Classify the following based on number
Question: Classify the following based on number of chambers in their heart : Rohu, Scolidon, Salamander, Flying Lizard, King Cobra, Crocodile, Ostrich, Pigeon, Bat, Whale. Solution: 1. Rohu. 2-Chambered. 2. Scoliodon. 2-chambered 3. Frog. 3-chambered 4. Salamander. 3-chambered 5. Flying Lizard. Incompletely 4-chambered. 6. King Cobra. Incompletely 4-chambered. 7. Crocodile. 4-chambered 8. Ostrich. 4-chambered 9. Pigeon. 4-chambered 10. Bat. 4-chambered 11. Whale. 4-chambered....
Read More →Endoskeleton of fishes is made up of cartilage and bone.
Question: Endoskeleton of fishes is made up of cartilage and bone. Classify the following fishes as cartilaginous or bony: : Xorpedo, Sting Ray, Dog fish, Rohu, Angler Fish, Exocoetus. Solution: 1. Xorpedo-Cartilaginous 2. Sting Ray-Cartilaginous 3. Dog Fish-Cartilaginous 4. Rohu-Bony 5. Angler fish-Bony 6. Exocoetus-Bony....
Read More →Show that the following numbers are not perfect squares:
Question: Show that the following numbers are not perfect squares: (i) 9327 (ii) 4058 (iii) 22453 (iv) 743522 Solution: A number ending with 2, 3, 7 or 8 cannot be a perfect square. (i) Its last digit is 7. Hence, 9327 is not a perfect square. (ii) Its last digit is 8. Hence, 4058 is not a perfect square. (iii) Its last digit is 3. Hence, 22453 is not a perfect square. (iv) Its last digit is 2. Hence, 743522 is not a perfect square....
Read More →If tan 2θ = cot (θ + 60°), where 2θ and
Question: If tan 2 = cot ( + 60), where 2 and ( + 6) an acute angles, find the value of . Solution: Given: tan2 = cot( + 60) $\tan 2 \theta=\cot \left(\theta+60^{\circ}\right)$ $\Rightarrow \cot \left(90^{\circ}-2 \theta\right)=\cot \left(\theta+60^{\circ}\right) \quad\left(\because \tan \theta=\cot \left(90^{\circ}-\theta\right)\right)$ $\Rightarrow 90^{\circ}-2 \theta=\theta+60^{\circ}$ $\Rightarrow 90^{\circ}-60^{\circ}=\theta+2 \theta$ $\Rightarrow 3 \theta=30^{\circ}$ $\Rightarrow \theta=\f...
Read More →Classify the following organisms based on absence
Question: Classify the following organisms based on absence or presence of true coelom as acoelomate, pseudocoelomate and coelomate : Spongilla, Sea Anemone, Planaria, Liver Fluke, Wuchereria, Ascaris, Nereis, Earthworm, Scorpion, Birds, Fishes and Horse. Solution: 1. Spongilla-Acoelomaxe 2. Sea Anemone-Acoelomate 3. Planaria-Acoelomate 4. Liver Fluke-Acoelomate 5. Wuchereria-Pseudocoelomate 6. Aszvzris-Pseudocoelomate 7. Nereis-Coelomate 8. Scorpion-Coelomate 9. Earthworm-Coelomate 10. Birds-Co...
Read More →The following numbers are not perfect squares.
Question: The following numbers are not perfect squares. Give reason. (i) 1547 (ii) 45743 (iii) 8948 (iv) 333333 Solution: A number ending with 2, 3, 7 or 8 cannot be a perfect square. (i) Its last digit is 7. Hence, 1547 cannot be a perfect square. (ii) Its last digit is 3. Hence, 45743 cannot be a perfect square. (iii) Its last digit is 8. Hence, 8948 cannot be a perfect square. (iv) Its last digit is 3. Hence, 333333 cannot be a perfect square....
