Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{e^{2 x}}{1+e^{x}} d x$ Solution: Assume $1+\mathrm{e}^{\mathrm{x}}=\mathrm{t}$ $e^{x}=t-1$ $d\left(1+e^{x}\right)=d t$ $e^{x} d x=d t$ $d x=\frac{d t}{e^{x}}$ Substitute $t$ and dt we get $\Rightarrow \int e^{2 x} \cdot \frac{d t}{e^{x}}$ $\Rightarrow \int e^{x} \cdot d t$ $\Rightarrow \int(t-1) d t$ $\Rightarrow \int t \cdot d t-\int d t$ $\Rightarrow \frac{t^{2}}{2}-t+c$ But $t=1+e^{x}$ $\Rightarrow \frac{\left(1+e^{x}\right)^{2}}{2}-\lef...
Read More →Comment upon the role of ear in maintaining
Question: Comment upon the role of ear in maintaining the balance of the body and posture. Solution: Maintaining the balance of the body and posture is done by the inner ear. There are two parts which are semicircular canals and vestibules are involved in the balancing....
Read More →Rearrange the following in the correct order
Question: Rearrange the following in the correct order of involvement in electrical impulse movementSynaptic knob, dendrites, cell body, Axon terminal, Axon Solution: The correct order of involvement of the given parts of neuron in electrical impulse is- Dendrites Cell body Axon Axon terminal Synaptic knob...
Read More →The organ of Corti is a structure present in
Question: The organ of Corti is a structure present in a. External ear b. Middle ear c. Semicircular canal d. Cochlea Solution: Option (d)Cochlea is the answer....
Read More →The part of the internal ear responsible
Question: The part of the internal ear responsible for hearing is a. Cochlea b. Semicircular canal c. Utriculus d. Sacculus Solution: Option (a)Cochleais the answer....
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Question: Wax secreting gland present in the ear canal is called a. Sweat gland b. Prostate gland c. Cowpers gland d. Ceruminous gland Solution: Option (d) Ceruminous gland is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int x e^{x^{2}} d x$ Solution: Assume $x^{2}=t$ $\Rightarrow 2 x \cdot d x=d t$ $\Rightarrow x \cdot d x=\frac{d t}{2}$ Substituting $\mathrm{t}$ and $\mathrm{dt}$ $\Rightarrow \int e^{t} \cdot \frac{d t}{2}$ $\Rightarrow \frac{1}{2} e^{t}+c$ But $x^{2}=t$ $\Rightarrow \frac{e^{x^{2}}}{2}+C$...
Read More →Human eyeball consists of three layers
Question: Human eyeball consists of three layers and it encloses a. Lens, iris, optic nerve b. Lens, aqueous humour and vitreous humour c. Cornea, lens, iris d. Cornea, lens, optic nerve Solution: Option (b)Lens, aqueous humour and vitreous humouris the answer....
Read More →Mark the vitamin present in Rhodopsin
Question: Mark the vitamin present in Rhodopsin a. Vit A b. Vit B c. Vit C d. Vit D Solution: Option (a)Vit Ais the answer....
Read More →An area in the brain which is associated
Question: An area in the brain which is associated with strong emotions is a. Cerebral cortex b. Cerebellum c. Limbic system d. Medulla Solution: Option (c)Limbic systemis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\sin (2+3 \log x)}{x} d x$ Solution: Assume $2+3 \log x=t$ $\mathrm{d}(2+3 \log \mathrm{x})=\mathrm{dt}$ $\Rightarrow \frac{3}{x} d x=d t$ $\Rightarrow \frac{1}{x} d x=\frac{d t}{3}$ Substituting $t$ and $d t$ $\Rightarrow \frac{1}{3} \int \sin t d t$ $=-\cos t+c$ But $t=2+3 \log x$ $\Rightarrow \frac{-1}{3} \cos (2+3 \log x)+c$...
Read More →Which of the following is not involved
Question: Which of the following is not involved in Knee-jerk reflex? a. Muscle spindle b. Motor neuron c. Brain d. Interneurons Solution: Option (c)Brain is the answer....
Read More →The function of our visceral organs
Question: The function of our visceral organs is controlled by a. Sympathetic and somatic neural system b. Sympathetic and parasympathetic neural system c. Central and somatic nervous system d. None of the above Solution: Option (b)Sympathetic and parasympathetic neural system is the answer....
Read More →Resting membrane potential is maintained by
Question: Resting membrane potential is maintained by a. Hormones b. Neurotransmitters c. Ion pump d. None of the above Solution: Option (c)Ion pump is the answer....
