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Let and are two real roots of the equation

Let and are two real roots of the equation ( + 1) tan2 − √2 tan = 1 − , where ( ≠ −1) and are real... View Article

If g(x) = x² + x – 1 and (gof)(x) = 4x² – 10x + 5, then f(5/4) is equal to

a) -3/2 b) -1/2 c) 1/2 d) 3/2 Answer: (b) g(x) = x2 + x - 1 gof(x) = 4x2 - 10x + 5 g(f(x) = 4x2 - 10x + 5 f2(x) + f(x) - 1 = 4x2 - 10x + 5... View Article

Let be a root of the equation x²+ x+ 1= 0

Let be a root of the equation x2 + x+ 1= 0 and the matrix A = then the matrix A31 is equal to a) A b) A2 c) A3 d) I3 Answer: (c) The... View Article

If y = mx + 4 is a tangent to both the parabolas

If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to a) -64 b) 128 c) -128 d) -32 Answer: (c) Any... View Article

If y(α) = [latex]sqrt{2(frac{tan alpha + cot alpha }{1+

a) -1/4 b) 4/3 c) 4 d) -4 Answer: (c) y(α) = y(α) = √(1+cotα )2 y(α) = -1 - cotα dy/dα... View Article

A vector ⃗ = ̂ + 2 ̂ + ̂ ( , ∈ ) lies in the plane of the vectors

A vector 𝑎⃗ = 𝛼𝑖̂ + 2𝑗̂ + 𝛽𝑘̂ (𝛼, 𝛽 ∈ 𝑹) lies in the plane of the vectors, ⃗𝑏 = 𝑖̂ + 𝑗̂ and 𝑐⃗ = 𝑖̂ − 𝑗̂ + 4𝑘̂. If 𝑎⃗ bisects the... View Article

The greatest positive integer , for which 49 + 1 is a factor of the sum 49¹²⁵ + 49¹²⁴ + ⋯ + 49² + 49 + 1, is

a) 32 b) 60 c) 65 d) 63 Answer: (d) 1 + 49 + 492 + …. + 49125 = (49126 - 1)/(49 - 1) = (4963 + 1)( 4963 - 1)/48 = (4963 + 1)((1 +... View Article

The logical statement (p⇒q) ∧ (q ⇒∼ p) is equivalent to

a) ∼ p b) p c) q d) ∼ q Answer: (a) 𝒑 𝒒 𝒑 ⇒ 𝒒 ∼ 𝒑 𝒒 ⇒∼ 𝒑 (𝒑 ⇒ 𝒒) ∧ (𝒒 ⇒∼ 𝒑) T T... View Article

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is

a) 2√3 b) √3 c) 3/√2 d) 3√2 Answer: (d) Let the equation of ellipse be x2/a2 + y2/b2 = 1 a>b Now 2ae = 6 2a/e... View Article

If f(a + b + 1 – x) = f(x) ∀x, where a and b are fixed positive real numbers

If f(a + b + 1 - x) = f(x) ∀x, where a and b are fixed positive real numbers, then is equal to a) b) c) d) Answer: (c) f(a... View Article

If Re (z-1)/(2z + i) = 1, where z = x+iy, then the point (x,y) lies on a

a) circle whose centre is at (-1/2, -3/2) b) straight line whose slope is 3/2. c) circle whose diameter is √5/2 d) straight line whose... View Article

An unbiased coin is tossed 5 times.

An unbiased coin is tossed 5 times. Suppose that a variable is assigned the value when consecutive heads are obtained for = 3, 4, 5,... View Article

Total number of six-digit numbers in which only and all the five digits 1,3,5,7 and 9 appear, is

a) 56 b) (½)(6!) c) 6! d) (5/2) 6! Answer: (d) Selecting all 5 digits = 5C5 = 1 way Now, we need to select one more digit to make it... View Article

The area of the region, enclosed by the circle x² + y² = 2

The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = and the straight line... View Article

A circular disc of mass M and radius R is rotating about its axis with angular speed ω₁ .

A circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another stationary disc having radius R/2 and... View Article

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece.

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens... View Article

ABC is a plane lamina of the shape of an equilateral triangle.

ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of... View Article

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K.

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium... View Article

In the line spectra of hydrogen atoms, difference between

In the line spectra of hydrogen atoms, difference between the largest and the shortest wavelengths of the Lyman series is 304Å. The... View Article

Take the breakdown voltage of the zener diode used in the given circuit as 6V.

Take the breakdown voltage of the zener diode used in the given circuit as 6V. For the input voltage shown in figure below, the time variation of... View Article

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