Read More →Match the articles of Column A with those of column B
Question: Match the articles of Column A with those of column B Solution: $a-($ iii $)$ $b-($ ii $)$ $c-($ vi) $d-($ i $)$ $e-($ v $)$ $f-($ iv $)$...
Read More →Match the items of Column $A$ with items of Column $B$
Question: Match the items of Column $A$ with items of Column $B$ Solution: (a) $-$ (ii), (b) -(i), (c) - (iv), (d) $-$ (iii), (e) $-$ (vi), (f) $-(v)$, (g) $-$ (vii)....
Read More →If sec 4A = cosec (A – 15°), where 4A is acute then find ∠A.
Question: If sec 4A= cosec (A 15), where 4Ais acute then find A. Solution: Given:sec4A= cosec(A 15) $\sec 4 A=\operatorname{cosec}\left(A-15^{\circ}\right)$ $\Rightarrow \operatorname{cosec}\left(90^{\circ}-4 A\right)=\operatorname{cosec}\left(A-15^{\circ}\right) \quad\left(\because \sec \theta=\operatorname{cosec}\left(90^{\circ}-\theta\right)\right)$ $\Rightarrow 90^{\circ}-4 A=A-15^{\circ}$ $\Rightarrow 90^{\circ}+15^{\circ}=A+4 A$ $\Rightarrow 5 A=105^{\circ}$ $\Rightarrow A=\frac{105^{\circ...
Read More →You are provided with seeds of Gram,
Question: You are provided with seeds of Gram, Wheat, Rice Pumpkin, Maize and Pea. Classify them whether they are monocot or dicot? Solution: Gram-Dicot. Wheat-Monocot. Rice-Monocot. Pumpkin-Dicot. Maize-Monocot. Pea-Dicot....
Read More →Construct a 2 × 3 matrix
Question: Construct a $2 \times 3$ matrix whose elements $a_{i j}$ are given by : (i) $a_{i j}=i . j$ (ii) $a_{i j}=2 j-j$ (iii) $a_{i j}=i+j$ (iv) $\mathrm{a}_{i j}=\frac{(i+j)^{2}}{2}$ Solution: (i) Here, $a_{i j}=i \cdot j, 1 \leq i \leq 2$ and $1 \leq j \leq 3$ $a_{11}=1 \times 1=1, a_{12}=1 \times 2=2, a_{13}=1 \times 3=3$ $a_{21}=2 \times 1=2, a_{22}=2 \times 2=4$ and $a_{23}=2 \times 3=6$ Required matrix $=A=\left[\begin{array}{lll}1 2 3 \\ 2 4 6\end{array}\right]$ $(i i)$ Here, $a_{i j}=...
Read More →Fill in the blanks :
Question: Fill in the blanks : (a) Fungi show . mode of nutrition. (b) Cell wall of fungi is made up of . (c) Association between blue-green algae and fungi is called as .. . (d) Chemical nature of chidn is . (e) . has smallest number of organisms with maximum number of similar characters. (f) are called amphibians of plant kingdom. Solution: (a) saprophytic (b) chitin (c) lichen (d) carbohydrate (e) Species (f) Bryophytes....
Read More →If cos 2A = sin (A – 15°), where 2A is acute then find ∠A.
Question: If cos 2A= sin (A 15), where 2Ais acute then find A. Solution: Given:cos2A= sin(A 15) $\cos 2 A=\sin \left(A-15^{\circ}\right)$ $\Rightarrow \sin \left(90^{\circ}-2 A\right)=\sin \left(A-15^{\circ}\right) \quad\left(\because \cos \theta=\sin \left(90^{\circ}-\theta\right)\right)$ $\Rightarrow 90^{\circ}-2 A=A-15^{\circ}$ $\Rightarrow 90^{\circ}+15^{\circ}=A+2 A$ $\Rightarrow 3 A=105^{\circ}$ $\Rightarrow A=\frac{105^{\circ}}{3}$ $\Rightarrow A=35^{\circ}$ Hence, $\angle A=35^{\circ}$....