Read More →The potential difference across the resting membrane
Question: The potential difference across the resting membrane is negative. This is due to the differential distribution of the following ions a. Na+and K+ b. CO3++and CI c. Ca++and Mg++ d. Ca++and CI Solution: Option (a)Na+and K+ is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\left(\sin ^{-1} x\right)^{3}}{\sqrt{1-x^{2}}} d x$ Solution: Assume $\sin ^{-1} x=t$ $d\left(\sin ^{-1} x\right)=d t$ $\Rightarrow \frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}^{2}}}=\mathrm{dt}$ $\therefore$ Substituting $t$ and dt in given equation we get $\Rightarrow \int \mathrm{t}^{3} \mathrm{dt}$ $\Rightarrow \frac{t^{4}}{4}+c$ But $t=\sin ^{-1} x$ $\Rightarrow \frac{\left(\sin ^{-1} x\right)^{4}}{4}+c$...
Read More →Chemicals which are released at the synaptic
Question: Chemicals which are released at the synaptic junction are called a. Hormones b. Neurotransmitters c. Cerebrospinal fluid d. Lymph Solution: Option (b) is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{x \tan ^{-1} x^{2}}{1+x^{4}} d x$ Solution: Assume $\tan ^{-1} x^{2}=t$' $d\left(\tan ^{-1} x^{2}\right)=d t$ $\Rightarrow \frac{2 x}{x^{4}+1}=d t$ $\Rightarrow \frac{x}{x^{4}+1}=\frac{d t}{2}$ Substituting $\mathrm{t}$ and $\mathrm{dt}$ $\Rightarrow \frac{1}{2} \int \mathrm{tdt}$ $\Rightarrow \frac{t^{2}}{4}+c$ But $t=\tan ^{-1} x^{2}$ $\Rightarrow \frac{\left(\tan ^{-1} x^{2}\right)^{2}}{4}+C$...
Read More →Differentiate between Pectoral and Pelvic girdle.
Question: Differentiate between Pectoral and Pelvic girdle. Solution:...
Read More →How does a muscle shorten during
Question: How does a muscle shorten during its contraction and return to its original form during relaxation? Solution: The steps followed during relaxation are 1. At the instant when the neural signal reaches the neuromuscular junction and acetylcholine the neurotransmitter acetylcholine is released which creates an action potential in the sarcolemma. 2. Due to this action potential, calcium ions are released which spread through muscle fibres. 3. Calcium ion bind to the subunit of troponin on ...
Read More →An elderly woman slipped in the bathroom and had severe pain in her lower back.
Question: An elderly woman slipped in the bathroom and had severe pain in her lower back. After X-ray examination doctors told her it is due to a slipped disc. What does that mean? How does it affect our health? Solution: A slipped disc is a condition in which the intervertebral disc is displaced from its original position. It affects by causing muscle weakness. It can cause numbness of the body and pain in the muscles of arms and legs and lower back. It feels difficulty in walking and standing ...
Read More →Calcium ion concentration in the blood affects
Question: Calcium ion concentration in the blood affects muscle contraction. Does it lead to tetany in certain cases? How will you correlate fluctuation in blood calcium with tetany? Solution: Yes, in certain cases calcium ion concentration in the blood leads to tetany. Calcium plays a significant role in muscle contraction. The parathyroid gland secretes parathyroid hormones, which increases the concentration of Ca2+ ions in the bloodstream. The deficiency of this hormone can cause the drop in ...
Read More →What are the points for the articulation
Question: What are the points for the articulation of Pelvic and Pectoral girdles? Solution: The pectoral girdle has two bones called the clavicle and scapula which is articulated by a cavity called glenoid cavity with the head of the humerus by forming a ball and socket joint. The pelvic girdle has three bones Ilium, Ischium, and Pubis which is articulated by a cavity called the acetabulum with the femur by forming a ball and socket joint....
Read More →What is the source of energy
Question: What is the source of energy for muscle contraction? Solution: The source of energy for muscle contraction is ATP (Adenine Triphosphate). An enzyme called myosin ATPase present on the head of the myosin molecule breaks down into ADP and inorganic phosphate in the presence of magnesium and calcium ions and releases energy in the head of the myosin. i.e., ATP ADP + Pi + Energy...
Read More →Write a few lines about Gout.
Question: Write a few lines about Gout. Solution: Gout is a form of arthritis which is caused by the accumulation of sodium urate crystal in the joints. Symptoms of gout are intensely painful joints, redness, and swollen joints....
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