All questions
- Find the area of the region enclosed by the curves \( y^{2}=x, x=\frac{1}{4}, y=0 \) and \( x=1 \), using integration. Bounded area = ∫limits_(1/4)¹ y dx = ∫limits_(1/4)¹sqrt x dx = 2/3[x^(3/2)]_(1/4)¹ = 2/3(1-1/8) = 7/3×7/8 = 7/12 square units 1
- Find the area enclosed by the curves y=x^2, x=1/4, y=0 and x=1, using integration. Enclosed area = ∫limits ¹_ 1/4 x² dx = [fracx³3]¹₁/4 = 1/3 (1 -frac164) = 63/64 × 3 = 21/64 1
- \( x\left(x^{2}+1\right)^{-1 / 2} \) find dy/dx using chain rule frac ddx x(x² + 1)^frac-12 = xfrac ddx (x² + 1)^frac-12 + dx/dx × (x² + 1)^frac-12 = x× frac-12 (x² + 1)^frac-12-1 d/dx (x² + 1) + (x² + 1)^... 1
- You have purchased an expensive phone of a reputed company from a store in Delhi. Rahul Sharma 123 TT Nagar Delhi Date : 24.06.2022 To, The Manager KMR Mobile Phones Delhi Dear Sir/ Ma'am, Subject : Complaint Regarding My... 1
- Total Number of lone pair in Melamine Correct option is a) 6 1
- Number of Pi bonds in Marshall’s acid (d) 4 Answer : 1
- Which of these is not a broad spectrum antibiotic? (c) Penicillin G Gram-positive or Gram-negative bacteria are narrow spectrum antibiotics. If effective against a single organism or disease,... 1
- Statement 1: Emulsion of water and oil is unstable and separates in two layers. (b) S1 is correct but S2 is incorrect. Emulsions of oil in water are unstable and sometimes they separate into two layers on standing. For s... 1
- The molecule which has minimum role in photochemical smog Correct option is (b) N2 The common components of photochemical smog are ozone, nitric oxide, acrolein, formaldehyde and peroxyacetyl nitrat... 1
- The difference between the oxidation number of Cr in chromate and dichromate ion is Correct option is (a) 0 2
- Which of the following is stable nitrogen halide? Option A is correct NF3 Nitrogen is an element of second period and it cannot hold 3 larger halogen atoms efficiently, hence NF3 is the only... 1
- Which of the following in correct statement? Correct option is A) B2H6 is Lewis Acid The four terminal hydrogen atoms and the two boron atoms lie in one plane. Above and below this plan... 1
- Which of the following is a polyester? Answer is (a) Dacron 1
- Which of the following have the maximum melting point? Answer is (a) Acetic acid Carboxylic acids with even number carbon atoms have higher melting point than those with odd number carbons atom.... 2
- In the production of which of the following compound, H2 is used? Answer : (b) NH3 Solution: N2 + 3H2 ⇌ 2NH3 In production of NH3 , H2 is used 1
- X is hcp, Y is 2/3 of tetrahedral voids…. Find percentage of X in the lattice Answer : 42.85 Explaination : X is hcp So atom per unit cell = 6 Y at 2/3 of T-void = 2/8 × 12 = 8 % of X = 6/14× 100 = 42.85% 1
- A tangent at (x1,y1) to the curve y=x3+2x2+4 and passes through origin, then (x1,y1) is Answer is C (1,7) 1
- A circle of equation x2+y2+ax+by+c= 0 passes through (0, 6) and touches y=x2 at (2, 4). Find a+c. Answer :: 16 Solution :: Given ,x²+y²+ax+by+c= 0 passes through (0, 6) Then , 0+36+0+6b+c=0 6b-+c=-36 ....(1) Touches y=x² at (2, 4) 4+16+2a... 2
- In a given AC circuit which has maximum voltage V0 and frequency 50 Hz. Find the time instant where the current option b is correct 2.5 2
- Stopping potential for e- for wavelength 491 nm is 0.410 V incidence wavelength is changed to new value It D Bro 1240 / 1.92 =645.83 2
- A ball when thrown up from a tower of height h takes 6 seconds to reach ground and when thrown downward with same Correct option is A) 3 sec 2
- The body is projected 10 m/sec. The angle of projection at 30° . Find range Options: (a) 10/3 (b) 20/3 (c) 10 (d) 40/3 Correct option is B) 20/3 2
- If one end of vertical spring is connected to the ground and other end is connected to horizontal platform at rest. Correct option is A) 120mg 2
- At what height from the surface of earth the weight of the body is 1/3rd of its weight at the surface? Answer is C) 4684.8 km 2