Let and are two real roots of the equation
Let and are two real roots of the equation ( + 1) tan2 − √2 tan = 1 − ,... View Article
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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... 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 = \(\begin{array}{l}\frac{1}{\sqrt{3}}\begin{bmatrix} 1 &... 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,... 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) = \(\begin{array}{l}\sqrt{2(\frac{\tan \alpha + \cot \alpha }{1+\tan ^{2}\alpha })+\frac{1}{\sin... 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,... 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 =... 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... 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 =... 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,... 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... 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... 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... 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... 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... 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... 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... 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... 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... 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... View Article