Read More →By what number should
Question: By what number should (15)1be divided so that the quotient may be equal to (5)1? Solution: Using the propertya1= 1/afor every natural numbera, we have (15)1= 1/15 and (5)1= 1/5. We have to find a numberxsuch that $\frac{\frac{-1}{15}}{\frac{x}{1}}=\frac{-1}{5}$ or $\frac{-1}{15} \times \frac{1}{\mathrm{x}}=\frac{-1}{5}$ or $x=\frac{1}{3}$ Hence, $(-15)^{-1}$ should be divided by $\frac{1}{3}$ to obtain $(-5)^{-1}$....
Read More →Write true (T) or false (F)
Question: Write true (T) or false (F) (a) Wittaker proposed five kingdom classification. (b) Monera is divided into Archaebacteria and Eubacteria. (c) Starting from Class, Species comes before Genus. (d) Anabaena belongs to kingdom Monera. (e) Blue-green algae belong to kingdom Protista. (f) All prokaryotes are classified under Monera. Solution: (a) $-T$ (b) $-T$, (c) $-F$ (d) $-T$, (e) $-F$, (f) $-T$....
Read More →By what number should
Question: By what number should $\left(\frac{1}{2}\right)^{-1}$ be multiplied so that the product may be equal to $\left(-\frac{4}{7}\right)^{-1} ?$ Solution: Using the propertya1= 1/afor every natural numbera, we have (1/2)1= 2 and (4/7)1= 7/4. We have to find a numberxsuch that $2 x=\frac{-7}{4}$ Dividing both sides by 2, we get: $x=\frac{-7}{8}$ Hence, the required number is 7/8....
Read More →It tan A = cot (A + 10°), where (A + 10°) is acute then find ∠A.
Question: It tanA= cot (A+ 10), where (A+ 10) is acute then find A. Solution: Given:tanA= cot(A + 10) $\tan A=\cot \left(A+10^{\circ}\right)$ $\Rightarrow \cot \left(90^{\circ}-A\right)=\cot \left(A+10^{\circ}\right) \quad\left(\because \tan \theta=\cot \left(90^{\circ}-\theta\right)\right)$ $\Rightarrow 90^{\circ}-A=A+10^{\circ}$ $\Rightarrow 90^{\circ}-10^{\circ}=A+A$ $\Rightarrow 2 A=80^{\circ}$ $\Rightarrow A=\frac{80^{\circ}}{2}$ $\Rightarrow A=40^{\circ}$ Hence, $\angle A=40^{\circ}$....
Read More →By what number should
Question: By what number should 51be multiplied so that the product may be equal to (7)1? Solution: Using the propertya1= 1/afor every natural numbera, we have 51= 1/5 and (7)1= 1/7. We have to find a numberxsuch that $\frac{1}{5} \times x=\frac{-1}{7}$ Multiplying both sides by 5, we get: $x=\frac{-5}{7}$ Hence, the required number is 5/7....
Read More →If B is a symmetric matrix,
Question: If $B$ is a symmetric matrix, write whether the matrix $A B A^{\top}$ is symmetric or skew-symmetric. Solution: If $B$ is a symmetric matrix, then $B^{T}=B$. $\left(A B A^{T}\right)^{T}=\left(A^{T}\right)^{T} B^{T} A^{T} \quad\left[\because(A B C)^{T}=C^{T} B^{T} A^{T}\right]$ $\Rightarrow\left(A B A^{T}\right)^{T}=A B^{T} A^{T} \quad\left[\because\left(A^{T}\right)^{T}=A\right]$ $\Rightarrow\left(A B A^{T}\right)^{T}=A B A^{T} \quad\left[\because B^{T}=B\right]$ $\therefore A B A^{T}$...
