Available Questions 833 found Page 1 of 42
Standalone Questions
#2082
Mathematics
Derivatives
SUBJECTIVE
REMEMBER
AI Import
KNOWLEDGE
4 Marks
Amusement parks heavily rely on mathematical curves to design roller coaster tracks, balancing intense thrill with absolute safety. For a safe ride, the track must have no breaks (it must be continuous) and no sharp, sudden corners (it must be differentiable/smooth).
An engineering team is designing a transition segment of a new coaster. The height $h(x)$ (in meters) of the track at a horizontal distance $x$ (in meters) from the starting platform is modeled by the following piecewise function:
$$h(x) = \begin{cases} \frac{1}{2}x^2 + 2x, & 0 \leq x < 2 \\ ax + b, & 2 \leq x \leq 5 \end{cases}$$
Based on the given information, answer the following questions:
(i) For the track to have no broken rails at the transition point $x = 2$, it must be continuous. Formulate the mathematical equation relating $a$ and $b$ to ensure this continuity. (1 Mark)
(ii) Find the left-hand derivative (the slope of the track just before the transition point) at $x = 2$. (1 Mark)
(iii) To ensure the transition at $x = 2$ is perfectly smooth (differentiable), calculate the exact values of $a$ and $b$ that the engineers must use. (2 Marks)
— OR —
(iii) If a junior engineer mistakenly designed the second track segment using $a = 3$ and $b = 0$, verify whether the track is mathematically safe (smooth and differentiable) at $x = 2$. Justify your answer. (2 Marks)
An engineering team is designing a transition segment of a new coaster. The height $h(x)$ (in meters) of the track at a horizontal distance $x$ (in meters) from the starting platform is modeled by the following piecewise function:
$$h(x) = \begin{cases} \frac{1}{2}x^2 + 2x, & 0 \leq x < 2 \\ ax + b, & 2 \leq x \leq 5 \end{cases}$$
Based on the given information, answer the following questions:
(i) For the track to have no broken rails at the transition point $x = 2$, it must be continuous. Formulate the mathematical equation relating $a$ and $b$ to ensure this continuity. (1 Mark)
(ii) Find the left-hand derivative (the slope of the track just before the transition point) at $x = 2$. (1 Mark)
(iii) To ensure the transition at $x = 2$ is perfectly smooth (differentiable), calculate the exact values of $a$ and $b$ that the engineers must use. (2 Marks)
— OR —
(iii) If a junior engineer mistakenly designed the second track segment using $a = 3$ and $b = 0$, verify whether the track is mathematically safe (smooth and differentiable) at $x = 2$. Justify your answer. (2 Marks)
Key:
Sol:
Sol:
#1894
Physics
Alternating Current
MCQ_SINGLE
APPLY
Competency
1 Marks
Mr. Iyer takes a grinder rated 220 V, 50 Hz to the U.S where supply is 110 V, 60 Hz. He needs to use a
(A) step -  downtransformer with turn ratio 2: 1
(B) step -  up transformer with turn ratio 1 : 3
(C) step -  up transformer with turn ratio 1 : 2
(D) step -  downtransformer with turn ratio 5: 2
Key: C
Sol:
Sol:
#1889
Chemistry
Chemical Kinetics
VSA
APPLY
2005
SNP
Competency
1 Marks
Find out the rate constant for the reaction $\text{C(s)} + \text{O}_2\text{(g)} \rightarrow \text{CO}_2\text{(g)}$
Key:
Sol:
Sol:
#1887
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Assertion : Endosperm is a nutritive tissue and it is triploid. Reason : Endosperm is formed by fusion of secondary nucleus to second male gamete. It is used by developing embryo.
(A) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(C) The Assertion is correct but Reason is incorrect.
(D) Both the Assertion and Reason are incorrect.
Key: A
Sol:
Sol:
Male gamete ( n ) + secondary nucleus (2 n ) = primary endosperm nucleus which develops into endosperm (3 n ) Endosperm is the reserve food used by developing embryo.
