alleryValue of ∫₀^(π/2) sin² x dx:
- π/4 (= ∫(1-cos2x)/2 dx from 0 to π/2)
- 1
- π
- π/2
Show answer and solution
Correct answer: A. π/4 (= ∫(1-cos2x)/2 dx from 0 to π/2)
sin²x = (1-cos2x)/2. ∫₀^(π/2) sin²x dx = (1/2)[π/2 - 0] = π/4.
JEE Main JEE Main 2023 Mixed — practice questions
Explore 25 free JEE Main 2023 Mixed questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Value of ∫₀^(π/2) sin² x dx:Read the answer and worked solution →Number of arrangements of letters in 'BANANA':Read the answer and worked solution →For matrix A = [[1, 2], [3, 4]], det(A):Read the answer and worked solution →lim_(x→0) (e^x - 1)/sin x =Read the answer and worked solution →Number of ways to choose 4 students from class of 10 if 2 specific students must be included:Read the answer and worked solution →Solution of differential equation dy/dx = y/x:Read the answer and worked solution →Two cards drawn from a deck of 52 (without replacement). P(both aces):Read the answer and worked solution →Number of solutions of sin x = 1/2 in [0, 2π]:Read the answer and worked solution →For vectors a, b with |a| = |b| = 1 and a · b = 1/2, angle:Read the answer and worked solution →Equation of circle with center (1, -2) and radius 3:Read the answer and worked solution →Coefficient of x² in expansion of (1 + 2x)¹⁰:Read the answer and worked solution →Number of integers between 1 and 100 (inclusive) divisible by 3 or 5:Read the answer and worked solution →Slope of tangent to y = x² + 3x at point (1, 4):Read the answer and worked solution →sec²(arctan(2)) =Read the answer and worked solution →Argument of complex number 1 + i:Read the answer and worked solution →Sum of first 10 terms of AP with a = 3, d = 2:Read the answer and worked solution →For GP with first term 2 and common ratio 1/2, sum to infinity:Read the answer and worked solution →Distance from point (1, 2, 3) to plane x + y + z - 6 = 0:Read the answer and worked solution →Roots of equation x² - 5x + 6 = 0:Read the answer and worked solution →sin(75°) =Read the answer and worked solution →In a triangle ABC, if a = 2, b = 3, C = 60°, find c (using cosine rule):Read the answer and worked solution →Find eigenvalues of [[3, 1], [1, 3]]:Read the answer and worked solution →For y = cos x, y'' + y =Read the answer and worked solution →If f(x) = x³ - 3x² + 2, find x where local maximum occurs:Read the answer and worked solution →Integration: ∫ tan(x) dx =Read the answer and worked solution →
Worked practice questions
Number of arrangements of letters in 'BANANA':
- 36
- 720
- 60 (= 6!/(3!2!) since 3 A's and 2 N's)
- 120
Show answer and solution
Correct answer: C. 60 (= 6!/(3!2!) since 3 A's and 2 N's)
6 letters, 3 A, 2 N, 1 B. Total permutations = 6!/(3! × 2! × 1!) = 720/12 = 60.
For matrix A = [[1, 2], [3, 4]], det(A):
- -2 (= 4 - 6)
- 10
- -10
- 2
Show answer and solution
Correct answer: A. -2 (= 4 - 6)
det = 1×4 - 2×3 = 4 - 6 = -2.
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