The nucleus is separated from the cytoplasm by the _______ .
(a) cytoplasm (b) cell membrane (c) nuclear membrane (d) protoplasmCorrect option: (c) nuclear membrane The nucleus is separated from the... View Article
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AIR Spotlight – PM’s Intervention at G7 Summit 2021
AIR Spotlight is an insightful programme featured daily on the All India Radio Newsonair. In this program, many eminent panelists... View Article
22 June 2021: PIB Summary & Analysis
June 22nd, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. MoU between India and Fiji 2. Indian Navy -... View Article
The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = 3π/2 is
1) (4√2 – 2)sq units 2) (4√2 + 2)sq units 3) (4√2 -1)sq units 4) (4√2 + 1)sq units Solution:... View Article
The area (in sq units) bounded by the curve y = 1 + loge x, the X – axis and the straight line x = e is equal to
1) 3e – 2 2) e 3) e – 1/e 4) e + 1/e Solution: (2) e \(\begin{array}{l}\text { Given... View Article
Find the area of a curve xy = 4, bounded by the lines x = 1 and x = 3 and x-axis
1) log 12 2) log 64 3) log 81 4) log 27 Solution: (3) log 81 \(\begin{array}{l}\begin{array}{l} \text { Area... View Article
The area enclosed between y2 = x and y = x is
1) 2/3 sq units 2) 1/2 sq units 3) 1/3 sq units 4) 1/6 sq units Solution: (4) 1/6 sq... View Article
If the area between y = mx2 and x = my2 (m > 0) is 1/4 sq units, then the value of m is
1) ± 3√2 2) ± 2/√3 3) √2 4) √3 Solution: (2) ± 2/√3 \(\begin{array}{l}y=m x^{2} \text \ and \... View Article
The area in the positive quadrant enclosed by the circle x2 + y2 = 4, the line x = y √3 and x-axis is
1) π/2 2) π/4 3) π/3 4) π Solution: (3) π/3 x2 + y2 = 4 — (i) x =... View Article
The area of the region enclosed by the curves y = x, x = e, y = 1/x and the positive x-axis is
1) 1 sq units 2) 3/2 sq units 3) 5/2 sq units 4) 1/2 sq units Solution: (2) 3/2 sq... View Article
If the straight line x = b divide the area enclosed by y = (1 – x)2, y = 0 and x = 0 into two parts R1 (0 ≤ x ≤ b) and R2 (b ≤ x ≤ 1) such that R1 – R2 = 1/4. Then, b equals
1) 3/4 2) 1/2 3) 1/3 4) 1/4 Solution: (2) ½ \(\begin{array}{l}\begin{array}{l} \int_{0}^{b}(1-x)^{2} d x-\int_{b}^{1}(1-x)^{2} d x=\frac{1}{4} \\ \Rightarrow\left[\frac{(x-1)^{3}}{3}\right]_{0}^{b}-\left[\frac{(x-1)^{3}}{3}\right]_{b}^{1}=\frac{1}{4} \\... View Article
The area of the region bounded by the curves y = x3, y = 1/x, x = 2 is
1) 4 – loge 2 2) 1/4 + loge 2 3) 3 – loge 2 4) 15/3 – loge 2... View Article
The area bounded between the parabolas x2 = y/4 and x2 = 9y and the straight line y = 2 is
1) 20√2 2) 10√2 / 3 3) 20√2 / 3 4) 10√2 Solution: (3) 20√2 / 3 \(\begin{array}{l}\begin{array}{l} x^{2}=\frac{y}{4}, x^{2}=9... View Article
If S is the area of the region enclosed by y = e-x2, y = 0, x = 0 and x = 1. Then,
1) S ≥ 1 / e 2) S ≥ 1 – (1 / e) 3) S ≤ (1 / 4) [1 + (1... View Article
The area bounded by the curves y = ex, y = e-x, straight line x = 1 is given by
1) e + e-1 – 2 2) e – e-1 3) e + e-1 4) e + e-1 + 2... View Article
The area bounded by the curves y = x and y = x3 is equal to
1) 0 2) 1/4 3) 1/2 4) 1 Solution: (3) ½ The line y = x lies above the curve... View Article
Area included between the parabola y = x2 / 4a and the curve y = 8a3 / (x2 + 4a2) is
1) (a2 / 3) (6π – 4) 2) (a2 / 3) (4π + 4) 3) (a2 / 3) (8π +... View Article
The area (in sq units) of the region bounded by the curves y2 = 4ax and x2 = 4ay, a > 0 is
1) 16 (a2 / 3) 2) 14 (a2 / 3) 3) 13 (a2 / 3) 4) 16a2 5) None of... View Article
The area (in sq units) bounded by the curves y = √x, 2y – x + 3 = 0, x-axis and lying in the first quadrant is
1) 9 2) 6 3) 18 4) 27/4 Solution: (1) 9 \(\begin{array}{l}y=\sqrt{x} \quad…(i)\\ 2 y-x+3=0 \quad \ldots (ii)\\ \text {... View Article
The area enclosed by the curves y = sinx + cos x and y = |cos x – sin x| over the interval [0, π/2] is
1) 4(√2 – 1) 2) 2√2(√2 – 1) 3) 2(√2 + 1) 4) 2√2(√2 + 1) Solution: (2) 2√2(√2 –... View Article