#1886
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Assertion : Double fertilization is characteristic feature of angiospersms. Reason : Double fertilization involves two fusions.
(A) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(C) The Assertion is correct but Reason is incorrect.
(D) Both the Assertion and Reason are incorrect.
Key: B
Sol:
Sol:
Double fertilization is a characteristic feature of angiosperms. It involves two fusions in which one female gametes fuse with egg cell to form zygote and other male gamete fuses with the diploid secondary nucleus.
#1885
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Assertion : Chasmogamous flowers require pollinating agents. Reason : Cleistogamous flowers do not expose their sex organs.
(A) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(C) The Assertion is correct but Reason is incorrect.
(D) Both the Assertion and Reason are incorrect.
Key: B
Sol:
Sol:
The majority of angiosperms bear chasmogamous flowers, which means the flowers expose their mature anthers and stigma to the pollinating agents. There is another group of plants which set seeds without exposing their sex organs.
#1884
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Assertion : Pollen mother cells (PMCs) are the first male gametophytic cells. Reason : Each PMC gives rise to two pollens.
(A) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(C) The Assertion is correct but Reason is incorrect.
(D) Both the Assertion and Reason are incorrect.
Key: D
Sol:
Sol:
Primary sporogenous cell gives rise to microspore mother cells or pollen mother cells (PMCs). They are sporophytic in nature i.e., diploid. Microspores represent the beginning of the gametophytic phase and they are haploid in nature.
#1883
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Assertion : Insects visit flower to gather honey. Reason : Attraction of flowers prevents the insects from damaging other parts of the plant.
(A) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(C) The Assertion is correct but Reason is incorrect.
(D) Both the Assertion and Reason are incorrect.
Key: D
Sol:
Sol:
Honey bee visit flowers to gather nectar and turn it into honey. Visiting of insects for nectar helps in pollination.
#1882
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Assertion : If pollen mother cells has 42 chromosomes, the pollen has only 21 chromosomes. Reason : Pollens are formed after meiosis in pollen mother cell.
(A) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(C) The Assertion is correct but Reason is incorrect.
(D) Both the Assertion and Reason are incorrect.
Key: A
Sol:
Sol:
Pollen mother cells undergo meiosis and produce pollen grains. The pollen grains have haploid number of chromosomes.
#1881
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2013
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Male gametophyte in angiosperms produces
(A) two sperms and a vegetative cell
(B) single sperm and a vegetative cell
(C) single sperm and two vegetative cells
(D) three sperms
Key: A
Sol:
Sol:
Pollen grain or male gametophyte in angiosperms contain one generative cell. The generative cell further divides meiotically to form two male gametes (sperms). So, a mature male gametophyte in angiosperms contains two sperms and one vegetative cell.
#1880
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2009
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The ovule of an angiosperm is technically equivalent to
(A) megasporangium
(B) megaspoophyll
(C) megaspore mother cell
(D) megaspore
Key: A
Sol:
Sol:
Ovule of an Angiosperm is equivalent to megasporangium which consists of 2 synergids, 1 egg, 3 antipodal cells and a secondary nucleus.
#1879
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2005
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Pollination in water hyacinth and water lily is brought about by the agency of
(A) water
(B) insects or wind
(C) birds
(D) bats
Key: B
Sol:
Sol:
Water hyacinth has single spike of 8-15 conspicuous attractive flowers which attract bees and other insects. These insects pollinate them. Water lily is also an aquatic plant with large conspicuous coloured flowers. Most of the species are bee pollinated.
#1878
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2007
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
In majority of angiosperms
(A) egg has a filiform apparatus
(B) there are numerous antipodal cells
(C) reduction division occurs in the megaspore mother cells
(D) a small central cell is present in the embryo
Key: C
Sol:
Sol:
In most of the angiosperms megaspore mother cell (2 n ) divides meiotically to produce 4 cells. Out of these 3 degenerate and one remains which forms functional megaspore. Egg does not have filiform apparatus.
#1877
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2015
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Which of the following statements is not correct?