Read More →Simplify:
Question: Simplify: (i) $\left(3^{2}+2^{2}\right) \times\left(\frac{1}{2}\right)^{3}$ (ii) $\left(3^{2}-2^{2}\right) \times\left(\frac{2}{3}\right)^{-3}$ (iii) $\left[\left(\frac{1}{3}\right)^{-3}-\left(\frac{1}{2}\right)^{-3}\right] \div\left(\frac{1}{4}\right)^{-3}$ (iv) $\left(2^{2}+3^{2}-4^{2}\right) \div\left(\frac{3}{2}\right)^{2}$ Solution: (i) $\left(3^{2}+2^{2}\right) \times\left(\frac{1}{2}\right)^{3}=(9+4) \times \frac{1}{8}=\frac{13}{8}$ (ii) $\left(3^{2}-2^{2}\right) \times\left(\fr...
Read More →If sin 3A = cos (A – 10°), where 3A is an acute angle then find ∠A.
Question: If sin 3A= cos (A 10), where 3Ais an acute angle then find A. Solution: Given:sin3A= cos(A 10) $\sin 3 A=\cos \left(A-10^{\circ}\right)$ $\Rightarrow \cos \left(90^{\circ}-3 A\right)=\cos \left(A-10^{\circ}\right) \quad\left(\because \sin \theta=\cos \left(90^{\circ}-\theta\right)\right)$ $\Rightarrow 90^{\circ}-3 A=A-10^{\circ}$ $\Rightarrow 90^{\circ}+10^{\circ}=A+3 A$ $\Rightarrow 4 A=100^{\circ}$ $\Rightarrow A=\frac{100^{\circ}}{4}$ $\Rightarrow A=25^{\circ}$ Hence, $\angle A=25^{...
Read More →(a) Differentiate between meristematic and permanent tissues in plants
Question: (a) Differentiate between meristematic and permanent tissues in plants (b) Define the process of differentiation. (c) Name any two simple and two complex permanent tissues in plants. Solution: (a) Differences between Meristematic and Permanent Tissues (b) Differentiation: The process of loss of ability to divide and taking up a permanent shape, size, structure and fucntion by newly formed cells is called differentiation. (c) 1. Simple Permanent Tissues : Parenchyma, Collenchyma, Sderen...
Read More →If B is a skew-symmetric matrix,
Question: If $B$ is a skew-symmetric matrix, write whether the matrix $A B A^{T}$ is symmetric or skew-symmetric. Solution: If $B$ is a skew-symmetric matrix, then $B^{T}=-B$. $\left(A B A^{T}\right)^{T}=\left(A^{T}\right)^{T} B^{T} A^{T} \quad\left[\because(A B C)^{T}=C^{T} B^{T} A^{T}\right]$ $\Rightarrow\left(A B A^{T}\right)^{T}=A B^{T} A^{T} \quad\left[\because\left(A^{T}\right)^{T}=A\right]$ $\Rightarrow\left(A B A^{T}\right)^{T}=A(-B) A^{T} \quad\left[\because B^{T}=-B\right]$ $\Rightarro...
Read More →Why are xylem and phloem called complex tissues?
Question: Why are xylem and phloem called complex tissues? How are they different from one another? Answer: Solution: Xylem and phloem are called complex tissues because each of them is made of more than one type of cells which coordinate their activities to perform a common function. Differences between Xylem and Phloem...
Read More →Express each of the following in terms of trigonometric ratios of angles between 0° and 45°.
Question: Express each of the following in terms of trigonometric ratios of angles between 0 and 45.(i) sin 72 + cosec 72(ii) cosec 66 + tan 66(iii) tan 68 + sec 68(iv) cot 59 + cosec 59(v) cos 51 + cot 49 sec 47(vi) sin 67 + cos 75 Solution: (i) sin72 + cosec72 $\sin 72^{\circ}+\operatorname{cosec} 72^{\circ}$ $=\sin \left(90^{\circ}-18^{\circ}\right)+\operatorname{cosec}\left(90^{\circ}-18^{\circ}\right)$ $=\cos 18^{\circ}+\sec 18^{\circ} \quad\left(\because \sin \left(90^{\circ}-\theta\right)...
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