x - x^3 - 1 )^5, x >...
- If A and B are two events such that P(A B) = 0.1, and P(A B) and P(B A) are the roots of the equation 12x^2 - 7x + 1 = 0 , then...
- If e^x ( ^ -1 x 1-x^2 + ^ -1 x (1-x^2)^ 3/2 + x 1-x^2 ) dx = g(x) + C, where C is the constant of integration, then g ( 1 2 )...
- Let a and b be two unit vectors such that the angle between them is 3 . If a + 2 b and 3 a - b are perpendicular to each other,...
- Let A = 1, 2, 3, 4 and B = 1, 4, 9, 16 . Then the number of many-one functions f: A B such that 1 f(A) is equal to :
- The perpendicular distance, of the line x-1 2 = y+2 -1 = z+3 2 from the point P(2, -10, 1), is :
- If x = f(y) is the solution of the differential equation (1+y^2) + (x - 2e^ ^ -1 y ) dy dx = 0, y (- 2 , 2 ) with f(0) = 1, then...
- Let the curve z(1+i) + z (1-i) = 4, z C , divide the region |z-3| 1 into two parts of areas and . Then | - | equals :
- If _ r=1 ^ 30 r^2(^ 30 C_r)^2 ^ 30 C_ r-1 = 2^ 29 , then is equal to _________.
- Let y = f(x) be the solution of the differential equation dy dx + xy x^2-1 = x^6+4x 1-x^2 , -1 < x < 1 such that f(0) = 0. If 6 _...
- Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables....
- A force F = 2 i + b j + k is applied on a particle and it undergoes a displacement d = i - 2 j - k . What will be the value of b,...
- The net current flowing in the given circuit is _______ A. 2 V 2 2.5 1 F 1 4 3 6 5 8 4
- Given below are two statements : Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are...
- The species which does not undergo disproportionation reaction is :
- The complex of Ni ^ 2+ ion and dimethyl glyoxime contains ________ number of Hydrogen (H) atoms.
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