(A) Insects that consume pollen or nectar without bringing about pollination are called pollen nectar robbers
(B) Pollen germination and pollen tube growth are requlated by chemical components of pollen interacting with those of the pistil
(C) Some reptiles have also been reported as pollinators in some plant species
(D) Pollen grains of many species can germinate on the stigma of a flower, but only one pollen tube of the same species grows into the style
Key: D
Sol:
Sol:
Pollen grains of different species are incompatible, so they fail to germinate. Only the pollen of the same species germinate and can form pollen tube which grows and finally dispatches male gamete to embryo sac.
#1876
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2010
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Cotyledon of maize grain is called
(A) coleorhiza
(B) coleoptile
(C) scutellum
(D) plumule
Key: C
Sol:
Sol:
Large, shield shaped cotyledon of grass family is called scutellum. Coleorhiza is a sheath protecting the root of germinating grass. Coleoptile is a sheath covering emerging shoot. Plumule is rudimentary shoot of an embryo plant.
#1875
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2012
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
The coconut water from tender coconut represents
(A) fleshy mesocarp
(B) free-nuclear proembryo
(C) free-nuclear endosperm
(D) endocarp
Key: C
Sol:
Sol:
Coconut milk represents free-nuclear endosperm where the division of primary endosperm nucleus is not followed by formation of cell walls (cytokinesis) thus all nucleus remain free in liquid form. It is rich in plant hormone cytokinin.
#1874
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2015
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Proximal end of the filament of stamen is attached to the
(A) connective
(B) placenta
(C) thalamus or petal
(D) anther
Key: C
Sol:
Sol:
A typical stamen consist of anther and filament. The proximal end of filament is attached to thalamus or petal of the flower whereas distal end bears anther.
#1873
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2013
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Seed formation without fertilisation in flowering plants involves the process of
(A) budding
(B) somatic hybridisation
(C) apomixis
(D) sporulation
Key: C
Sol:
Sol:
Apomixis is a special mechanism found in flowering plants to produce seeds without fertilisation. It is a type of asexual reproduction which mimics the sexual reproduction and is commonly found in Citrus varieties.
#1872
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2005
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Which one of the following statements is not true?
(A) Exine of pollen grains is made up of sporopollenin.
(B) Pollen grains of many species cause severe allergies.
(C) Stored pollen in liquid nitrogen can be used in the crop breeding programmes.
(D) Tapetum helps in the dehiscence of anther.
Key: D
Sol:
Sol:
Tapetum is the inner layer of microsporangium (anther) which provides nourishment to developing pollen grain after meiotic cell division.
#1871
Biology
Sexual Reproduction in Flowering Plants
MCQ_SINGLE
REMEMBER
2007
AISSCE(Board Exam)
KNOWLEDGE
1 Marks
Double fertilisation is exhibited by
(A) gymnosperms
(B) algae
(C) fungi
(D) angiosperms
Key: D
Sol:
Sol:
Double fertilisation is the characteristic feature of angiosperms. In this type of fertilisation one male gamete fuses with an egg and forms zygote. The second male gamete fuses with diploid secondary nucleus of central cell to form a triploidy primary endosperm nucleus.
Case-Based Questions
CASE ID: #118
Cl: CBSE Class 12
Mathematics
A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their manufacturing a defective smartphone are only 5%, 4% and 2% respectively. In his inventory he has 25% smartphones from company A, 35% smartphones from company B and 40% smartphones from company C.
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
4 Marks
A person buys a smartphone from this shop.
(i) Find the probability that it was defective.
(ii) What is the probability that this defective smartphone was manufactured by company B ?
(i) Find the probability that it was defective.
(ii) What is the probability that this defective smartphone was manufactured by company B ?
Key:
Sol:
Sol:
CASE ID: #117
Cl: CBSE Class 12
Mathematics
Three students, Neha, Rani and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads and 2 erasers and pays â‚ą 60. Rani buys 2 pens, 4 notepads and 6 erasers for â‚ą 90. Sam pays â‚ą 70 for 6 pens, 2 notepads and 3 erasers.
