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The equations of one of the straight lines which pass through the point (1, 3) and make an angle tan^-1 √2 with the straight line, y + 1 = 3√2x is:

Let \(\begin{array}{l}A+2B=\begin{bmatrix} 1&2 &0 \\ 6&-3 &3 \\ -5&3 &1 \end{bmatrix}\end{array} \) and \(\begin{array}{l}2A-B=\begin{bmatrix} 2&-1 &5 \\ 2&-1 &6 \\... View Article

Tr(A) – Tr(B) has value equal to:

a. 220(220 + 21) b. 219(220 + 21) c. 220(220 – 21) d. 219(220 – 21) Solution: Answer: (d) Put... View Article

Let (1 + x + 2x²)²⁰ = a₀ + a₁x + a₂x² + …… + a₄₀x⁴⁰. Then, a₁ + a₃ +a₅ + ….+ a₃₇ is equal to

For all four circles M, N, O and P, the following four equations are given: Circle M : x2 +... View Article

For all four circles M, N, O and P, the following four equations are given

a. 1/2 b. 2 c. 1/6 d. 6 Solution: Answer: (b) limx→0 [sin-1 x – tan-1 x]/3x3 L = limx→0... View Article

If lim_x→0 [sin^-1 x – tan^-1 x] / 3x³ is equal to L, then the value of (6L + 1) is:

a. all non- integers except the interval [–1, 1] b. all integers except 0, –1, 1 c. all reals except... View Article

The real-valued function f (x) = cosec^-1 x /√(x – [x]) where [x] denotes the greatest integer less than or equal to x

a. y (dy/dx) + 2x (dy/dx) – y = 0 b. y (dy/dx)2 + 2x (dy/dx) – y = 0... View Article

The differential equations satisfied by the system of parabolas y² = 4a (x + a) is:

a. (1/2) sin √(2x + 1)2 + 5 + c b. (1/2) sin √(2x – 1)2 + 5 + c... View Article

The value of given expression is equal to

The value of is equal to: a. 3 + 2√3 b. 4 + √3 c. 2 + √3 d. 1.5... View Article

If α, β are natural numbers such that 100^α – 199β = (100) (100) + (99) (101) + (98) (102) + …. + (1) (199), then the slope of the line passing through (α, β) and origin is

a. 510 b. 550 c. 540 d. 530 Solution: Answer: (b) RHS = ∑r=099 (100 – r) (100 + r)... View Article

Choose the correct statement about two circles whose equations are given below

Choose the correct statement about two circles whose equations are given below: x2 + y2 – 10x – 10y +... View Article

The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is

a. 26664 b. 122664 c. 122234 d. 22264 Solution: Answer: (a) 1 2 2 3 1 2 3 2 1... View Article

A vector a has components 3p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle

A vector a has components 3p and 1 with respect to a rectangular Cartesian system. This system is rotated through... View Article

If function is differentiable at every point of the domain, then the values of a and b are respectively:

a. 5/2, – 3/2 b. – 1/2, 3/2 c. 1/2, 1/2 d. 1/2, – 3/2 Solution: Answer: (b) f (x)... View Article

The solutions of the equation [1+sin2x sin2x sin2x cos2x 1+cos2x cos2x 4sin2x4 sin2x 1+4sin2x ]=0, (0 lt x lt pi), are:

a. π/6, 5π/6 b. 7π/12, 11π/12 c. 5π/12, 7π / 12 d. π/12, π/6 Solution: Answer: (b) \(\begin{array}{l}\\R_{1}\rightarrow R_{1}+R_{2}\\ \begin{vmatrix} 2... View Article

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:

a. 3 b. 2 c. 1 d. 0 Solution: Answer: (b) 3x + 4(mx + 1) = 9 x(3 +... View Article

1 / (3² – 1) + 1 / (5² – 1) + 1 / (7² – 1) + ……. + 1 / (201² – 1) is equal to

a. 101/404 b. 101/408 c. 99/400 d. 25/101 Solution: Answer: (d) S = ∑r=1100 [1/[(2r + 1)2 – 1]] =... View Article

Let α, β, γ be the roots of the equations, x³ + ax² + bx + c = 0

Let α, β, γ be the roots of the equations, x3 + ax2 + bx + c = 0, (a,... View Article

If the functions are defined as f (x) = √x and g(x) = √(1 – x), then what is the common domain of the following functions: f + g, f – g, f / g, g / f, g – f where (f ± g) (x) = f (x) ± g (x), (f / g) (x) =

a. 0 < x ≤ 1 b. 0 ≤ x < 1 c. 0 ≤ x ≤ 1 d. 0... View Article

Let y = y (x) be the solution of the differential equation xdy – ydx = √(x² – y²) dx

Let y = y (x) be the solution of the differential equation xdy – ydx = √(x2 – y2) dx,... View Article

Let f : R → R satisfy the equation f (x + y) = f (x) . f (y) for all x, y ∈ R and f (x) ≠ 0 for any x ∈ R. If the function f is differentiable at x = 0 and f’ (0) = 3, then lim_h→0 (1 / h) [f (h) – 1] is equal to

Solution: Answer: (3) f (x + y) = f (x) . f (y) then f (x) = akx f’(x) =... View Article

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