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
4 Marks
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form $AX = B$.
(ii) Find $|A|$ and confirm if it is possible to find $A^{-1}$.
(iii) (a) Find $A^{-1}$, if possible, and write the formula to find $X$.
OR
(iii) (b) Find $A^2 - 8I$, where $I$ is an identity matrix.
(ii) Find $|A|$ and confirm if it is possible to find $A^{-1}$.
(iii) (a) Find $A^{-1}$, if possible, and write the formula to find $X$.
OR
(iii) (b) Find $A^2 - 8I$, where $I$ is an identity matrix.
Key:
Sol:
Sol:
CASE ID: #116
Cl: CBSE Class 12
Mathematics
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let $A_1$: People with good health,
$A_2$: People with average health,
and $A_3$: People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category $A_1$, $A_2$ and $A_3$ are 25%, 35% and 50%, respectively.
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
4 Marks
(i) A person was tested randomly. What is the probability that he/she has contracted the disease ?
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category $A_2$ ?
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category $A_2$ ?
Key:
Sol:
Sol:
Based on the information provided, here are the step-by-step calculations:Let the events be defined as:$A_1$: Person has good health$A_2$: Person has average health$A_3$: Person has poor health$E$: Person contracts the diseaseFrom the data given:$P(A_1) = \frac{700}{1000} = 0.7$$P(A_2) = \frac{200}{1000} = 0.2$$P(A_3) = \frac{100}{1000} = 0.1$The conditional probabilities of contracting the disease are:$P(E|A_1) = 25\% = 0.25$$P(E|A_2) = 35\% = 0.35$$P(E|A_3) = 50\% = 0.50$(i) Probability that a randomly selected person has contracted the diseaseWe use the Law of Total Probability:$$P(E) = P(E|A_1)P(A_1) + P(E|A_2)P(A_2) + P(E|A_3)P(A_3)$$Substitute the values:$$P(E) = (0.25 \times 0.7) + (0.35 \times 0.2) + (0.50 \times 0.1)$$$$P(E) = 0.175 + 0.07 + 0.05$$$$P(E) = 0.295$$Answer: The probability that the person has contracted the disease is 0.295 (or 29.5%).(ii) Probability that the person is from category $A_2$, given that they have not contracted the diseaseLet $E'$ be the event that the person has not contracted the disease.We need to find $P(A_2|E')$.First, calculate the probability of not contracting the disease, $P(E')$:$$P(E') = 1 - P(E) = 1 - 0.295 = 0.705$$Next, calculate the probability of not contracting the disease given the person is in category $A_2$:$$P(E'|A_2) = 1 - P(E|A_2) = 1 - 0.35 = 0.65$$Now, apply Bayes' Theorem:$$P(A_2|E') = \frac{P(E'|A_2) \cdot P(A_2)}{P(E')}$$Substitute the values:$$P(A_2|E') = \frac{0.65 \times 0.2}{0.705}$$$$P(A_2|E') = \frac{0.13}{0.705}$$$$P(A_2|E') = \frac{130}{705} = \frac{26}{141}$$$$P(A_2|E') \approx 0.1844$$Answer: The probability that the person is from category $A_2$ given they have not contracted the disease is $\frac{26}{141}$ or approximately 0.184.
CASE ID: #115
Cl: CBSE Class 12
Mathematics
Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if left in the open at room temperature.
A cylindrical camphor tablet whose height is equal to its radius (r) evaporates when exposed to air such that that the rate of reduction of its volume is proportional to its total surface area. Thus, $\frac{dV}{dt} = kS$ is the differential equation, where V is the volume, S is the surface area and t is the time in hours.
SUBJECTIVE
REMEMBER
2025
AISSCE(Board Exam)
Competency
1 Marks
(i) Write the order and degree of the given differential equation.
(ii) Substituting $V = \pi r^3$ and $S = 2\pi r^2$, we get the differential equation $\frac{dr}{dt} = \frac{2}{3}k$. Solve it, given that $r(0) = 5$ mm.
(iii) (a) If it is given that $r = 3$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
OR
(iii) (b) If it is given that $r = 1$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
(ii) Substituting $V = \pi r^3$ and $S = 2\pi r^2$, we get the differential equation $\frac{dr}{dt} = \frac{2}{3}k$. Solve it, given that $r(0) = 5$ mm.
(iii) (a) If it is given that $r = 3$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
OR
(iii) (b) If it is given that $r = 1$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
Key:
Sol:
Sol:
CASE ID: #114
Cl: CBSE Class 12
Mathematics
Three friends A, B and C move out from the same location O at the same time in three different directions to reach their destinations. They move out on straight paths and decide that A and B after reaching their destinations will meet up with C at his predecided destination, following straight paths from A to C and B to C in such a way that $\overrightarrow{OA} = \vec{a}$, $\overrightarrow{OB} = \vec{b}$ and $\overrightarrow{OC} = 5\vec{a}-2\vec{b}$ respectively.
SUBJECTIVE
2025
AISSCE(Board Exam)
4 Marks
(i) Complete the given figure to explain their entire movement plan along the respective vectors.
(ii) Find vectors $\vec{AC}$ and $\vec{BC}$.
(iii) (a) If $\vec{a} \cdot \vec{b} = 1$, distance of O to A is 1 km and that from O to B is 2 km, then find the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$. Also, find $|
\vec{a} \times \vec{b}|$.
OR
(iii) (b) If $\vec{a} = 2\hat{i} - \hat{j} + 4\hat{k}$ and $\vec{b} = \hat{j} - \hat{k}$, then find a unit vector perpendicular to $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$.
(ii) Find vectors $\vec{AC}$ and $\vec{BC}$.
(iii) (a) If $\vec{a} \cdot \vec{b} = 1$, distance of O to A is 1 km and that from O to B is 2 km, then find the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$. Also, find $|
\vec{a} \times \vec{b}|$.
OR
(iii) (b) If $\vec{a} = 2\hat{i} - \hat{j} + 4\hat{k}$ and $\vec{b} = \hat{j} - \hat{k}$, then find a unit vector perpendicular to $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$.
Key:
Sol:
Sol:
CASE ID: #109
Cl: CBSE Class 12
Mathematics
A technical company is designing a rectangular solar panel installation on a roof using 300 metres of boundary material. The design includes a partition running parallel to one of the sides dividing the area (roof) into two sections.
Let the length of the side perpendicular to the partition be $x$ metres and with parallel to the partition be $y$ metres.,
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
Write the equation for the total boundary material used in the boundary and parallel to the partition in terms of
x and y..
x and y..
Key:
Sol:
Sol:
k
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
Write the area of the solar panel as a function of $x$
Key:
Sol:
Sol:
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
Find the critical points of the area function. Use second derivative test to determine critical points at the maximum area. Also, find the maximum area.
Key:
Sol:
Sol:
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
2 Marks
Using first derivative test, calculate the maximum area the company can enclose with the 300 metres of boundary material, considering the parallel partition.
Key:
Sol:
Sol:
CASE ID: #108
Cl: CBSE Class 12
Mathematics
A bank offers loan to its customers on different types of interest namely, fixed rate, floating rate and variable rate. From the past data with the bank, it is known that a customer avails loan on fixed rate, floating rate or variable rate with probabilities 10%, 20% and 70% respectively. A customer after availing loan can pay the loan or default on loan repayment. The bank data suggests that the probability that a person defaults on loan after availing it at fixed rate, floating rate and variable rate is 5%, 3% and 1% respectively.
VSA
APPLY
2025
AISSCE(Board Exam)
Competency
2 Marks
What is the probability that a customer after availing the loan will default on the loan repayment?
Key:
Sol:
Sol:
VSA
APPLY
2025
AISSCE(Board Exam)
Competency
2 Marks
A customer after availing the loan, defaults on loan repayment. What is the probability that he availed the loan at a variable rate of interest?
Key:
Sol:
Sol: